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braucht:",[569,1128,1131],{"className":1129},[1130],"katex-display",[569,1132,1134,1217],{"className":1133},[572],[569,1135,1137],{"className":1136},[576],[578,1138,1140],{"xmlns":580,"display":1139},"block",[582,1141,1142,1214],{},[585,1143,1144,1147,1168,1172,1175,1177,1179,1185,1187,1189,1195,1197,1200,1203,1206,1208,1211],{},[599,1145,1146],{},"∫",[588,1148,1149,1151],{},[591,1150,593],{},[585,1152,1153,1160,1162],{},[603,1154,1155,1158],{},[606,1156,1157],{},"a",[591,1159,611],{},[599,1161,601],{},[603,1163,1164,1166],{},[606,1165,608],{},[591,1167,611],{},[1169,1170,1171],"mtext",{}," ",[606,1173,1174],{},"d",[606,1176,608],{},[599,1178,804],{},[588,1180,1181,1183],{},[591,1182,593],{},[606,1184,1157],{},[606,1186,786],{},[599,1188,789],{},[588,1190,1191,1193],{},[606,1192,608],{},[606,1194,1157],{},[599,1196,601],{},[606,1198,1199],{},"C",[599,1201,1202],{"separator":621},",",[844,1204],{"width":1205},"2em",[606,1207,1157],{},[599,1209,1210],{},">",[591,1212,1213],{},"0",[613,1215,1216],{"encoding":615},"\\int \\frac{1}{a^2 + x^2}\\,dx = \\frac{1}{a} \\arctan\\frac{x}{a} + C, \\qquad a > 0",[569,1218,1220,1386,1537,1571],{"className":1219,"ariaHidden":621},[620],[569,1221,1223,1227,1233,1236,1368,1371,1374,1377,1380,1383],{"className":1222},[625],[569,1224],{"className":1225,"style":1226},[629],"height:2.2222em;vertical-align:-0.8622em;",[569,1228,1146],{"className":1229,"style":1232},[840,1230,1231],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[569,1234],{"className":1235,"style":845},[844],[569,1237,1239,1242,1365],{"className":1238},[634],[569,1240],{"className":1241},[638,639],[569,1243,1245],{"className":1244},[588],[569,1246,1248,1356],{"className":1247},[646,647],[569,1249,1251,1353],{"className":1250},[651],[569,1252,1255,1333,1341],{"className":1253,"style":1254},[655],"height:1.3214em;",[569,1256,1258,1261],{"style":1257},"top:-2.314em;",[569,1259],{"className":1260,"style":664},[663],[569,1262,1264,1295,1298,1301,1304],{"className":1263},[634],[569,1265,1267,1270],{"className":1266},[634],[569,1268,1157],{"className":1269},[634,688],[569,1271,1273],{"className":1272},[692],[569,1274,1276],{"className":1275},[646],[569,1277,1279],{"className":1278},[651],[569,1280,1283],{"className":1281,"style":1282},[655],"height:0.7401em;",[569,1284,1286,1289],{"style":1285},"top:-2.989em;margin-right:0.05em;",[569,1287],{"className":1288,"style":874},[663],[569,1290,1292],{"className":1291},[668,669,670,671],[569,1293,611],{"className":1294},[634,671],[569,1296],{"className":1297,"style":1046},[844],[569,1299,601],{"className":1300},[681],[569,1302],{"className":1303,"style":1046},[844],[569,1305,1307,1310],{"className":1306},[634],[569,1308,608],{"className":1309},[634,688],[569,1311,1313],{"className":1312},[692],[569,1314,1316],{"className":1315},[646],[569,1317,1319],{"className":1318},[651],[569,1320,1322],{"className":1321,"style":1282},[655],[569,1323,1324,1327],{"style":1285},[569,1325],{"className":1326,"style":874},[663],[569,1328,1330],{"className":1329},[668,669,670,671],[569,1331,611],{"className":1332},[634,671],[569,1334,1335,1338],{"style":720},[569,1336],{"className":1337,"style":664},[663],[569,1339],{"className":1340,"style":728},[727],[569,1342,1344,1347],{"style":1343},"top:-3.677em;",[569,1345],{"className":1346,"style":664},[663],[569,1348,1350],{"className":1349},[634],[569,1351,593],{"className":1352},[634],[569,1354,748],{"className":1355},[747],[569,1357,1359],{"className":1358},[651],[569,1360,1363],{"className":1361,"style":1362},[655],"height:0.7693em;",[569,1364],{},[569,1366],{"className":1367},[761,639],[569,1369],{"className":1370,"style":845},[844],[569,1372,1174],{"className":1373},[634,688],[569,1375,608],{"className":1376},[634,688],[569,1378],{"className":1379,"style":887},[844],[569,1381,804],{"className":1382},[891],[569,1384],{"className":1385,"style":887},[844],[569,1387,1389,1393,1456,1459,1462,1465,1528,1531,1534],{"className":1388},[625],[569,1390],{"className":1391,"style":1392},[629],"height:2.0074em;vertical-align:-0.686em;",[569,1394,1396,1399,1453],{"className":1395},[634],[569,1397],{"className":1398},[638,639],[569,1400,1402],{"className":1401},[588],[569,1403,1405,1444],{"className":1404},[646,647],[569,1406,1408,1441],{"className":1407},[651],[569,1409,1411,1422,1430],{"className":1410,"style":1254},[655],[569,1412,1413,1416],{"style":1257},[569,1414],{"className":1415,"style":664},[663],[569,1417,1419],{"className":1418},[634],[569,1420,1157],{"className":1421},[634,688],[569,1423,1424,1427],{"style":720},[569,1425],{"className":1426,"style":664},[663],[569,1428],{"className":1429,"style":728},[727],[569,1431,1432,1435],{"style":1343},[569,1433],{"className":1434,"style":664},[663],[569,1436,1438],{"className":1437},[634],[569,1439,593],{"className":1440},[634],[569,1442,748],{"className":1443},[747],[569,1445,1447],{"className":1446},[651],[569,1448,1451],{"className":1449,"style":1450},[655],"height:0.686em;",[569,1452],{},[569,1454],{"className":1455},[761,639],[569,1457],{"className":1458,"style":845},[844],[569,1460,786],{"className":1461},[840],[569,1463],{"className":1464,"style":845},[844],[569,1466,1468,1471,1525],{"className":1467},[634],[569,1469],{"className":1470},[638,639],[569,1472,1474],{"className":1473},[588],[569,1475,1477,1517],{"className":1476},[646,647],[569,1478,1480,1514],{"className":1479},[651],[569,1481,1484,1495,1503],{"className":1482,"style":1483},[655],"height:1.1076em;",[569,1485,1486,1489],{"style":1257},[569,1487],{"className":1488,"style":664},[663],[569,1490,1492],{"className":1491},[634],[569,1493,1157],{"className":1494},[634,688],[569,1496,1497,1500],{"style":720},[569,1498],{"className":1499,"style":664},[663],[569,1501],{"className":1502,"style":728},[727],[569,1504,1505,1508],{"style":1343},[569,1506],{"className":1507,"style":664},[663],[569,1509,1511],{"className":1510},[634],[569,1512,608],{"className":1513},[634,688],[569,1515,748],{"className":1516},[747],[569,1518,1520],{"className":1519},[651],[569,1521,1523],{"className":1522,"style":1450},[655],[569,1524],{},[569,1526],{"className":1527},[761,639],[569,1529],{"className":1530,"style":1046},[844],[569,1532,601],{"className":1533},[681],[569,1535],{"className":1536,"style":1046},[844],[569,1538,1540,1544,1548,1552,1556,1559,1562,1565,1568],{"className":1539},[625],[569,1541],{"className":1542,"style":1543},[629],"height:0.8778em;vertical-align:-0.1944em;",[569,1545,1199],{"className":1546,"style":1547},[634,688],"margin-right:0.0715em;",[569,1549,1202],{"className":1550},[1551],"mpunct",[569,1553],{"className":1554,"style":1555},[844],"margin-right:2em;",[569,1557],{"className":1558,"style":845},[844],[569,1560,1157],{"className":1561},[634,688],[569,1563],{"className":1564,"style":887},[844],[569,1566,1210],{"className":1567},[891],[569,1569],{"className":1570,"style":887},[844],[569,1572,1574,1578],{"className":1573},[625],[569,1575],{"className":1576,"style":1577},[629],"height:0.6444em;",[569,1579,1213],{"className":1580},[634],[560,1582,1584],{"id":1583},"herleitung","Herleitung",[565,1586,1587,1588,1647,1648,1773,1774,1846],{},"Man klammert ",[569,1589,1591,1609],{"className":1590},[572],[569,1592,1594],{"className":1593},[576],[578,1595,1596],{"xmlns":580},[582,1597,1598,1606],{},[585,1599,1600],{},[603,1601,1602,1604],{},[606,1603,1157],{},[591,1605,611],{},[613,1607,1608],{"encoding":615},"a^2",[569,1610,1612],{"className":1611,"ariaHidden":621},[620],[569,1613,1615,1618],{"className":1614},[625],[569,1616],{"className":1617,"style":1059},[629],[569,1619,1621,1624],{"className":1620},[634],[569,1622,1157],{"className":1623},[634,688],[569,1625,1627],{"className":1626},[692],[569,1628,1630],{"className":1629},[646],[569,1631,1633],{"className":1632},[651],[569,1634,1636],{"className":1635,"style":1059},[655],[569,1637,1638,1641],{"style":870},[569,1639],{"className":1640,"style":874},[663],[569,1642,1644],{"className":1643},[668,669,670,671],[569,1645,611],{"className":1646},[634,671]," im Nenner aus und substituiert ",[569,1649,1651,1674],{"className":1650},[572],[569,1652,1654],{"className":1653},[576],[578,1655,1656],{"xmlns":580},[582,1657,1658,1671],{},[585,1659,1660,1663,1665],{},[606,1661,1662],{},"u",[599,1664,804],{},[588,1666,1667,1669],{},[606,1668,608],{},[606,1670,1157],{},[613,1672,1673],{"encoding":615},"u = \\frac{x}{a}",[569,1675,1677,1696],{"className":1676,"ariaHidden":621},[620],[569,1678,1680,1684,1687,1690,1693],{"className":1679},[625],[569,1681],{"className":1682,"style":1683},[629],"height:0.4306em;",[569,1685,1662],{"className":1686},[634,688],[569,1688],{"className":1689,"style":887},[844],[569,1691,804],{"className":1692},[891],[569,1694],{"className":1695,"style":887},[844],[569,1697,1699,1703],{"className":1698},[625],[569,1700],{"className":1701,"style":1702},[629],"height:1.0404em;vertical-align:-0.345em;",[569,1704,1706,1709,1770],{"className":1705},[634],[569,1707],{"className":1708},[638,639],[569,1710,1712],{"className":1711},[588],[569,1713,1715,1761],{"className":1714},[646,647],[569,1716,1718,1758],{"className":1717},[651],[569,1719,1722,1736,1744],{"className":1720,"style":1721},[655],"height:0.6954em;",[569,1723,1724,1727],{"style":659},[569,1725],{"className":1726,"style":664},[663],[569,1728,1730],{"className":1729},[668,669,670,671],[569,1731,1733],{"className":1732},[634,671],[569,1734,1157],{"className":1735},[634,688,671],[569,1737,1738,1741],{"style":720},[569,1739],{"className":1740,"style":664},[663],[569,1742],{"className":1743,"style":728},[727],[569,1745,1746,1749],{"style":731},[569,1747],{"className":1748,"style":664},[663],[569,1750,1752],{"className":1751},[668,669,670,671],[569,1753,1755],{"className":1754},[634,671],[569,1756,608],{"className":1757},[634,688,671],[569,1759,748],{"className":1760},[747],[569,1762,1764],{"className":1763},[651],[569,1765,1768],{"className":1766,"style":1767},[655],"height:0.345em;",[569,1769],{},[569,1771],{"className":1772},[761,639],", also ",[569,1775,1777,1803],{"className":1776},[572],[569,1778,1780],{"className":1779},[576],[578,1781,1782],{"xmlns":580},[582,1783,1784,1800],{},[585,1785,1786,1788,1790,1792,1794,1796,1798],{},[606,1787,1174],{},[606,1789,608],{},[599,1791,804],{},[606,1793,1157],{},[1169,1795,1171],{},[606,1797,1174],{},[606,1799,1662],{},[613,1801,1802],{"encoding":615},"dx = 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\\frac{1}{a^2\\left(1 + \\left(\\frac{x}{a}\\right)^2\\right)}\\,dx = \\frac{1}{a^2} \\cdot a \\int \\frac{1}{1 + u^2}\\,du = \\frac{1}{a} \\arctan\\frac{x}{a} + 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\\frac{1}{1 + x^2}\\,dx = \\arctan 1 - \\arctan 0 = \\frac{\\pi}{4} \\approx 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",[569,3179,3181,3194],{"className":3180},[572],[569,3182,3184],{"className":3183},[576],[578,3185,3186],{"xmlns":580},[582,3187,3188,3192],{},[585,3189,3190],{},[591,3191,1213],{},[613,3193,1213],{"encoding":615},[569,3195,3197],{"className":3196,"ariaHidden":621},[620],[569,3198,3200,3203],{"className":3199},[625],[569,3201],{"className":3202,"style":1577},[629],[569,3204,1213],{"className":3205},[634],[569,3207,3209,3222],{"className":3208},[572],[569,3210,3212],{"className":3211},[576],[578,3213,3214],{"xmlns":580},[582,3215,3216,3220],{},[585,3217,3218],{},[591,3219,611],{},[613,3221,611],{"encoding":615},[569,3223,3225],{"className":3224,"ariaHidden":621},[620],[569,3226,3228,3231],{"className":3227},[625],[569,3229],{"className":3230,"style":1577},[629],[569,3232,611],{"className":3233},[634],[569,3235,3237],{"className":3236},[1130],[569,3238,3240,3324],{"className":3239},[572],[569,3241,3243],{"className":3242},[576],[578,3244,3245],{"xmlns":580,"display":1139},[582,3246,3247,3321],{},[585,3248,3249,3257,3273,3275,3277,3279,3281,3287,3289,3291,3293,3295,3301,3303,3305,3307,3309,3316,3318],{},[2724,3250,3251,3253,3255],{},[599,3252,1146],{},[591,3254,1213],{},[591,3256,611],{},[588,3258,3259,3261],{},[591,3260,593],{},[585,3262,3263,3265,3267],{},[591,3264,2780],{},[599,3266,601],{},[603,3268,3269,3271],{},[606,3270,608],{},[591,3272,611],{},[1169,3274,1171],{},[606,3276,1174],{},[606,3278,608],{},[599,3280,804],{},[588,3282,3283,3285],{},[591,3284,593],{},[591,3286,611],{},[606,3288,786],{},[599,3290,789],{},[591,3292,593],{},[599,3294,2764],{},[588,3296,3297,3299],{},[591,3298,593],{},[591,3300,611],{},[606,3302,786],{},[599,3304,789],{},[591,3306,1213],{},[599,3308,804],{},[588,3310,3311,3313],{},[606,3312,2777],{},[591,3314,3315],{},"8",[599,3317,2783],{},[591,3319,3320],{},"0,3927",[613,3322,3323],{"encoding":615},"\\int_0^2 \\frac{1}{4 + x^2}\\,dx = \\frac{1}{2}\\arctan 1 - \\frac{1}{2}\\arctan 0 = \\frac{\\pi}{8} \\approx 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uneigentliches Integral über ganz ",[569,3783,3785,3798],{"className":3784},[572],[569,3786,3788],{"className":3787},[576],[578,3789,3790],{"xmlns":580},[582,3791,3792,3796],{},[585,3793,3794],{},[606,3795,1105],{"mathvariant":1104},[613,3797,1108],{"encoding":615},[569,3799,3801],{"className":3800,"ariaHidden":621},[620],[569,3802,3804,3807],{"className":3803},[625],[569,3805],{"className":3806,"style":1118},[629],[569,3808,1105],{"className":3809},[634,1122],[569,3811,3813,3831],{"className":3812},[572],[569,3814,3816],{"className":3815},[576],[578,3817,3818],{"xmlns":580},[582,3819,3820,3828],{},[585,3821,3822,3824,3826],{},[606,3823,786],{},[599,3825,789],{},[606,3827,608],{},[613,3829,3830],{"encoding":615},"\\arctan 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strebt:",[569,4017,4019],{"className":4018},[1130],[569,4020,4022,4096],{"className":4021},[572],[569,4023,4025],{"className":4024},[576],[578,4026,4027],{"xmlns":580,"display":1139},[582,4028,4029,4093],{},[585,4030,4031,4043,4059,4061,4063,4065,4067,4073,4075,4089,4091],{},[2724,4032,4033,4035,4041],{},[599,4034,1146],{},[585,4036,4037,4039],{},[599,4038,2764],{},[606,4040,3873],{"mathvariant":799},[606,4042,3873],{"mathvariant":799},[588,4044,4045,4047],{},[591,4046,593],{},[585,4048,4049,4051,4053],{},[591,4050,593],{},[599,4052,601],{},[603,4054,4055,4057],{},[606,4056,608],{},[591,4058,611],{},[1169,4060,1171],{},[606,4062,1174],{},[606,4064,608],{},[599,4066,804],{},[588,4068,4069,4071],{},[606,4070,2777],{},[591,4072,611],{},[599,4074,2764],{},[585,4076,4077,4079,4081,4087],{},[599,4078,783],{"fence":621},[599,4080,2764],{},[588,4082,4083,4085],{},[606,4084,2777],{},[591,4086,611],{},[599,4088,796],{"fence":621},[599,4090,804],{},[606,4092,2777],{},[613,4094,4095],{"encoding":615},"\\int_{-\\infty}^{\\infty} \\frac{1}{1 + x^2}\\,dx = \\frac{\\pi}{2} - \\left(-\\frac{\\pi}{2}\\right) = \\pi",[569,4097,4099,4289,4366,4462],{"className":4098,"ariaHidden":621},[620],[569,4100,4102,4106,4168,4171,4271,4274,4277,4280,4283,4286],{"className":4101},[625],[569,4103],{"className":4104,"style":4105},[629],"height:2.3846em;vertical-align:-0.9703em;",[569,4107,4109,4112],{"className":4108},[840],[569,4110,1146],{"className":4111,"style":1232},[840,1230,1231],[569,4113,4115],{"className":4114},[692],[569,4116,4118,4159],{"className":4117},[646,647],[569,4119,4121,4156],{"className":4120},[651],[569,4122,4125,4142],{"className":4123,"style":4124},[655],"height:1.4143em;",[569,4126,4127,4130],{"style":2821},[569,4128],{"className":4129,"style":874},[663],[569,4131,4133],{"className":4132},[668,669,670,671],[569,4134,4136,4139],{"className":4135},[634,671],[569,4137,2764],{"className":4138},[634,671],[569,4140,3873],{"className":4141},[634,671],[569,4143,4144,4147],{"style":2833},[569,4145],{"className":4146,"style":874},[663],[569,4148,4150],{"className":4149},[668,669,670,671],[569,4151,4153],{"className":4152},[634,671],[569,4154,3873],{"className":4155},[634,671],[569,4157,748],{"className":4158},[747],[569,4160,4162],{"className":4161},[651],[569,4163,4166],{"className":4164,"style":4165},[655],"height:0.9703em;",[569,4167],{},[569,4169],{"className":4170,"style":845},[844],[569,4172,4174,4177,4268],{"className":4173},[634],[569,4175],{"className":4176},[638,639],[569,4178,4180],{"className":4179},[588],[569,4181,4183,4260],{"className":4182},[646,647],[569,4184,4186,4257],{"className":4185},[651],[569,4187,4189,4238,4246],{"className":4188,"style":1254},[655],[569,4190,4191,4194],{"style":1257},[569,4192],{"className":4193,"style":664},[663],[569,4195,4197,4200,4203,4206,4209],{"className":4196},[634],[569,4198,593],{"className":4199},[634],[569,4201],{"className":4202,"style":1046},[844],[569,4204,601],{"className":4205},[681],[569,4207],{"className":4208,"style":1046},[844],[569,4210,4212,4215],{"className":4211},[634],[569,4213,608],{"className":4214},[634,688],[569,4216,4218],{"className":4217},[692],[569,4219,4221],{"className":4220},[646],[569,4222,4224],{"className":4223},[651],[569,4225,4227],{"className":4226,"style":1282},[655],[569,4228,4229,4232],{"style":1285},[569,4230],{"className":4231,"style":874},[663],[569,4233,4235],{"className":4234},[668,669,670,671],[569,4236,611],{"className":4237},[634,671],[569,4239,4240,4243],{"style":720},[569,4241],{"className":4242,"style":664},[663],[569,4244],{"className":4245,"style":728},[727],[569,4247,4248,4251],{"style":1343},[569,4249],{"className":4250,"style":664},[663],[569,4252,4254],{"className":4253},[634],[569,4255,593],{"className":4256},[634],[569,4258,748],{"className":4259},[747],[569,4261,4263],{"className":4262},[651],[569,4264,4266],{"className":4265,"style":1362},[655],[569,4267],{},[569,4269],{"className":4270},[761,639],[569,4272],{"className":4273,"style":845},[844],[569,4275,1174],{"className":4276},[634,688],[569,4278,608],{"className":4279},[634,688],[569,4281],{"className":4282,"style":887},[844],[569,4284,804],{"className":4285},[891],[569,4287],{"className":4288,"style":887},[844],[569,4290,4292,4295,4357,4360,4363],{"className":4291},[625],[569,4293],{"className":4294,"style":3030},[629],[569,4296,4298,4301,4354],{"className":4297},[634],[569,4299],{"className":4300},[638,639],[569,4302,4304],{"className":4303},[588],[569,4305,4307,4346],{"className":4306},[646,647],[569,4308,4310,4343],{"className":4309},[651],[569,4311,4313,4324,4332],{"className":4312,"style":1483},[655],[569,4314,4315,4318],{"style":1257},[569,4316],{"className":4317,"style":664},[663],[569,4319,4321],{"className":4320},[634],[569,4322,611],{"className":4323},[634],[569,4325,4326,4329],{"style":720},[569,4327],{"className":4328,"style":664},[663],[569,4330],{"className":4331,"style":728},[727],[569,4333,4334,4337],{"style":1343},[569,4335],{"className":4336,"style":664},[663],[569,4338,4340],{"className":4339},[634],[569,4341,2777],{"className":4342,"style":3079},[634,688],[569,4344,748],{"className":4345},[747],[569,4347,4349],{"className":4348},[651],[569,4350,4352],{"className":4351,"style":1450},[655],[569,4353],{},[569,4355],{"className":4356},[761,639],[569,4358],{"className":4359,"style":1046},[844],[569,4361,2764],{"className":4362},[681],[569,4364],{"className":4365,"style":1046},[844],[569,4367,4369,4373,4453,4456,4459],{"className":4368},[625],[569,4370],{"className":4371,"style":4372},[629],"height:1.836em;vertical-align:-0.686em;",[569,4374,4376,4382,4385,4447],{"className":4375},[2053],[569,4377,4379],{"className":4378,"style":2058},[638,2057],[569,4380,783],{"className":4381},[2062,2063],[569,4383,2764],{"className":4384},[634],[569,4386,4388,4391,4444],{"className":4387},[634],[569,4389],{"className":4390},[638,639],[569,4392,4394],{"className":4393},[588],[569,4395,4397,4436],{"className":4396},[646,647],[569,4398,4400,4433],{"className":4399},[651],[569,4401,4403,4414,4422],{"className":4402,"style":1483},[655],[569,4404,4405,4408]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den Faktor 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oder die Division im Argument vergessen.",[4479,5130,5131,5271],{},[569,5132,5134,5162],{"className":5133},[572],[569,5135,5137],{"className":5136},[576],[578,5138,5139],{"xmlns":580},[582,5140,5141,5159],{},[585,5142,5143],{},[588,5144,5145,5147],{},[591,5146,593],{},[585,5148,5149,5151,5153],{},[591,5150,593],{},[599,5152,2764],{},[603,5154,5155,5157],{},[606,5156,608],{},[591,5158,611],{},[613,5160,5161],{"encoding":615},"\\frac{1}{1 - 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genauso behandeln. Dieser Nenner hat Nullstellen, die Stammfunktion enthält Logarithmen statt des Arkustangens.",{"title":5273,"searchDepth":5274,"depth":5274,"links":5275},"",2,[5276,5277,5278,5279],{"id":562,"depth":5274,"text":563},{"id":1583,"depth":5274,"text":1584},{"id":2646,"depth":5274,"text":2647},{"id":4473,"depth":5274,"text":4474},[5281,5283,5285,5288,5291,5293,5296,5299,5301],{"lhs":5282,"rhs":1213},"round((atan(x+1e-5) - atan(x-1e-5))\u002F(2e-5) - 1\u002F(1 + x^2), 6)",{"lhs":5284,"rhs":1213},"round((atan((x+1e-5)\u002Fa)\u002Fa - atan((x-1e-5)\u002Fa)\u002Fa)\u002F(2e-5) - 1\u002F(a^2 + x^2), 6)",{"lhs":5286,"rhs":5287},"atan(1) - atan(0)","pi\u002F4",{"lhs":5289,"rhs":5290},"round(pi\u002F4, 4)","0.7854",{"lhs":5292,"rhs":5290},"round(sum(map(0:999, f(k) = 1\u002F(1 + ((k + 0.5)\u002F1000)^2))) \u002F 1000, 4)",{"lhs":5294,"rhs":5295},"atan(2\u002F2)\u002F2 - atan(0\u002F2)\u002F2","pi\u002F8",{"lhs":5297,"rhs":5298},"round(pi\u002F8, 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display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo>∫\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>arctan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int \\frac{1}{1 + x^2}\\,dx = \\arctan x + 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\" 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style=\"height:0.7693em;\">\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\">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:0.6984em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">arctan\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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