[{"data":1,"prerenderedAt":5082},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution":5069},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":101,"checks":5008,"conditions":5030,"conditionsHtml":5031,"deprecated":5032,"description":5001,"extension":5033,"figure":5032,"figureCaption":5032,"figureHtml":5032,"formulaId":5034,"latex":5035,"latexHtml":5036,"level":5037,"meta":5038,"navigation":5039,"path":5040,"redirectFrom":5041,"related":5042,"seo":5047,"stem":5048,"subject":577,"summary":5049,"tags":5050,"variables":5055,"__hash__":5068},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution.md","Lineare Substitution",[550,551,552,553,554],"lineare Substitution Integral","Integral mit linearer innerer Funktion","Integral f(ax+b)","innere Funktion linear integrieren","Stammfunktion verkettete Funktion",{"type":556,"value":557,"toc":5000},"minimark",[558,563,765,1094,1101,1105,1108,1565,1569,1698,2259,2823,3584,4177,4181],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,670,671,675,676,734,735,764],"p",{},"Bei einer verketteten Funktion ",[568,569,572,615],"span",{"className":570},[571],"katex",[568,573,576],{"className":574},[575],"katex-mathml",[577,578,580],"math",{"xmlns":579},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[581,582,583,610],"semantics",{},[584,585,586,590,595,598,601,604,607],"mrow",{},[587,588,589],"mi",{},"f",[591,592,594],"mo",{"stretchy":593},"false","(",[587,596,597],{},"a",[587,599,600],{},"x",[591,602,603],{},"+",[587,605,606],{},"b",[591,608,609],{"stretchy":593},")",[611,612,614],"annotation",{"encoding":613},"application\u002Fx-tex","f(ax + b)",[568,616,620,657],{"className":617,"ariaHidden":619},[618],"katex-html","true",[568,621,624,629,635,639,642,645,650,654],{"className":622},[623],"base",[568,625],{"className":626,"style":628},[627],"strut","height:1em;vertical-align:-0.25em;",[568,630,589],{"className":631,"style":634},[632,633],"mord","mathnormal","margin-right:0.1076em;",[568,636,594],{"className":637},[638],"mopen",[568,640,597],{"className":641},[632,633],[568,643,600],{"className":644},[632,633],[568,646],{"className":647,"style":649},[648],"mspace","margin-right:0.2222em;",[568,651,603],{"className":652},[653],"mbin",[568,655],{"className":656,"style":649},[648],[568,658,660,663,666],{"className":659},[623],[568,661],{"className":662,"style":628},[627],[568,664,606],{"className":665},[632,633],[568,667,609],{"className":668},[669],"mclose"," mit ",[672,673,674],"strong",{},"linearer"," innerer Funktion gibt es eine einfache Regel: Man bildet die Stammfunktion der äußeren Funktion, setzt ",[568,677,679,699],{"className":678},[571],[568,680,682],{"className":681},[575],[577,683,684],{"xmlns":579},[581,685,686,696],{},[584,687,688,690,692,694],{},[587,689,597],{},[587,691,600],{},[591,693,603],{},[587,695,606],{},[611,697,698],{"encoding":613},"ax + b",[568,700,702,724],{"className":701,"ariaHidden":619},[618],[568,703,705,709,712,715,718,721],{"className":704},[623],[568,706],{"className":707,"style":708},[627],"height:0.6667em;vertical-align:-0.0833em;",[568,710,597],{"className":711},[632,633],[568,713,600],{"className":714},[632,633],[568,716],{"className":717,"style":649},[648],[568,719,603],{"className":720},[653],[568,722],{"className":723,"style":649},[648],[568,725,727,731],{"className":726},[623],[568,728],{"className":729,"style":730},[627],"height:0.6944em;",[568,732,606],{"className":733},[632,633]," ein und teilt durch ",[568,736,738,751],{"className":737},[571],[568,739,741],{"className":740},[575],[577,742,743],{"xmlns":579},[581,744,745,749],{},[584,746,747],{},[587,748,597],{},[611,750,597],{"encoding":613},[568,752,754],{"className":753,"ariaHidden":619},[618],[568,755,757,761],{"className":756},[623],[568,758],{"className":759,"style":760},[627],"height:0.4306em;",[568,762,597],{"className":763},[632,633],".",[564,766,767,768,890,891,964,965,993,994,1022,1023,1093],{},"Der Faktor ",[568,769,771,792],{"className":770},[571],[568,772,774],{"className":773},[575],[577,775,776],{"xmlns":579},[581,777,778,789],{},[584,779,780],{},[781,782,783,787],"mfrac",{},[784,785,786],"mn",{},"1",[587,788,597],{},[611,790,791],{"encoding":613},"\\frac{1}{a}",[568,793,795],{"className":794,"ariaHidden":619},[618],[568,796,798,802],{"className":797},[623],[568,799],{"className":800,"style":801},[627],"height:1.1901em;vertical-align:-0.345em;",[568,803,805,809,887],{"className":804},[632],[568,806],{"className":807},[638,808],"nulldelimiter",[568,810,812],{"className":811},[781],[568,813,817,878],{"className":814},[815,816],"vlist-t","vlist-t2",[568,818,821,873],{"className":819},[820],"vlist-r",[568,822,826,847,858],{"className":823,"style":825},[824],"vlist","height:0.8451em;",[568,827,829,834],{"style":828},"top:-2.655em;",[568,830],{"className":831,"style":833},[832],"pstrut","height:3em;",[568,835,841],{"className":836},[837,838,839,840],"sizing","reset-size6","size3","mtight",[568,842,844],{"className":843},[632,840],[568,845,597],{"className":846},[632,633,840],[568,848,850,853],{"style":849},"top:-3.23em;",[568,851],{"className":852,"style":833},[832],[568,854],{"className":855,"style":857},[856],"frac-line","border-bottom-width:0.04em;",[568,859,861,864],{"style":860},"top:-3.394em;",[568,862],{"className":863,"style":833},[832],[568,865,867],{"className":866},[837,838,839,840],[568,868,870],{"className":869},[632,840],[568,871,786],{"className":872},[632,840],[568,874,877],{"className":875},[876],"vlist-s","​",[568,879,881],{"className":880},[820],[568,882,885],{"className":883,"style":884},[824],"height:0.345em;",[568,886],{},[568,888],{"className":889},[669,808]," gleicht die innere Ableitung aus: Leitet man ",[568,892,894,921],{"className":893},[571],[568,895,897],{"className":896},[575],[577,898,899],{"xmlns":579},[581,900,901,918],{},[584,902,903,906,908,910,912,914,916],{},[587,904,905],{},"F",[591,907,594],{"stretchy":593},[587,909,597],{},[587,911,600],{},[591,913,603],{},[587,915,606],{},[591,917,609],{"stretchy":593},[611,919,920],{"encoding":613},"F(ax + b)",[568,922,924,952],{"className":923,"ariaHidden":619},[618],[568,925,927,930,934,937,940,943,946,949],{"className":926},[623],[568,928],{"className":929,"style":628},[627],[568,931,905],{"className":932,"style":933},[632,633],"margin-right:0.1389em;",[568,935,594],{"className":936},[638],[568,938,597],{"className":939},[632,633],[568,941,600],{"className":942},[632,633],[568,944],{"className":945,"style":649},[648],[568,947,603],{"className":948},[653],[568,950],{"className":951,"style":649},[648],[568,953,955,958,961],{"className":954},[623],[568,956],{"className":957,"style":628},[627],[568,959,606],{"className":960},[632,633],[568,962,609],{"className":963},[669]," nach der Kettenregel ab, entsteht der Faktor ",[568,966,968,981],{"className":967},[571],[568,969,971],{"className":970},[575],[577,972,973],{"xmlns":579},[581,974,975,979],{},[584,976,977],{},[587,978,597],{},[611,980,597],{"encoding":613},[568,982,984],{"className":983,"ariaHidden":619},[618],[568,985,987,990],{"className":986},[623],[568,988],{"className":989,"style":760},[627],[568,991,597],{"className":992},[632,633],". Teilt man vorher durch ",[568,995,997,1010],{"className":996},[571],[568,998,1000],{"className":999},[575],[577,1001,1002],{"xmlns":579},[581,1003,1004,1008],{},[584,1005,1006],{},[587,1007,597],{},[611,1009,597],{"encoding":613},[568,1011,1013],{"className":1012,"ariaHidden":619},[618],[568,1014,1016,1019],{"className":1015},[623],[568,1017],{"className":1018,"style":760},[627],[568,1020,597],{"className":1021},[632,633],", bleibt genau ",[568,1024,1026,1051],{"className":1025},[571],[568,1027,1029],{"className":1028},[575],[577,1030,1031],{"xmlns":579},[581,1032,1033,1049],{},[584,1034,1035,1037,1039,1041,1043,1045,1047],{},[587,1036,589],{},[591,1038,594],{"stretchy":593},[587,1040,597],{},[587,1042,600],{},[591,1044,603],{},[587,1046,606],{},[591,1048,609],{"stretchy":593},[611,1050,614],{"encoding":613},[568,1052,1054,1081],{"className":1053,"ariaHidden":619},[618],[568,1055,1057,1060,1063,1066,1069,1072,1075,1078],{"className":1056},[623],[568,1058],{"className":1059,"style":628},[627],[568,1061,589],{"className":1062,"style":634},[632,633],[568,1064,594],{"className":1065},[638],[568,1067,597],{"className":1068},[632,633],[568,1070,600],{"className":1071},[632,633],[568,1073],{"className":1074,"style":649},[648],[568,1076,603],{"className":1077},[653],[568,1079],{"className":1080,"style":649},[648],[568,1082,1084,1087,1090],{"className":1083},[623],[568,1085],{"className":1086,"style":628},[627],[568,1088,606],{"className":1089},[632,633],[568,1091,609],{"className":1092},[669]," übrig.",[564,1095,1096,1097,1100],{},"Die Regel ist ein Spezialfall der Integration durch Substitution. Sie gilt ",[672,1098,1099],{},"nur",", wenn die innere Funktion linear ist.",[559,1102,1104],{"id":1103},"herleitung","Herleitung",[564,1106,1107],{},"Ableiten der rechten Seite mit der Kettenregel:",[568,1109,1112],{"className":1110},[1111],"katex-display",[568,1113,1115,1212],{"className":1114},[571],[568,1116,1118],{"className":1117},[575],[577,1119,1121],{"xmlns":579,"display":1120},"block",[581,1122,1123,1209],{},[584,1124,1125,1163,1166,1172,1175,1177,1179,1181,1183,1185,1187,1189,1191,1193,1195,1197,1199,1201,1203,1205,1207],{},[1126,1127,1128,1158],"msup",{},[584,1129,1130,1132,1138,1142,1144,1146,1148,1150,1152,1154,1156],{},[591,1131,594],{"fence":619},[781,1133,1134,1136],{},[784,1135,786],{},[587,1137,597],{},[1139,1140,1141],"mtext",{}," ",[587,1143,905],{},[591,1145,594],{"stretchy":593},[587,1147,597],{},[587,1149,600],{},[591,1151,603],{},[587,1153,606],{},[591,1155,609],{"stretchy":593},[591,1157,609],{"fence":619},[591,1159,1162],{"mathvariant":1160,"lspace":1161,"rspace":1161},"normal","0em","′",[591,1164,1165],{},"=",[781,1167,1168,1170],{},[784,1169,786],{},[587,1171,597],{},[591,1173,1174],{},"⋅",[587,1176,589],{},[591,1178,594],{"stretchy":593},[587,1180,597],{},[587,1182,600],{},[591,1184,603],{},[587,1186,606],{},[591,1188,609],{"stretchy":593},[591,1190,1174],{},[587,1192,597],{},[591,1194,1165],{},[587,1196,589],{},[591,1198,594],{"stretchy":593},[587,1200,597],{},[587,1202,600],{},[591,1204,603],{},[587,1206,606],{},[591,1208,609],{"stretchy":593},[611,1210,1211],{"encoding":613},"\\left(\\frac{1}{a}\\,F(ax + b)\\right)' = \\frac{1}{a} \\cdot f(ax + b) \\cdot a = f(ax + b)",[568,1213,1215,1382,1460,1487,1508,1526,1553],{"className":1214,"ariaHidden":619},[618],[568,1216,1218,1222,1371,1375,1379],{"className":1217},[623],[568,1219],{"className":1220,"style":1221},[627],"height:2.5418em;vertical-align:-0.95em;",[568,1223,1226,1341],{"className":1224},[1225],"minner",[568,1227,1229,1238,1304,1308,1311,1314,1317,1320,1323,1326,1329,1332,1335],{"className":1228},[1225],[568,1230,1234],{"className":1231,"style":1233},[638,1232],"delimcenter","top:0em;",[568,1235,594],{"className":1236},[1237,839],"delimsizing",[568,1239,1241,1244,1301],{"className":1240},[632],[568,1242],{"className":1243},[638,808],[568,1245,1247],{"className":1246},[781],[568,1248,1250,1292],{"className":1249},[815,816],[568,1251,1253,1289],{"className":1252},[820],[568,1254,1257,1269,1277],{"className":1255,"style":1256},[824],"height:1.3214em;",[568,1258,1260,1263],{"style":1259},"top:-2.314em;",[568,1261],{"className":1262,"style":833},[832],[568,1264,1266],{"className":1265},[632],[568,1267,597],{"className":1268},[632,633],[568,1270,1271,1274],{"style":849},[568,1272],{"className":1273,"style":833},[832],[568,1275],{"className":1276,"style":857},[856],[568,1278,1280,1283],{"style":1279},"top:-3.677em;",[568,1281],{"className":1282,"style":833},[832],[568,1284,1286],{"className":1285},[632],[568,1287,786],{"className":1288},[632],[568,1290,877],{"className":1291},[876],[568,1293,1295],{"className":1294},[820],[568,1296,1299],{"className":1297,"style":1298},[824],"height:0.686em;",[568,1300],{},[568,1302],{"className":1303},[669,808],[568,1305],{"className":1306,"style":1307},[648],"margin-right:0.1667em;",[568,1309,905],{"className":1310,"style":933},[632,633],[568,1312,594],{"className":1313},[638],[568,1315,597],{"className":1316},[632,633],[568,1318,600],{"className":1319},[632,633],[568,1321],{"className":1322,"style":649},[648],[568,1324,603],{"className":1325},[653],[568,1327],{"className":1328,"style":649},[648],[568,1330,606],{"className":1331},[632,633],[568,1333,609],{"className":1334},[669],[568,1336,1338],{"className":1337,"style":1233},[669,1232],[568,1339,609],{"className":1340},[1237,839],[568,1342,1345],{"className":1343},[1344],"msupsub",[568,1346,1348],{"className":1347},[815],[568,1349,1351],{"className":1350},[820],[568,1352,1355],{"className":1353,"style":1354},[824],"height:1.5918em;",[568,1356,1358,1362],{"style":1357},"top:-3.9029em;margin-right:0.05em;",[568,1359],{"className":1360,"style":1361},[832],"height:2.7em;",[568,1363,1365],{"className":1364},[837,838,839,840],[568,1366,1368],{"className":1367},[632,840],[568,1369,1162],{"className":1370},[632,840],[568,1372],{"className":1373,"style":1374},[648],"margin-right:0.2778em;",[568,1376,1165],{"className":1377},[1378],"mrel",[568,1380],{"className":1381,"style":1374},[648],[568,1383,1385,1389,1451,1454,1457],{"className":1384},[623],[568,1386],{"className":1387,"style":1388},[627],"height:2.0074em;vertical-align:-0.686em;",[568,1390,1392,1395,1448],{"className":1391},[632],[568,1393],{"className":1394},[638,808],[568,1396,1398],{"className":1397},[781],[568,1399,1401,1440],{"className":1400},[815,816],[568,1402,1404,1437],{"className":1403},[820],[568,1405,1407,1418,1426],{"className":1406,"style":1256},[824],[568,1408,1409,1412],{"style":1259},[568,1410],{"className":1411,"style":833},[832],[568,1413,1415],{"className":1414},[632],[568,1416,597],{"className":1417},[632,633],[568,1419,1420,1423],{"style":849},[568,1421],{"className":1422,"style":833},[832],[568,1424],{"className":1425,"style":857},[856],[568,1427,1428,1431],{"style":1279},[568,1429],{"className":1430,"style":833},[832],[568,1432,1434],{"className":1433},[632],[568,1435,786],{"className":1436},[632],[568,1438,877],{"className":1439},[876],[568,1441,1443],{"className":1442},[820],[568,1444,1446],{"className":1445,"style":1298},[824],[568,1447],{},[568,1449],{"className":1450},[669,808],[568,1452],{"className":1453,"style":649},[648],[568,1455,1174],{"className":1456},[653],[568,1458],{"className":1459,"style":649},[648],[568,1461,1463,1466,1469,1472,1475,1478,1481,1484],{"className":1462},[623],[568,1464],{"className":1465,"style":628},[627],[568,1467,589],{"className":1468,"style":634},[632,633],[568,1470,594],{"className":1471},[638],[568,1473,597],{"className":1474},[632,633],[568,1476,600],{"className":1477},[632,633],[568,1479],{"className":1480,"style":649},[648],[568,1482,603],{"className":1483},[653],[568,1485],{"className":1486,"style":649},[648],[568,1488,1490,1493,1496,1499,1502,1505],{"className":1489},[623],[568,1491],{"className":1492,"style":628},[627],[568,1494,606],{"className":1495},[632,633],[568,1497,609],{"className":1498},[669],[568,1500],{"className":1501,"style":649},[648],[568,1503,1174],{"className":1504},[653],[568,1506],{"className":1507,"style":649},[648],[568,1509,1511,1514,1517,1520,1523],{"className":1510},[623],[568,1512],{"className":1513,"style":760},[627],[568,1515,597],{"className":1516},[632,633],[568,1518],{"className":1519,"style":1374},[648],[568,1521,1165],{"className":1522},[1378],[568,1524],{"className":1525,"style":1374},[648],[568,1527,1529,1532,1535,1538,1541,1544,1547,1550],{"className":1528},[623],[568,1530],{"className":1531,"style":628},[627],[568,1533,589],{"className":1534,"style":634},[632,633],[568,1536,594],{"className":1537},[638],[568,1539,597],{"className":1540},[632,633],[568,1542,600],{"className":1543},[632,633],[568,1545],{"className":1546,"style":649},[648],[568,1548,603],{"className":1549},[653],[568,1551],{"className":1552,"style":649},[648],[568,1554,1556,1559,1562],{"className":1555},[623],[568,1557],{"className":1558,"style":628},[627],[568,1560,606],{"className":1561},[632,633],[568,1563,609],{"className":1564},[669],[559,1566,1568],{"id":1567},"beispiele","Beispiele",[564,1570,1571,1572,1635,1636,1697],{},"Äußere Funktion ",[568,1573,1575,1595],{"className":1574},[571],[568,1576,1578],{"className":1577},[575],[577,1579,1580],{"xmlns":579},[581,1581,1582,1592],{},[584,1583,1584],{},[1126,1585,1586,1589],{},[587,1587,1588],{},"t",[784,1590,1591],{},"4",[611,1593,1594],{"encoding":613},"t^4",[568,1596,1598],{"className":1597,"ariaHidden":619},[618],[568,1599,1601,1605],{"className":1600},[623],[568,1602],{"className":1603,"style":1604},[627],"height:0.8141em;",[568,1606,1608,1611],{"className":1607},[632],[568,1609,1588],{"className":1610},[632,633],[568,1612,1614],{"className":1613},[1344],[568,1615,1617],{"className":1616},[815],[568,1618,1620],{"className":1619},[820],[568,1621,1623],{"className":1622,"style":1604},[824],[568,1624,1626,1629],{"style":1625},"top:-3.063em;margin-right:0.05em;",[568,1627],{"className":1628,"style":1361},[832],[568,1630,1632],{"className":1631},[837,838,839,840],[568,1633,1591],{"className":1634},[632,840],", innere Funktion ",[568,1637,1639,1662],{"className":1638},[571],[568,1640,1642],{"className":1641},[575],[577,1643,1644],{"xmlns":579},[581,1645,1646,1659],{},[584,1647,1648,1651,1653,1656],{},[784,1649,1650],{},"3",[587,1652,600],{},[591,1654,1655],{},"−",[784,1657,1658],{},"2",[611,1660,1661],{"encoding":613},"3x - 2",[568,1663,1665,1687],{"className":1664,"ariaHidden":619},[618],[568,1666,1668,1672,1675,1678,1681,1684],{"className":1667},[623],[568,1669],{"className":1670,"style":1671},[627],"height:0.7278em;vertical-align:-0.0833em;",[568,1673,1650],{"className":1674},[632],[568,1676,600],{"className":1677},[632,633],[568,1679],{"className":1680,"style":649},[648],[568,1682,1655],{"className":1683},[653],[568,1685],{"className":1686,"style":649},[648],[568,1688,1690,1694],{"className":1689},[623],[568,1691],{"className":1692,"style":1693},[627],"height:0.6444em;",[568,1695,1658],{"className":1696},[632],":",[568,1699,1701],{"className":1700},[1111],[568,1702,1704,1809],{"className":1703},[571],[568,1705,1707],{"className":1706},[575],[577,1708,1709],{"xmlns":579,"display":1120},[581,1710,1711,1806],{},[584,1712,1713,1716,1718,1720,1722,1724,1726,1732,1734,1737,1739,1741,1747,1749,1772,1774,1777,1779,1802,1804],{},[591,1714,1715],{},"∫",[591,1717,594],{"stretchy":593},[784,1719,1650],{},[587,1721,600],{},[591,1723,1655],{},[784,1725,1658],{},[1126,1727,1728,1730],{},[591,1729,609],{"stretchy":593},[784,1731,1591],{},[1139,1733,1141],{},[587,1735,1736],{},"d",[587,1738,600],{},[591,1740,1165],{},[781,1742,1743,1745],{},[784,1744,786],{},[784,1746,1650],{},[591,1748,1174],{},[781,1750,1751,1770],{},[584,1752,1753,1755,1757,1759,1761,1763],{},[591,1754,594],{"stretchy":593},[784,1756,1650],{},[587,1758,600],{},[591,1760,1655],{},[784,1762,1658],{},[1126,1764,1765,1767],{},[591,1766,609],{"stretchy":593},[784,1768,1769],{},"5",[784,1771,1769],{},[591,1773,603],{},[587,1775,1776],{},"C",[591,1778,1165],{},[781,1780,1781,1799],{},[584,1782,1783,1785,1787,1789,1791,1793],{},[591,1784,594],{"stretchy":593},[784,1786,1650],{},[587,1788,600],{},[591,1790,1655],{},[784,1792,1658],{},[1126,1794,1795,1797],{},[591,1796,609],{"stretchy":593},[784,1798,1769],{},[784,1800,1801],{},"15",[591,1803,603],{},[587,1805,1776],{},[611,1807,1808],{"encoding":613},"\\int (3x - 2)^4\\,dx = \\frac{1}{3} \\cdot \\frac{(3x - 2)^5}{5} + C = \\frac{(3x - 2)^5}{15} + C",[568,1810,1812,1844,1903,1980,2106,2126,2250],{"className":1811,"ariaHidden":619},[618],[568,1813,1815,1819,1826,1829,1832,1835,1838,1841],{"className":1814},[623],[568,1816],{"className":1817,"style":1818},[627],"height:2.2222em;vertical-align:-0.8622em;",[568,1820,1715],{"className":1821,"style":1825},[1822,1823,1824],"mop","op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,1827,594],{"className":1828},[638],[568,1830,1650],{"className":1831},[632],[568,1833,600],{"className":1834},[632,633],[568,1836],{"className":1837,"style":649},[648],[568,1839,1655],{"className":1840},[653],[568,1842],{"className":1843,"style":649},[648],[568,1845,1847,1851,1854,1885,1888,1891,1894,1897,1900],{"className":1846},[623],[568,1848],{"className":1849,"style":1850},[627],"height:1.1141em;vertical-align:-0.25em;",[568,1852,1658],{"className":1853},[632],[568,1855,1857,1860],{"className":1856},[669],[568,1858,609],{"className":1859},[669],[568,1861,1863],{"className":1862},[1344],[568,1864,1866],{"className":1865},[815],[568,1867,1869],{"className":1868},[820],[568,1870,1873],{"className":1871,"style":1872},[824],"height:0.8641em;",[568,1874,1876,1879],{"style":1875},"top:-3.113em;margin-right:0.05em;",[568,1877],{"className":1878,"style":1361},[832],[568,1880,1882],{"className":1881},[837,838,839,840],[568,1883,1591],{"className":1884},[632,840],[568,1886],{"className":1887,"style":1307},[648],[568,1889,1736],{"className":1890},[632,633],[568,1892,600],{"className":1893},[632,633],[568,1895],{"className":1896,"style":1374},[648],[568,1898,1165],{"className":1899},[1378],[568,1901],{"className":1902,"style":1374},[648],[568,1904,1906,1909,1971,1974,1977],{"className":1905},[623],[568,1907],{"className":1908,"style":1388},[627],[568,1910,1912,1915,1968],{"className":1911},[632],[568,1913],{"className":1914},[638,808],[568,1916,1918],{"className":1917},[781],[568,1919,1921,1960],{"className":1920},[815,816],[568,1922,1924,1957],{"className":1923},[820],[568,1925,1927,1938,1946],{"className":1926,"style":1256},[824],[568,1928,1929,1932],{"style":1259},[568,1930],{"className":1931,"style":833},[832],[568,1933,1935],{"className":1934},[632],[568,1936,1650],{"className":1937},[632],[568,1939,1940,1943],{"style":849},[568,1941],{"className":1942,"style":833},[832],[568,1944],{"className":1945,"style":857},[856],[568,1947,1948,1951],{"style":1279},[568,1949],{"className":1950,"style":833},[832],[568,1952,1954],{"className":1953},[632],[568,1955,786],{"className":1956},[632],[568,1958,877],{"className":1959},[876],[568,1961,1963],{"className":1962},[820],[568,1964,1966],{"className":1965,"style":1298},[824],[568,1967],{},[568,1969],{"className":1970},[669,808],[568,1972],{"className":1973,"style":649},[648],[568,1975,1174],{"className":1976},[653],[568,1978],{"className":1979,"style":649},[648],[568,1981,1983,1987,2097,2100,2103],{"className":1982},[623],[568,1984],{"className":1985,"style":1986},[627],"height:2.1771em;vertical-align:-0.686em;",[568,1988,1990,1993,2094],{"className":1989},[632],[568,1991],{"className":1992},[638,808],[568,1994,1996],{"className":1995},[781],[568,1997,1999,2086],{"className":1998},[815,816],[568,2000,2002,2083],{"className":2001},[820],[568,2003,2006,2017,2025],{"className":2004,"style":2005},[824],"height:1.4911em;",[568,2007,2008,2011],{"style":1259},[568,2009],{"className":2010,"style":833},[832],[568,2012,2014],{"className":2013},[632],[568,2015,1769],{"className":2016},[632],[568,2018,2019,2022],{"style":849},[568,2020],{"className":2021,"style":833},[832],[568,2023],{"className":2024,"style":857},[856],[568,2026,2027,2030],{"style":1279},[568,2028],{"className":2029,"style":833},[832],[568,2031,2033,2036,2039,2042,2045,2048,2051,2054],{"className":2032},[632],[568,2034,594],{"className":2035},[638],[568,2037,1650],{"className":2038},[632],[568,2040,600],{"className":2041},[632,633],[568,2043],{"className":2044,"style":649},[648],[568,2046,1655],{"className":2047},[653],[568,2049],{"className":2050,"style":649},[648],[568,2052,1658],{"className":2053},[632],[568,2055,2057,2060],{"className":2056},[669],[568,2058,609],{"className":2059},[669],[568,2061,2063],{"className":2062},[1344],[568,2064,2066],{"className":2065},[815],[568,2067,2069],{"className":2068},[820],[568,2070,2072],{"className":2071,"style":1604},[824],[568,2073,2074,2077],{"style":1625},[568,2075],{"className":2076,"style":1361},[832],[568,2078,2080],{"className":2079},[837,838,839,840],[568,2081,1769],{"className":2082},[632,840],[568,2084,877],{"className":2085},[876],[568,2087,2089],{"className":2088},[820],[568,2090,2092],{"className":2091,"style":1298},[824],[568,2093],{},[568,2095],{"className":2096},[669,808],[568,2098],{"className":2099,"style":649},[648],[568,2101,603],{"className":2102},[653],[568,2104],{"className":2105,"style":649},[648],[568,2107,2109,2113,2117,2120,2123],{"className":2108},[623],[568,2110],{"className":2111,"style":2112},[627],"height:0.6833em;",[568,2114,1776],{"className":2115,"style":2116},[632,633],"margin-right:0.0715em;",[568,2118],{"className":2119,"style":1374},[648],[568,2121,1165],{"className":2122},[1378],[568,2124],{"className":2125,"style":1374},[648],[568,2127,2129,2132,2241,2244,2247],{"className":2128},[623],[568,2130],{"className":2131,"style":1986},[627],[568,2133,2135,2138,2238],{"className":2134},[632],[568,2136],{"className":2137},[638,808],[568,2139,2141],{"className":2140},[781],[568,2142,2144,2230],{"className":2143},[815,816],[568,2145,2147,2227],{"className":2146},[820],[568,2148,2150,2161,2169],{"className":2149,"style":2005},[824],[568,2151,2152,2155],{"style":1259},[568,2153],{"className":2154,"style":833},[832],[568,2156,2158],{"className":2157},[632],[568,2159,1801],{"className":2160},[632],[568,2162,2163,2166],{"style":849},[568,2164],{"className":2165,"style":833},[832],[568,2167],{"className":2168,"style":857},[856],[568,2170,2171,2174],{"style":1279},[568,2172],{"className":2173,"style":833},[832],[568,2175,2177,2180,2183,2186,2189,2192,2195,2198],{"className":2176},[632],[568,2178,594],{"className":2179},[638],[568,2181,1650],{"className":2182},[632],[568,2184,600],{"className":2185},[632,633],[568,2187],{"className":2188,"style":649},[648],[568,2190,1655],{"className":2191},[653],[568,2193],{"className":2194,"style":649},[648],[568,2196,1658],{"className":2197},[632],[568,2199,2201,2204],{"className":2200},[669],[568,2202,609],{"className":2203},[669],[568,2205,2207],{"className":2206},[1344],[568,2208,2210],{"className":2209},[815],[568,2211,2213],{"className":2212},[820],[568,2214,2216],{"className":2215,"style":1604},[824],[568,2217,2218,2221],{"style":1625},[568,2219],{"className":2220,"style":1361},[832],[568,2222,2224],{"className":2223},[837,838,839,840],[568,2225,1769],{"className":2226},[632,840],[568,2228,877],{"className":2229},[876],[568,2231,2233],{"className":2232},[820],[568,2234,2236],{"className":2235,"style":1298},[824],[568,2237],{},[568,2239],{"className":2240},[669,808],[568,2242],{"className":2243,"style":649},[648],[568,2245,603],{"className":2246},[653],[568,2248],{"className":2249,"style":649},[648],[568,2251,2253,2256],{"className":2252},[623],[568,2254],{"className":2255,"style":2112},[627],[568,2257,1776],{"className":2258,"style":2116},[632,633],[568,2260,2262],{"className":2261},[1111],[568,2263,2265,2370],{"className":2264},[571],[568,2266,2268],{"className":2267},[575],[577,2269,2270],{"xmlns":579,"display":1120},[581,2271,2272,2367],{},[584,2273,2274,2284,2299,2301,2303,2305,2307,2343,2345,2361,2364],{},[2275,2276,2277,2279,2282],"msubsup",{},[591,2278,1715],{},[784,2280,2281],{},"0",[784,2283,786],{},[1126,2285,2286,2289],{},[587,2287,2288],{},"e",[584,2290,2291,2293,2295,2297],{},[784,2292,1658],{},[587,2294,600],{},[591,2296,603],{},[784,2298,786],{},[1139,2300,1141],{},[587,2302,1736],{},[587,2304,600],{},[591,2306,1165],{},[2275,2308,2309,2339,2341],{},[584,2310,2311,2314,2320,2322,2336],{},[591,2312,2313],{"fence":619},"[",[781,2315,2316,2318],{},[784,2317,786],{},[784,2319,1658],{},[1139,2321,1141],{},[1126,2323,2324,2326],{},[587,2325,2288],{},[584,2327,2328,2330,2332,2334],{},[784,2329,1658],{},[587,2331,600],{},[591,2333,603],{},[784,2335,786],{},[591,2337,2338],{"fence":619},"]",[784,2340,2281],{},[784,2342,786],{},[591,2344,1165],{},[781,2346,2347,2359],{},[584,2348,2349,2355,2357],{},[1126,2350,2351,2353],{},[587,2352,2288],{},[784,2354,1650],{},[591,2356,1655],{},[587,2358,2288],{},[784,2360,1658],{},[591,2362,2363],{},"≈",[784,2365,2366],{},"8,6836",[611,2368,2369],{"encoding":613},"\\int_0^1 e^{2x + 1}\\,dx = \\left[\\frac{1}{2}\\,e^{2x + 1}\\right]_0^1 = \\frac{e^3 - e}{2} \\approx 8{,}6836",[568,2371,2373,2497,2685,2800],{"className":2372,"ariaHidden":619},[618],[568,2374,2376,2380,2435,2438,2479,2482,2485,2488,2491,2494],{"className":2375},[623],[568,2377],{"className":2378,"style":2379},[627],"height:2.476em;vertical-align:-0.9119em;",[568,2381,2383,2386],{"className":2382},[1822],[568,2384,1715],{"className":2385,"style":1825},[1822,1823,1824],[568,2387,2389],{"className":2388},[1344],[568,2390,2392,2426],{"className":2391},[815,816],[568,2393,2395,2423],{"className":2394},[820],[568,2396,2399,2411],{"className":2397,"style":2398},[824],"height:1.564em;",[568,2400,2402,2405],{"style":2401},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,2403],{"className":2404,"style":1361},[832],[568,2406,2408],{"className":2407},[837,838,839,840],[568,2409,2281],{"className":2410},[632,840],[568,2412,2414,2417],{"style":2413},"top:-3.8129em;margin-right:0.05em;",[568,2415],{"className":2416,"style":1361},[832],[568,2418,2420],{"className":2419},[837,838,839,840],[568,2421,786],{"className":2422},[632,840],[568,2424,877],{"className":2425},[876],[568,2427,2429],{"className":2428},[820],[568,2430,2433],{"className":2431,"style":2432},[824],"height:0.9119em;",[568,2434],{},[568,2436],{"className":2437,"style":1307},[648],[568,2439,2441,2444],{"className":2440},[632],[568,2442,2288],{"className":2443},[632,633],[568,2445,2447],{"className":2446},[1344],[568,2448,2450],{"className":2449},[815],[568,2451,2453],{"className":2452},[820],[568,2454,2456],{"className":2455,"style":1872},[824],[568,2457,2458,2461],{"style":1875},[568,2459],{"className":2460,"style":1361},[832],[568,2462,2464],{"className":2463},[837,838,839,840],[568,2465,2467,2470,2473,2476],{"className":2466},[632,840],[568,2468,1658],{"className":2469},[632,840],[568,2471,600],{"className":2472},[632,633,840],[568,2474,603],{"className":2475},[653,840],[568,2477,786],{"className":2478},[632,840],[568,2480],{"className":2481,"style":1307},[648],[568,2483,1736],{"className":2484},[632,633],[568,2486,600],{"className":2487},[632,633],[568,2489],{"className":2490,"style":1374},[648],[568,2492,1165],{"className":2493},[1378],[568,2495],{"className":2496,"style":1374},[648],[568,2498,2500,2504,2676,2679,2682],{"className":2499},[623],[568,2501],{"className":2502,"style":2503},[627],"height:2.6537em;vertical-align:-0.9997em;",[568,2505,2507,2628],{"className":2506},[1225],[568,2508,2510,2516,2578,2581,2622],{"className":2509},[1225],[568,2511,2513],{"className":2512,"style":1233},[638,1232],[568,2514,2313],{"className":2515},[1237,839],[568,2517,2519,2522,2575],{"className":2518},[632],[568,2520],{"className":2521},[638,808],[568,2523,2525],{"className":2524},[781],[568,2526,2528,2567],{"className":2527},[815,816],[568,2529,2531,2564],{"className":2530},[820],[568,2532,2534,2545,2553],{"className":2533,"style":1256},[824],[568,2535,2536,2539],{"style":1259},[568,2537],{"className":2538,"style":833},[832],[568,2540,2542],{"className":2541},[632],[568,2543,1658],{"className":2544},[632],[568,2546,2547,2550],{"style":849},[568,2548],{"className":2549,"style":833},[832],[568,2551],{"className":2552,"style":857},[856],[568,2554,2555,2558],{"style":1279},[568,2556],{"className":2557,"style":833},[832],[568,2559,2561],{"className":2560},[632],[568,2562,786],{"className":2563},[632],[568,2565,877],{"className":2566},[876],[568,2568,2570],{"className":2569},[820],[568,2571,2573],{"className":2572,"style":1298},[824],[568,2574],{},[568,2576],{"className":2577},[669,808],[568,2579],{"className":2580,"style":1307},[648],[568,2582,2584,2587],{"className":2583},[632],[568,2585,2288],{"className":2586},[632,633],[568,2588,2590],{"className":2589},[1344],[568,2591,2593],{"className":2592},[815],[568,2594,2596],{"className":2595},[820],[568,2597,2599],{"className":2598,"style":1872},[824],[568,2600,2601,2604],{"style":1875},[568,2602],{"className":2603,"style":1361},[832],[568,2605,2607],{"className":2606},[837,838,839,840],[568,2608,2610,2613,2616,2619],{"className":2609},[632,840],[568,2611,1658],{"className":2612},[632,840],[568,2614,600],{"className":2615},[632,633,840],[568,2617,603],{"className":2618},[653,840],[568,2620,786],{"className":2621},[632,840],[568,2623,2625],{"className":2624,"style":1233},[669,1232],[568,2626,2338],{"className":2627},[1237,839],[568,2629,2631],{"className":2630},[1344],[568,2632,2634,2667],{"className":2633},[815,816],[568,2635,2637,2664],{"className":2636},[820],[568,2638,2641,2653],{"className":2639,"style":2640},[824],"height:1.654em;",[568,2642,2644,2647],{"style":2643},"top:-1.7003em;margin-right:0.05em;",[568,2645],{"className":2646,"style":1361},[832],[568,2648,2650],{"className":2649},[837,838,839,840],[568,2651,2281],{"className":2652},[632,840],[568,2654,2655,2658],{"style":1357},[568,2656],{"className":2657,"style":1361},[832],[568,2659,2661],{"className":2660},[837,838,839,840],[568,2662,786],{"className":2663},[632,840],[568,2665,877],{"className":2666},[876],[568,2668,2670],{"className":2669},[820],[568,2671,2674],{"className":2672,"style":2673},[824],"height:0.9997em;",[568,2675],{},[568,2677],{"className":2678,"style":1374},[648],[568,2680,1165],{"className":2681},[1378],[568,2683],{"className":2684,"style":1374},[648],[568,2686,2688,2691,2791,2794,2797],{"className":2687},[623],[568,2689],{"className":2690,"style":1986},[627],[568,2692,2694,2697,2788],{"className":2693},[632],[568,2695],{"className":2696},[638,808],[568,2698,2700],{"className":2699},[781],[568,2701,2703,2780],{"className":2702},[815,816],[568,2704,2706,2777],{"className":2705},[820],[568,2707,2709,2720,2728],{"className":2708,"style":2005},[824],[568,2710,2711,2714],{"style":1259},[568,2712],{"className":2713,"style":833},[832],[568,2715,2717],{"className":2716},[632],[568,2718,1658],{"className":2719},[632],[568,2721,2722,2725],{"style":849},[568,2723],{"className":2724,"style":833},[832],[568,2726],{"className":2727,"style":857},[856],[568,2729,2730,2733],{"style":1279},[568,2731],{"className":2732,"style":833},[832],[568,2734,2736,2765,2768,2771,2774],{"className":2735},[632],[568,2737,2739,2742],{"className":2738},[632],[568,2740,2288],{"className":2741},[632,633],[568,2743,2745],{"className":2744},[1344],[568,2746,2748],{"className":2747},[815],[568,2749,2751],{"className":2750},[820],[568,2752,2754],{"className":2753,"style":1604},[824],[568,2755,2756,2759],{"style":1625},[568,2757],{"className":2758,"style":1361},[832],[568,2760,2762],{"className":2761},[837,838,839,840],[568,2763,1650],{"className":2764},[632,840],[568,2766],{"className":2767,"style":649},[648],[568,2769,1655],{"className":2770},[653],[568,2772],{"className":2773,"style":649},[648],[568,2775,2288],{"className":2776},[632,633],[568,2778,877],{"className":2779},[876],[568,2781,2783],{"className":2782},[820],[568,2784,2786],{"className":2785,"style":1298},[824],[568,2787],{},[568,2789],{"className":2790},[669,808],[568,2792],{"className":2793,"style":1374},[648],[568,2795,2363],{"className":2796},[1378],[568,2798],{"className":2799,"style":1374},[648],[568,2801,2803,2807,2811,2819],{"className":2802},[623],[568,2804],{"className":2805,"style":2806},[627],"height:0.8389em;vertical-align:-0.1944em;",[568,2808,2810],{"className":2809},[632],"8",[568,2812,2814],{"className":2813},[632],[568,2815,2818],{"className":2816},[2817],"mpunct",",",[568,2820,2822],{"className":2821},[632],"6836",[568,2824,2826],{"className":2825},[1111],[568,2827,2829,2941],{"className":2828},[571],[568,2830,2832],{"className":2831},[575],[577,2833,2834],{"xmlns":579,"display":1120},[581,2835,2836,2938],{},[584,2837,2838,2851,2854,2857,2859,2861,2863,2865,2867,2869,2871,2873,2908,2910,2916,2918,2920,2926,2928,2930,2932],{},[2275,2839,2840,2842,2844],{},[591,2841,1715],{},[784,2843,2281],{},[781,2845,2846,2849],{},[587,2847,2848],{},"π",[784,2850,2810],{},[587,2852,2853],{},"cos",[591,2855,2856],{},"⁡",[591,2858,594],{"stretchy":593},[784,2860,1591],{},[587,2862,600],{},[591,2864,609],{"stretchy":593},[1139,2866,1141],{},[587,2868,1736],{},[587,2870,600],{},[591,2872,1165],{},[2275,2874,2875,2900,2902],{},[584,2876,2877,2879,2885,2888,2890,2892,2894,2896,2898],{},[591,2878,2313],{"fence":619},[781,2880,2881,2883],{},[784,2882,786],{},[784,2884,1591],{},[587,2886,2887],{},"sin",[591,2889,2856],{},[591,2891,594],{"stretchy":593},[784,2893,1591],{},[587,2895,600],{},[591,2897,609],{"stretchy":593},[591,2899,2338],{"fence":619},[784,2901,2281],{},[781,2903,2904,2906],{},[587,2905,2848],{},[784,2907,2810],{},[591,2909,1165],{},[781,2911,2912,2914],{},[784,2913,786],{},[784,2915,1591],{},[587,2917,2887],{},[591,2919,2856],{},[781,2921,2922,2924],{},[587,2923,2848],{},[784,2925,1658],{},[591,2927,1655],{},[784,2929,2281],{},[591,2931,1165],{},[781,2933,2934,2936],{},[784,2935,786],{},[784,2937,1591],{},[611,2939,2940],{"encoding":613},"\\int_0^{\\frac{\\pi}{8}} \\cos(4x)\\,dx = \\left[\\frac{1}{4}\\sin(4x)\\right]_0^{\\frac{\\pi}{8}} = \\frac{1}{4}\\sin\\frac{\\pi}{2} - 0 = \\frac{1}{4}",[568,2942,2944,3119,3349,3498,3516],{"className":2943,"ariaHidden":619},[618],[568,2945,2947,2951,3083,3086,3089,3092,3095,3098,3101,3104,3107,3110,3113,3116],{"className":2946},[623],[568,2948],{"className":2949,"style":2950},[627],"height:2.5089em;vertical-align:-0.9119em;",[568,2952,2954,2957],{"className":2953},[1822],[568,2955,1715],{"className":2956,"style":1825},[1822,1823,1824],[568,2958,2960],{"className":2959},[1344],[568,2961,2963,3075],{"className":2962},[815,816],[568,2964,2966,3072],{"className":2965},[820],[568,2967,2970,2982],{"className":2968,"style":2969},[824],"height:1.597em;",[568,2971,2973,2976],{"style":2972},"top:-2.088em;margin-left:-0.4445em;margin-right:0.05em;",[568,2974],{"className":2975,"style":833},[832],[568,2977,2979],{"className":2978},[837,838,839,840],[568,2980,2281],{"className":2981},[632,840],[568,2983,2985,2988],{"style":2984},"top:-4.1129em;margin-right:0.05em;",[568,2986],{"className":2987,"style":833},[832],[568,2989,2991],{"className":2990},[837,838,839,840],[568,2992,2994],{"className":2993},[632,840],[568,2995,2997,3002,3069],{"className":2996},[632,840],[568,2998],{"className":2999},[638,808,837,3000,3001],"reset-size3","size6",[568,3003,3005],{"className":3004},[781],[568,3006,3008,3060],{"className":3007},[815,816],[568,3009,3011,3057],{"className":3010},[820],[568,3012,3015,3031,3041],{"className":3013,"style":3014},[824],"height:0.6915em;",[568,3016,3018,3021],{"style":3017},"top:-2.656em;",[568,3019],{"className":3020,"style":833},[832],[568,3022,3025],{"className":3023},[837,3000,3024,840],"size1",[568,3026,3028],{"className":3027},[632,840],[568,3029,2810],{"className":3030},[632,840],[568,3032,3034,3037],{"style":3033},"top:-3.2255em;",[568,3035],{"className":3036,"style":833},[832],[568,3038],{"className":3039,"style":3040},[856,840],"border-bottom-width:0.049em;",[568,3042,3044,3047],{"style":3043},"top:-3.384em;",[568,3045],{"className":3046,"style":833},[832],[568,3048,3050],{"className":3049},[837,3000,3024,840],[568,3051,3053],{"className":3052},[632,840],[568,3054,2848],{"className":3055,"style":3056},[632,633,840],"margin-right:0.0359em;",[568,3058,877],{"className":3059},[876],[568,3061,3063],{"className":3062},[820],[568,3064,3067],{"className":3065,"style":3066},[824],"height:0.344em;",[568,3068],{},[568,3070],{"className":3071},[669,808,837,3000,3001],[568,3073,877],{"className":3074},[876],[568,3076,3078],{"className":3077},[820],[568,3079,3081],{"className":3080,"style":2432},[824],[568,3082],{},[568,3084],{"className":3085,"style":1307},[648],[568,3087,2853],{"className":3088},[1822],[568,3090,594],{"className":3091},[638],[568,3093,1591],{"className":3094},[632],[568,3096,600],{"className":3097},[632,633],[568,3099,609],{"className":3100},[669],[568,3102],{"className":3103,"style":1307},[648],[568,3105,1736],{"className":3106},[632,633],[568,3108,600],{"className":3109},[632,633],[568,3111],{"className":3112,"style":1374},[648],[568,3114,1165],{"className":3115},[1378],[568,3117],{"className":3118,"style":1374},[648],[568,3120,3122,3126,3340,3343,3346],{"className":3121},[623],[568,3123],{"className":3124,"style":3125},[627],"height:2.6867em;vertical-align:-0.9997em;",[568,3127,3129,3224],{"className":3128},[1225],[568,3130,3132,3138,3200,3203,3206,3209,3212,3215,3218],{"className":3131},[1225],[568,3133,3135],{"className":3134,"style":1233},[638,1232],[568,3136,2313],{"className":3137},[1237,839],[568,3139,3141,3144,3197],{"className":3140},[632],[568,3142],{"className":3143},[638,808],[568,3145,3147],{"className":3146},[781],[568,3148,3150,3189],{"className":3149},[815,816],[568,3151,3153,3186],{"className":3152},[820],[568,3154,3156,3167,3175],{"className":3155,"style":1256},[824],[568,3157,3158,3161],{"style":1259},[568,3159],{"className":3160,"style":833},[832],[568,3162,3164],{"className":3163},[632],[568,3165,1591],{"className":3166},[632],[568,3168,3169,3172],{"style":849},[568,3170],{"className":3171,"style":833},[832],[568,3173],{"className":3174,"style":857},[856],[568,3176,3177,3180],{"style":1279},[568,3178],{"className":3179,"style":833},[832],[568,3181,3183],{"className":3182},[632],[568,3184,786],{"className":3185},[632],[568,3187,877],{"className":3188},[876],[568,3190,3192],{"className":3191},[820],[568,3193,3195],{"className":3194,"style":1298},[824],[568,3196],{},[568,3198],{"className":3199},[669,808],[568,3201],{"className":3202,"style":1307},[648],[568,3204,2887],{"className":3205},[1822],[568,3207,594],{"className":3208},[638],[568,3210,1591],{"className":3211},[632],[568,3213,600],{"className":3214},[632,633],[568,3216,609],{"className":3217},[669],[568,3219,3221],{"className":3220,"style":1233},[669,1232],[568,3222,2338],{"className":3223},[1237,839],[568,3225,3227],{"className":3226},[1344],[568,3228,3230,3332],{"className":3229},[815,816],[568,3231,3233,3329],{"className":3232},[820],[568,3234,3237,3249],{"className":3235,"style":3236},[824],"height:1.687em;",[568,3238,3240,3243],{"style":3239},"top:-2.0003em;margin-right:0.05em;",[568,3241],{"className":3242,"style":833},[832],[568,3244,3246],{"className":3245},[837,838,839,840],[568,3247,2281],{"className":3248},[632,840],[568,3250,3252,3255],{"style":3251},"top:-4.2029em;margin-right:0.05em;",[568,3253],{"className":3254,"style":833},[832],[568,3256,3258],{"className":3257},[837,838,839,840],[568,3259,3261],{"className":3260},[632,840],[568,3262,3264,3267,3326],{"className":3263},[632,840],[568,3265],{"className":3266},[638,808,837,3000,3001],[568,3268,3270],{"className":3269},[781],[568,3271,3273,3318],{"className":3272},[815,816],[568,3274,3276,3315],{"className":3275},[820],[568,3277,3279,3293,3301],{"className":3278,"style":3014},[824],[568,3280,3281,3284],{"style":3017},[568,3282],{"className":3283,"style":833},[832],[568,3285,3287],{"className":3286},[837,3000,3024,840],[568,3288,3290],{"className":3289},[632,840],[568,3291,2810],{"className":3292},[632,840],[568,3294,3295,3298],{"style":3033},[568,3296],{"className":3297,"style":833},[832],[568,3299],{"className":3300,"style":3040},[856,840],[568,3302,3303,3306],{"style":3043},[568,3304],{"className":3305,"style":833},[832],[568,3307,3309],{"className":3308},[837,3000,3024,840],[568,3310,3312],{"className":3311},[632,840],[568,3313,2848],{"className":3314,"style":3056},[632,633,840],[568,3316,877],{"className":3317},[876],[568,3319,3321],{"className":3320},[820],[568,3322,3324],{"className":3323,"style":3066},[824],[568,3325],{},[568,3327],{"className":3328},[669,808,837,3000,3001],[568,3330,877],{"className":3331},[876],[568,3333,3335],{"className":3334},[820],[568,3336,3338],{"className":3337,"style":2673},[824],[568,3339],{},[568,3341],{"className":3342,"style":1374},[648],[568,3344,1165],{"className":3345},[1378],[568,3347],{"className":3348,"style":1374},[648],[568,3350,3352,3355,3417,3420,3423,3426,3489,3492,3495],{"className":3351},[623],[568,3353],{"className":3354,"style":1388},[627],[568,3356,3358,3361,3414],{"className":3357},[632],[568,3359],{"className":3360},[638,808],[568,3362,3364],{"className":3363},[781],[568,3365,3367,3406],{"className":3366},[815,816],[568,3368,3370,3403],{"className":3369},[820],[568,3371,3373,3384,3392],{"className":3372,"style":1256},[824],[568,3374,3375,3378],{"style":1259},[568,3376],{"className":3377,"style":833},[832],[568,3379,3381],{"className":3380},[632],[568,3382,1591],{"className":3383},[632],[568,3385,3386,3389],{"style":849},[568,3387],{"className":3388,"style":833},[832],[568,3390],{"className":3391,"style":857},[856],[568,3393,3394,3397],{"style":1279},[568,3395],{"className":3396,"style":833},[832],[568,3398,3400],{"className":3399},[632],[568,3401,786],{"className":3402},[632],[568,3404,877],{"className":3405},[876],[568,3407,3409],{"className":3408},[820],[568,3410,3412],{"className":3411,"style":1298},[824],[568,3413],{},[568,3415],{"className":3416},[669,808],[568,3418],{"className":3419,"style":1307},[648],[568,3421,2887],{"className":3422},[1822],[568,3424],{"className":3425,"style":1307},[648],[568,3427,3429,3432,3486],{"className":3428},[632],[568,3430],{"className":3431},[638,808],[568,3433,3435],{"className":3434},[781],[568,3436,3438,3478],{"className":3437},[815,816],[568,3439,3441,3475],{"className":3440},[820],[568,3442,3445,3456,3464],{"className":3443,"style":3444},[824],"height:1.1076em;",[568,3446,3447,3450],{"style":1259},[568,3448],{"className":3449,"style":833},[832],[568,3451,3453],{"className":3452},[632],[568,3454,1658],{"className":3455},[632],[568,3457,3458,3461],{"style":849},[568,3459],{"className":3460,"style":833},[832],[568,3462],{"className":3463,"style":857},[856],[568,3465,3466,3469],{"style":1279},[568,3467],{"className":3468,"style":833},[832],[568,3470,3472],{"className":3471},[632],[568,3473,2848],{"className":3474,"style":3056},[632,633],[568,3476,877],{"className":3477},[876],[568,3479,3481],{"className":3480},[820],[568,3482,3484],{"className":3483,"style":1298},[824],[568,3485],{},[568,3487],{"className":3488},[669,808],[568,3490],{"className":3491,"style":649},[648],[568,3493,1655],{"className":3494},[653],[568,3496],{"className":3497,"style":649},[648],[568,3499,3501,3504,3507,3510,3513],{"className":3500},[623],[568,3502],{"className":3503,"style":1693},[627],[568,3505,2281],{"className":3506},[632],[568,3508],{"className":3509,"style":1374},[648],[568,3511,1165],{"className":3512},[1378],[568,3514],{"className":3515,"style":1374},[648],[568,3517,3519,3522],{"className":3518},[623],[568,3520],{"className":3521,"style":1388},[627],[568,3523,3525,3528,3581],{"className":3524},[632],[568,3526],{"className":3527},[638,808],[568,3529,3531],{"className":3530},[781],[568,3532,3534,3573],{"className":3533},[815,816],[568,3535,3537,3570],{"className":3536},[820],[568,3538,3540,3551,3559],{"className":3539,"style":1256},[824],[568,3541,3542,3545],{"style":1259},[568,3543],{"className":3544,"style":833},[832],[568,3546,3548],{"className":3547},[632],[568,3549,1591],{"className":3550},[632],[568,3552,3553,3556],{"style":849},[568,3554],{"className":3555,"style":833},[832],[568,3557],{"className":3558,"style":857},[856],[568,3560,3561,3564],{"style":1279},[568,3562],{"className":3563,"style":833},[832],[568,3565,3567],{"className":3566},[632],[568,3568,786],{"className":3569},[632],[568,3571,877],{"className":3572},[876],[568,3574,3576],{"className":3575},[820],[568,3577,3579],{"className":3578,"style":1298},[824],[568,3580],{},[568,3582],{"className":3583},[669,808],[568,3585,3587],{"className":3586},[1111],[568,3588,3590,3690],{"className":3589},[571],[568,3591,3593],{"className":3592},[575],[577,3594,3595],{"xmlns":579,"display":1120},[581,3596,3597,3687],{},[584,3598,3599,3607,3609,3611,3613,3615,3617,3623,3625,3627,3629,3631,3665,3667,3674,3676,3682,3684],{},[2275,3600,3601,3603,3605],{},[591,3602,1715],{},[784,3604,2281],{},[784,3606,786],{},[591,3608,594],{"stretchy":593},[784,3610,1658],{},[587,3612,600],{},[591,3614,603],{},[784,3616,786],{},[1126,3618,3619,3621],{},[591,3620,609],{"stretchy":593},[784,3622,1650],{},[1139,3624,1141],{},[587,3626,1736],{},[587,3628,600],{},[591,3630,1165],{},[2275,3632,3633,3661,3663],{},[584,3634,3635,3637,3659],{},[591,3636,2313],{"fence":619},[781,3638,3639,3657],{},[584,3640,3641,3643,3645,3647,3649,3651],{},[591,3642,594],{"stretchy":593},[784,3644,1658],{},[587,3646,600],{},[591,3648,603],{},[784,3650,786],{},[1126,3652,3653,3655],{},[591,3654,609],{"stretchy":593},[784,3656,1591],{},[784,3658,2810],{},[591,3660,2338],{"fence":619},[784,3662,2281],{},[784,3664,786],{},[591,3666,1165],{},[781,3668,3669,3672],{},[784,3670,3671],{},"81",[784,3673,2810],{},[591,3675,1655],{},[781,3677,3678,3680],{},[784,3679,786],{},[784,3681,2810],{},[591,3683,1165],{},[784,3685,3686],{},"10",[611,3688,3689],{"encoding":613},"\\int_0^1 (2x + 1)^3\\,dx = \\left[\\frac{(2x + 1)^4}{8}\\right]_0^1 = \\frac{81}{8} - \\frac{1}{8} = 10",[568,3691,3693,3768,3824,4014,4091,4168],{"className":3692,"ariaHidden":619},[618],[568,3694,3696,3699,3750,3753,3756,3759,3762,3765],{"className":3695},[623],[568,3697],{"className":3698,"style":2379},[627],[568,3700,3702,3705],{"className":3701},[1822],[568,3703,1715],{"className":3704,"style":1825},[1822,1823,1824],[568,3706,3708],{"className":3707},[1344],[568,3709,3711,3742],{"className":3710},[815,816],[568,3712,3714,3739],{"className":3713},[820],[568,3715,3717,3728],{"className":3716,"style":2398},[824],[568,3718,3719,3722],{"style":2401},[568,3720],{"className":3721,"style":1361},[832],[568,3723,3725],{"className":3724},[837,838,839,840],[568,3726,2281],{"className":3727},[632,840],[568,3729,3730,3733],{"style":2413},[568,3731],{"className":3732,"style":1361},[832],[568,3734,3736],{"className":3735},[837,838,839,840],[568,3737,786],{"className":3738},[632,840],[568,3740,877],{"className":3741},[876],[568,3743,3745],{"className":3744},[820],[568,3746,3748],{"className":3747,"style":2432},[824],[568,3749],{},[568,3751,594],{"className":3752},[638],[568,3754,1658],{"className":3755},[632],[568,3757,600],{"className":3758},[632,633],[568,3760],{"className":3761,"style":649},[648],[568,3763,603],{"className":3764},[653],[568,3766],{"className":3767,"style":649},[648],[568,3769,3771,3774,3777,3806,3809,3812,3815,3818,3821],{"className":3770},[623],[568,3772],{"className":3773,"style":1850},[627],[568,3775,786],{"className":3776},[632],[568,3778,3780,3783],{"className":3779},[669],[568,3781,609],{"className":3782},[669],[568,3784,3786],{"className":3785},[1344],[568,3787,3789],{"className":3788},[815],[568,3790,3792],{"className":3791},[820],[568,3793,3795],{"className":3794,"style":1872},[824],[568,3796,3797,3800],{"style":1875},[568,3798],{"className":3799,"style":1361},[832],[568,3801,3803],{"className":3802},[837,838,839,840],[568,3804,1650],{"className":3805},[632,840],[568,3807],{"className":3808,"style":1307},[648],[568,3810,1736],{"className":3811},[632,633],[568,3813,600],{"className":3814},[632,633],[568,3816],{"className":3817,"style":1374},[648],[568,3819,1165],{"className":3820},[1378],[568,3822],{"className":3823,"style":1374},[648],[568,3825,3827,3831,4005,4008,4011],{"className":3826},[623],[568,3828],{"className":3829,"style":3830},[627],"height:2.6948em;vertical-align:-0.9997em;",[568,3832,3834,3958],{"className":3833},[1225],[568,3835,3837,3843,3952],{"className":3836},[1225],[568,3838,3840],{"className":3839,"style":1233},[638,1232],[568,3841,2313],{"className":3842},[1237,839],[568,3844,3846,3849,3949],{"className":3845},[632],[568,3847],{"className":3848},[638,808],[568,3850,3852],{"className":3851},[781],[568,3853,3855,3941],{"className":3854},[815,816],[568,3856,3858,3938],{"className":3857},[820],[568,3859,3861,3872,3880],{"className":3860,"style":2005},[824],[568,3862,3863,3866],{"style":1259},[568,3864],{"className":3865,"style":833},[832],[568,3867,3869],{"className":3868},[632],[568,3870,2810],{"className":3871},[632],[568,3873,3874,3877],{"style":849},[568,3875],{"className":3876,"style":833},[832],[568,3878],{"className":3879,"style":857},[856],[568,3881,3882,3885],{"style":1279},[568,3883],{"className":3884,"style":833},[832],[568,3886,3888,3891,3894,3897,3900,3903,3906,3909],{"className":3887},[632],[568,3889,594],{"className":3890},[638],[568,3892,1658],{"className":3893},[632],[568,3895,600],{"className":3896},[632,633],[568,3898],{"className":3899,"style":649},[648],[568,3901,603],{"className":3902},[653],[568,3904],{"className":3905,"style":649},[648],[568,3907,786],{"className":3908},[632],[568,3910,3912,3915],{"className":3911},[669],[568,3913,609],{"className":3914},[669],[568,3916,3918],{"className":3917},[1344],[568,3919,3921],{"className":3920},[815],[568,3922,3924],{"className":3923},[820],[568,3925,3927],{"className":3926,"style":1604},[824],[568,3928,3929,3932],{"style":1625},[568,3930],{"className":3931,"style":1361},[832],[568,3933,3935],{"className":3934},[837,838,839,840],[568,3936,1591],{"className":3937},[632,840],[568,3939,877],{"className":3940},[876],[568,3942,3944],{"className":3943},[820],[568,3945,3947],{"className":3946,"style":1298},[824],[568,3948],{},[568,3950],{"className":3951},[669,808],[568,3953,3955],{"className":3954,"style":1233},[669,1232],[568,3956,2338],{"className":3957},[1237,839],[568,3959,3961],{"className":3960},[1344],[568,3962,3964,3997],{"className":3963},[815,816],[568,3965,3967,3994],{"className":3966},[820],[568,3968,3971,3982],{"className":3969,"style":3970},[824],"height:1.6951em;",[568,3972,3973,3976],{"style":2643},[568,3974],{"className":3975,"style":1361},[832],[568,3977,3979],{"className":3978},[837,838,839,840],[568,3980,2281],{"className":3981},[632,840],[568,3983,3985,3988],{"style":3984},"top:-3.944em;margin-right:0.05em;",[568,3986],{"className":3987,"style":1361},[832],[568,3989,3991],{"className":3990},[837,838,839,840],[568,3992,786],{"className":3993},[632,840],[568,3995,877],{"className":3996},[876],[568,3998,4000],{"className":3999},[820],[568,4001,4003],{"className":4002,"style":2673},[824],[568,4004],{},[568,4006],{"className":4007,"style":1374},[648],[568,4009,1165],{"className":4010},[1378],[568,4012],{"className":4013,"style":1374},[648],[568,4015,4017,4020,4082,4085,4088],{"className":4016},[623],[568,4018],{"className":4019,"style":1388},[627],[568,4021,4023,4026,4079],{"className":4022},[632],[568,4024],{"className":4025},[638,808],[568,4027,4029],{"className":4028},[781],[568,4030,4032,4071],{"className":4031},[815,816],[568,4033,4035,4068],{"className":4034},[820],[568,4036,4038,4049,4057],{"className":4037,"style":1256},[824],[568,4039,4040,4043],{"style":1259},[568,4041],{"className":4042,"style":833},[832],[568,4044,4046],{"className":4045},[632],[568,4047,2810],{"className":4048},[632],[568,4050,4051,4054],{"style":849},[568,4052],{"className":4053,"style":833},[832],[568,4055],{"className":4056,"style":857},[856],[568,4058,4059,4062],{"style":1279},[568,4060],{"className":4061,"style":833},[832],[568,4063,4065],{"className":4064},[632],[568,4066,3671],{"className":4067},[632],[568,4069,877],{"className":4070},[876],[568,4072,4074],{"className":4073},[820],[568,4075,4077],{"className":4076,"style":1298},[824],[568,4078],{},[568,4080],{"className":4081},[669,808],[568,4083],{"className":4084,"style":649},[648],[568,4086,1655],{"className":4087},[653],[568,4089],{"className":4090,"style":649},[648],[568,4092,4094,4097,4159,4162,4165],{"className":4093},[623],[568,4095],{"className":4096,"style":1388},[627],[568,4098,4100,4103,4156],{"className":4099},[632],[568,4101],{"className":4102},[638,808],[568,4104,4106],{"className":4105},[781],[568,4107,4109,4148],{"className":4108},[815,816],[568,4110,4112,4145],{"className":4111},[820],[568,4113,4115,4126,4134],{"className":4114,"style":1256},[824],[568,4116,4117,4120],{"style":1259},[568,4118],{"className":4119,"style":833},[832],[568,4121,4123],{"className":4122},[632],[568,4124,2810],{"className":4125},[632],[568,4127,4128,4131],{"style":849},[568,4129],{"className":4130,"style":833},[832],[568,4132],{"className":4133,"style":857},[856],[568,4135,4136,4139],{"style":1279},[568,4137],{"className":4138,"style":833},[832],[568,4140,4142],{"className":4141},[632],[568,4143,786],{"className":4144},[632],[568,4146,877],{"className":4147},[876],[568,4149,4151],{"className":4150},[820],[568,4152,4154],{"className":4153,"style":1298},[824],[568,4155],{},[568,4157],{"className":4158},[669,808],[568,4160],{"className":4161,"style":1374},[648],[568,4163,1165],{"className":4164},[1378],[568,4166],{"className":4167,"style":1374},[648],[568,4169,4171,4174],{"className":4170},[623],[568,4172],{"className":4173,"style":1693},[627],[568,4175,3686],{"className":4176},[632],[559,4178,4180],{"id":4179},"typische-fehler","Typische Fehler",[4182,4183,4184,4246,4453,4900],"ul",{},[4185,4186,4187,4188,4216,4217,4245],"li",{},"Mit ",[568,4189,4191,4204],{"className":4190},[571],[568,4192,4194],{"className":4193},[575],[577,4195,4196],{"xmlns":579},[581,4197,4198,4202],{},[584,4199,4200],{},[587,4201,597],{},[611,4203,597],{"encoding":613},[568,4205,4207],{"className":4206,"ariaHidden":619},[618],[568,4208,4210,4213],{"className":4209},[623],[568,4211],{"className":4212,"style":760},[627],[568,4214,597],{"className":4215},[632,633]," multiplizieren statt durch ",[568,4218,4220,4233],{"className":4219},[571],[568,4221,4223],{"className":4222},[575],[577,4224,4225],{"xmlns":579},[581,4226,4227,4231],{},[584,4228,4229],{},[587,4230,597],{},[611,4232,597],{"encoding":613},[568,4234,4236],{"className":4235,"ariaHidden":619},[618],[568,4237,4239,4242],{"className":4238},[623],[568,4240],{"className":4241,"style":760},[627],[568,4243,597],{"className":4244},[632,633]," teilen. Das wäre die Regel fürs Ableiten.",[4185,4247,4248,4249,4449,4450,764],{},"Den Faktor ganz vergessen: ",[568,4250,4252,4306],{"className":4251},[571],[568,4253,4255],{"className":4254},[575],[577,4256,4257],{"xmlns":579},[581,4258,4259,4303],{},[584,4260,4261,4263,4277,4279,4281,4283,4285,4299,4301],{},[591,4262,1715],{},[1126,4264,4265,4267],{},[587,4266,2288],{},[584,4268,4269,4271,4273,4275],{},[784,4270,1658],{},[587,4272,600],{},[591,4274,603],{},[784,4276,786],{},[1139,4278,1141],{},[587,4280,1736],{},[587,4282,600],{},[591,4284,1165],{},[1126,4286,4287,4289],{},[587,4288,2288],{},[584,4290,4291,4293,4295,4297],{},[784,4292,1658],{},[587,4294,600],{},[591,4296,603],{},[784,4298,786],{},[591,4300,603],{},[587,4302,1776],{},[611,4304,4305],{"encoding":613},"\\int e^{2x+1}\\,dx = e^{2x+1} + C",[568,4307,4309,4383,4440],{"className":4308,"ariaHidden":619},[618],[568,4310,4312,4316,4321,4324,4365,4368,4371,4374,4377,4380],{"className":4311},[623],[568,4313],{"className":4314,"style":4315},[627],"height:1.1202em;vertical-align:-0.3061em;",[568,4317,1715],{"className":4318,"style":4320},[1822,1823,4319],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[568,4322],{"className":4323,"style":1307},[648],[568,4325,4327,4330],{"className":4326},[632],[568,4328,2288],{"className":4329},[632,633],[568,4331,4333],{"className":4332},[1344],[568,4334,4336],{"className":4335},[815],[568,4337,4339],{"className":4338},[820],[568,4340,4342],{"className":4341,"style":1604},[824],[568,4343,4344,4347],{"style":1625},[568,4345],{"className":4346,"style":1361},[832],[568,4348,4350],{"className":4349},[837,838,839,840],[568,4351,4353,4356,4359,4362],{"className":4352},[632,840],[568,4354,1658],{"className":4355},[632,840],[568,4357,600],{"className":4358},[632,633,840],[568,4360,603],{"className":4361},[653,840],[568,4363,786],{"className":4364},[632,840],[568,4366],{"className":4367,"style":1307},[648],[568,4369,1736],{"className":4370},[632,633],[568,4372,600],{"className":4373},[632,633],[568,4375],{"className":4376,"style":1374},[648],[568,4378,1165],{"className":4379},[1378],[568,4381],{"className":4382,"style":1374},[648],[568,4384,4386,4390,4431,4434,4437],{"className":4385},[623],[568,4387],{"className":4388,"style":4389},[627],"height:0.8974em;vertical-align:-0.0833em;",[568,4391,4393,4396],{"className":4392},[632],[568,4394,2288],{"className":4395},[632,633],[568,4397,4399],{"className":4398},[1344],[568,4400,4402],{"className":4401},[815],[568,4403,4405],{"className":4404},[820],[568,4406,4408],{"className":4407,"style":1604},[824],[568,4409,4410,4413],{"style":1625},[568,4411],{"className":4412,"style":1361},[832],[568,4414,4416],{"className":4415},[837,838,839,840],[568,4417,4419,4422,4425,4428],{"className":4418},[632,840],[568,4420,1658],{"className":4421},[632,840],[568,4423,600],{"className":4424},[632,633,840],[568,4426,603],{"className":4427},[653,840],[568,4429,786],{"className":4430},[632,840],[568,4432],{"className":4433,"style":649},[648],[568,4435,603],{"className":4436},[653],[568,4438],{"className":4439,"style":649},[648],[568,4441,4443,4446],{"className":4442},[623],[568,4444],{"className":4445,"style":2112},[627],[568,4447,1776],{"className":4448,"style":2116},[632,633]," ist ",[672,4451,4452],{},"falsch",[4185,4454,4455,4456,4806,4807,4899],{},"Die Regel auf nichtlineare innere Funktionen übertragen: ",[568,4457,4459,4514],{"className":4458},[571],[568,4460,4462],{"className":4461},[575],[577,4463,4464],{"xmlns":579},[581,4465,4466,4511],{},[584,4467,4468,4470,4480,4482,4484,4486,4489,4507,4509],{},[591,4469,1715],{},[1126,4471,4472,4474],{},[587,4473,2288],{},[1126,4475,4476,4478],{},[587,4477,600],{},[784,4479,1658],{},[1139,4481,1141],{},[587,4483,1736],{},[587,4485,600],{},[591,4487,4488],{"mathvariant":1160},"≠",[781,4490,4491,4501],{},[1126,4492,4493,4495],{},[587,4494,2288],{},[1126,4496,4497,4499],{},[587,4498,600],{},[784,4500,1658],{},[584,4502,4503,4505],{},[784,4504,1658],{},[587,4506,600],{},[591,4508,603],{},[587,4510,1776],{},[611,4512,4513],{"encoding":613},"\\int e^{x^2}\\,dx \\neq \\frac{e^{x^2}}{2x} + C",[568,4515,4517,4651,4797],{"className":4516,"ariaHidden":619},[618],[568,4518,4520,4524,4527,4530,4592,4595,4598,4601,4604,4648],{"className":4519},[623],[568,4521],{"className":4522,"style":4523},[627],"height:1.293em;vertical-align:-0.3061em;",[568,4525,1715],{"className":4526,"style":4320},[1822,1823,4319],[568,4528],{"className":4529,"style":1307},[648],[568,4531,4533,4536],{"className":4532},[632],[568,4534,2288],{"className":4535},[632,633],[568,4537,4539],{"className":4538},[1344],[568,4540,4542],{"className":4541},[815],[568,4543,4545],{"className":4544},[820],[568,4546,4549],{"className":4547,"style":4548},[824],"height:0.9869em;",[568,4550,4551,4554],{"style":1625},[568,4552],{"className":4553,"style":1361},[832],[568,4555,4557],{"className":4556},[837,838,839,840],[568,4558,4560],{"className":4559},[632,840],[568,4561,4563,4566],{"className":4562},[632,840],[568,4564,600],{"className":4565},[632,633,840],[568,4567,4569],{"className":4568},[1344],[568,4570,4572],{"className":4571},[815],[568,4573,4575],{"className":4574},[820],[568,4576,4579],{"className":4577,"style":4578},[824],"height:0.8913em;",[568,4580,4582,4586],{"style":4581},"top:-2.931em;margin-right:0.0714em;",[568,4583],{"className":4584,"style":4585},[832],"height:2.5em;",[568,4587,4589],{"className":4588},[837,3000,3024,840],[568,4590,1658],{"className":4591},[632,840],[568,4593],{"className":4594,"style":1307},[648],[568,4596,1736],{"className":4597},[632,633],[568,4599,600],{"className":4600},[632,633],[568,4602],{"className":4603,"style":1374},[648],[568,4605,4607,4641,4645],{"className":4606},[1378],[568,4608,4610],{"className":4609},[1378],[568,4611,4614],{"className":4612},[632,4613],"vbox",[568,4615,4618],{"className":4616},[4617],"thinbox",[568,4619,4622,4626,4637],{"className":4620},[4621],"rlap",[568,4623],{"className":4624,"style":4625},[627],"height:0.8889em;vertical-align:-0.1944em;",[568,4627,4630],{"className":4628},[4629],"inner",[568,4631,4633],{"className":4632},[632],[568,4634,4636],{"className":4635},[1378],"",[568,4638],{"className":4639},[4640],"fix",[568,4642],{"className":4643},[648,4644],"nobreak",[568,4646,1165],{"className":4647},[1378],[568,4649],{"className":4650,"style":1374},[648],[568,4652,4654,4658,4788,4791,4794],{"className":4653},[623],[568,4655],{"className":4656,"style":4657},[627],"height:1.5649em;vertical-align:-0.345em;",[568,4659,4661,4664,4785],{"className":4660},[632],[568,4662],{"className":4663},[638,808],[568,4665,4667],{"className":4666},[781],[568,4668,4670,4777],{"className":4669},[815,816],[568,4671,4673,4774],{"className":4672},[820],[568,4674,4677,4694,4702],{"className":4675,"style":4676},[824],"height:1.2199em;",[568,4678,4679,4682],{"style":828},[568,4680],{"className":4681,"style":833},[832],[568,4683,4685],{"className":4684},[837,838,839,840],[568,4686,4688,4691],{"className":4687},[632,840],[568,4689,1658],{"className":4690},[632,840],[568,4692,600],{"className":4693},[632,633,840],[568,4695,4696,4699],{"style":849},[568,4697],{"className":4698,"style":833},[832],[568,4700],{"className":4701,"style":857},[856],[568,4703,4704,4707],{"style":860},[568,4705],{"className":4706,"style":833},[832],[568,4708,4710],{"className":4709},[837,838,839,840],[568,4711,4713],{"className":4712},[632,840],[568,4714,4716,4719],{"className":4715},[632,840],[568,4717,2288],{"className":4718},[632,633,840],[568,4720,4722],{"className":4721},[1344],[568,4723,4725],{"className":4724},[815],[568,4726,4728],{"className":4727},[820],[568,4729,4732],{"className":4730,"style":4731},[824],"height:1.1799em;",[568,4733,4735,4739],{"style":4734},"top:-3.1799em;margin-right:0.0714em;",[568,4736],{"className":4737,"style":4738},[832],"height:2.7489em;",[568,4740,4742],{"className":4741},[837,3000,3024,840],[568,4743,4745],{"className":4744},[632,840],[568,4746,4748,4751],{"className":4747},[632,840],[568,4749,600],{"className":4750},[632,633,840],[568,4752,4754],{"className":4753},[1344],[568,4755,4757],{"className":4756},[815],[568,4758,4760],{"className":4759},[820],[568,4761,4764],{"className":4762,"style":4763},[824],"height:1.0484em;",[568,4765,4767,4771],{"style":4766},"top:-3.0484em;margin-right:0.1em;",[568,4768],{"className":4769,"style":4770},[832],"height:2.6444em;",[568,4772,1658],{"className":4773},[632,840],[568,4775,877],{"className":4776},[876],[568,4778,4780],{"className":4779},[820],[568,4781,4783],{"className":4782,"style":884},[824],[568,4784],{},[568,4786],{"className":4787},[669,808],[568,4789],{"className":4790,"style":649},[648],[568,4792,603],{"className":4793},[653],[568,4795],{"className":4796,"style":649},[648],[568,4798,4800,4803],{"className":4799},[623],[568,4801],{"className":4802,"style":2112},[627],[568,4804,1776],{"className":4805,"style":2116},[632,633],". Für ",[568,4808,4810,4832],{"className":4809},[571],[568,4811,4813],{"className":4812},[575],[577,4814,4815],{"xmlns":579},[581,4816,4817,4829],{},[584,4818,4819],{},[1126,4820,4821,4823],{},[587,4822,2288],{},[1126,4824,4825,4827],{},[587,4826,600],{},[784,4828,1658],{},[611,4830,4831],{"encoding":613},"e^{x^2}",[568,4833,4835],{"className":4834,"ariaHidden":619},[618],[568,4836,4838,4841],{"className":4837},[623],[568,4839],{"className":4840,"style":4548},[627],[568,4842,4844,4847],{"className":4843},[632],[568,4845,2288],{"className":4846},[632,633],[568,4848,4850],{"className":4849},[1344],[568,4851,4853],{"className":4852},[815],[568,4854,4856],{"className":4855},[820],[568,4857,4859],{"className":4858,"style":4548},[824],[568,4860,4861,4864],{"style":1625},[568,4862],{"className":4863,"style":1361},[832],[568,4865,4867],{"className":4866},[837,838,839,840],[568,4868,4870],{"className":4869},[632,840],[568,4871,4873,4876],{"className":4872},[632,840],[568,4874,600],{"className":4875},[632,633,840],[568,4877,4879],{"className":4878},[1344],[568,4880,4882],{"className":4881},[815],[568,4883,4885],{"className":4884},[820],[568,4886,4888],{"className":4887,"style":4578},[824],[568,4889,4890,4893],{"style":4581},[568,4891],{"className":4892,"style":4585},[832],[568,4894,4896],{"className":4895},[837,3000,3024,840],[568,4897,1658],{"className":4898},[632,840]," gibt es keine Stammfunktion aus elementaren Funktionen.",[4185,4901,4902,4999],{},[568,4903,4905,4933],{"className":4904},[571],[568,4906,4908],{"className":4907},[575],[577,4909,4910],{"xmlns":579},[581,4911,4912,4930],{},[584,4913,4914,4916,4918,4920,4922,4924],{},[591,4915,594],{"stretchy":593},[784,4917,1658],{},[587,4919,600],{},[591,4921,603],{},[784,4923,786],{},[1126,4925,4926,4928],{},[591,4927,609],{"stretchy":593},[784,4929,1650],{},[611,4931,4932],{"encoding":613},"(2x + 1)^3",[568,4934,4936,4960],{"className":4935,"ariaHidden":619},[618],[568,4937,4939,4942,4945,4948,4951,4954,4957],{"className":4938},[623],[568,4940],{"className":4941,"style":628},[627],[568,4943,594],{"className":4944},[638],[568,4946,1658],{"className":4947},[632],[568,4949,600],{"className":4950},[632,633],[568,4952],{"className":4953,"style":649},[648],[568,4955,603],{"className":4956},[653],[568,4958],{"className":4959,"style":649},[648],[568,4961,4963,4967,4970],{"className":4962},[623],[568,4964],{"className":4965,"style":4966},[627],"height:1.0641em;vertical-align:-0.25em;",[568,4968,786],{"className":4969},[632],[568,4971,4973,4976],{"className":4972},[669],[568,4974,609],{"className":4975},[669],[568,4977,4979],{"className":4978},[1344],[568,4980,4982],{"className":4981},[815],[568,4983,4985],{"className":4984},[820],[568,4986,4988],{"className":4987,"style":1604},[824],[568,4989,4990,4993],{"style":1625},[568,4991],{"className":4992,"style":1361},[832],[568,4994,4996],{"className":4995},[837,838,839,840],[568,4997,1650],{"className":4998},[632,840]," erst umständlich ausmultiplizieren. Das geht, ist aber fehleranfällig.",{"title":5001,"searchDepth":5002,"depth":5002,"links":5003},"",2,[5004,5005,5006,5007],{"id":561,"depth":5002,"text":562},{"id":1103,"depth":5002,"text":1104},{"id":1567,"depth":5002,"text":1568},{"id":4179,"depth":5002,"text":4180},[5009,5012,5015,5018,5020,5023,5026,5028],{"lhs":5010,"rhs":5011},"1\u002F3 * (3*x - 2)^5 \u002F 5","(3*x - 2)^5 \u002F 15",{"lhs":5013,"rhs":5014},"exp(2*1 + 1)\u002F2 - exp(2*0 + 1)\u002F2","(exp(3) - exp(1)) \u002F 2",{"lhs":5016,"rhs":5017},"round((exp(3) - exp(1)) \u002F 2, 4)","8.6836",{"lhs":5019,"rhs":5017},"round(sum(map(0:999, f(k) = exp(2 * (k + 0.5) \u002F 1000 + 1))) \u002F 1000, 4)",{"lhs":5021,"rhs":5022},"sin(4 * pi\u002F8)\u002F4 - sin(0)\u002F4","1\u002F4",{"lhs":5024,"rhs":5025},"round(sum(map(0:999, f(k) = cos(4 * (k + 0.5) * pi \u002F 8000))) * pi \u002F 8000, 4)","0.25",{"lhs":5027,"rhs":3686},"(2*1 + 1)^4 \u002F 8 - (2*0 + 1)^4 \u002F 8",{"lhs":5029,"rhs":3686},"round(sum(map(0:999, f(k) = (2 * (k + 0.5) \u002F 1000 + 1)^3)) \u002F 1000, 4)","a \\neq 0,\\ F' = f","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>F\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F' = f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7519em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","linear-substitution","\\int f(ax + b)\\,dx = \\frac{1}{a}\\,F(ax + b) + C","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>F\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int f(ax + b)\\,dx = \\frac{1}{a}\\,F(ax + b) + C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2222em;vertical-align:-0.8622em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution",[],[5043,5044,5045,5046],"integration-by-substitution","integral-exp","antiderivative-power","integral-cosine",{"title":548,"description":5001},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution","Ist die innere Funktion linear, integriert man die äußere Funktion und teilt durch die Steigung der inneren.",[5051,5052,5053,5054],"integral","substitution","verkettung","stammfunktion",[5056,5059,5062,5065],{"symbol":589,"meaning":5057,"symbolHtml":5058},"äußere Funktion","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":905,"meaning":5060,"symbolHtml":5061},"eine Stammfunktion von f","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":698,"meaning":5063,"symbolHtml":5064},"lineare innere Funktion mit Steigung a und Achsenabschnitt b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">ax + b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1776,"meaning":5066,"symbolHtml":5067},"Integrationskonstante","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","mtWXFWJ4gpSXPDGxvjmKOy7K5QEYn7jxUFXNEeYXeT4",[5070,5073,5076,5079],{"stem":5071,"title":5072,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-e-funktion","Integral der e-Funktion",{"stem":5074,"title":5075,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus","Integral des Kosinus",{"stem":5077,"title":5078,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegration-durch-substitution","Integration durch Substitution",{"stem":5080,"title":5081,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fstammfunktion-potenzfunktion","Stammfunktion einer Potenzfunktion",1793824282709]