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Genau diese Lücke füllt der ",[988,989,990],"strong",{},"natürliche Logarithmus",": Die Ableitung von ",[569,993,995,1015],{"className":994},[572],[569,996,998],{"className":997},[576],[578,999,1000],{"xmlns":580},[582,1001,1002,1012],{},[585,1003,1004,1007,1010],{},[595,1005,1006],{},"ln",[588,1008,1009],{},"⁡",[595,1011,597],{},[645,1013,1014],{"encoding":647},"\\ln x",[569,1016,1018],{"className":1017,"ariaHidden":653},[652],[569,1019,1021,1025,1028,1031],{"className":1020},[657],[569,1022],{"className":1023,"style":1024},[661],"height:0.6944em;",[569,1026,1006],{"className":1027},[666],[569,1029],{"className":1030,"style":674},[673],[569,1032,597],{"className":1033},[678,682]," ist ",[569,1036,1038,1056],{"className":1037},[572],[569,1039,1041],{"className":1040},[576],[578,1042,1043],{"xmlns":580},[582,1044,1045,1053],{},[585,1046,1047],{},[614,1048,1049,1051],{},[628,1050,630],{},[595,1052,597],{},[645,1054,1055],{"encoding":647},"\\frac{1}{x}",[569,1057,1059],{"className":1058,"ariaHidden":653},[652],[569,1060,1062,1066],{"className":1061},[657],[569,1063],{"className":1064,"style":1065},[661],"height:1.1901em;vertical-align:-0.345em;",[569,1067,1069,1072,1133],{"className":1068},[678],[569,1070],{"className":1071},[751,752],[569,1073,1075],{"className":1074},[614],[569,1076,1078,1124],{"className":1077},[690,759],[569,1079,1081,1121],{"className":1080},[694],[569,1082,1085,1099,1107],{"className":1083,"style":1084},[698],"height:0.8451em;",[569,1086,1087,1090],{"style":769},[569,1088],{"className":1089,"style":773},[706],[569,1091,1093],{"className":1092},[711,712,713,714],[569,1094,1096],{"className":1095},[678,714],[569,1097,597],{"className":1098},[678,682,714],[569,1100,1101,1104],{"style":792},[569,1102],{"className":1103,"style":773},[706],[569,1105],{"className":1106,"style":800},[799],[569,1108,1109,1112],{"style":803},[569,1110],{"className":1111,"style":773},[706],[569,1113,1115],{"className":1114},[711,712,713,714],[569,1116,1118],{"className":1117},[678,714],[569,1119,630],{"className":1120},[678,714],[569,1122,860],{"className":1123},[859],[569,1125,1127],{"className":1126},[694],[569,1128,1131],{"className":1129,"style":1130},[698],"height:0.345em;",[569,1132],{},[569,1134],{"className":1135},[873,752],".",[565,1138,1139,1140,1143,1144,1172,1173,1226],{},"Der ",[988,1141,1142],{},"Betrag"," sorgt dafür, dass die Formel auch für negative ",[569,1145,1147,1160],{"className":1146},[572],[569,1148,1150],{"className":1149},[576],[578,1151,1152],{"xmlns":580},[582,1153,1154,1158],{},[585,1155,1156],{},[595,1157,597],{},[645,1159,597],{"encoding":647},[569,1161,1163],{"className":1162,"ariaHidden":653},[652],[569,1164,1166,1169],{"className":1165},[657],[569,1167],{"className":1168,"style":929},[661],[569,1170,597],{"className":1171},[678,682]," gilt. Für ",[569,1174,1176,1195],{"className":1175},[572],[569,1177,1179],{"className":1178},[576],[578,1180,1181],{"xmlns":580},[582,1182,1183,1192],{},[585,1184,1185,1187,1190],{},[595,1186,597],{},[588,1188,1189],{},"\u003C",[628,1191,970],{},[645,1193,1194],{"encoding":647},"x \u003C 0",[569,1196,1198,1217],{"className":1197,"ariaHidden":653},[652],[569,1199,1201,1205,1208,1211,1214],{"className":1200},[657],[569,1202],{"className":1203,"style":1204},[661],"height:0.5782em;vertical-align:-0.0391em;",[569,1206,597],{"className":1207},[678,682],[569,1209],{"className":1210,"style":730},[673],[569,1212,1189],{"className":1213},[734],[569,1215],{"className":1216,"style":730},[673],[569,1218,1220,1223],{"className":1219},[657],[569,1221],{"className":1222,"style":982},[661],[569,1224,970],{"className":1225},[678]," ist nach der Kettenregel",[569,1228,1231],{"className":1229},[1230],"katex-display",[569,1232,1234,1305],{"className":1233},[572],[569,1235,1237],{"className":1236},[576],[578,1238,1240],{"xmlns":580,"display":1239},"block",[582,1241,1242,1302],{},[585,1243,1244,1249,1251,1253,1255,1257,1259,1262,1271,1273,1283,1286,1288,1290,1292,1294,1296],{},[588,1245,1248],{"fence":1246,"stretchy":653,"minsize":1247,"maxsize":1247},"false","1.2em","(",[595,1250,1006],{},[588,1252,1009],{},[588,1254,1248],{"stretchy":1246},[588,1256,914],{},[595,1258,597],{},[588,1260,1261],{"stretchy":1246},")",[592,1263,1264,1266],{},[588,1265,1261],{"fence":1246,"stretchy":653,"minsize":1247,"maxsize":1247},[588,1267,1270],{"mathvariant":1268,"lspace":1269,"rspace":1269},"normal","0em","′",[588,1272,612],{},[614,1274,1275,1277],{},[628,1276,630],{},[585,1278,1279,1281],{},[588,1280,914],{},[595,1282,597],{},[588,1284,1285],{},"⋅",[588,1287,1248],{"stretchy":1246},[588,1289,914],{},[628,1291,630],{},[588,1293,1261],{"stretchy":1246},[588,1295,612],{},[614,1297,1298,1300],{},[628,1299,630],{},[595,1301,597],{},[645,1303,1304],{"encoding":647},"\\big(\\ln(-x)\\big)' = \\frac{1}{-x} \\cdot (-1) = \\frac{1}{x}",[569,1306,1308,1386,1471,1499],{"className":1307,"ariaHidden":653},[652],[569,1309,1311,1315,1322,1325,1328,1331,1334,1337,1340,1377,1380,1383],{"className":1310},[657],[569,1312],{"className":1313,"style":1314},[661],"height:1.3418em;vertical-align:-0.35em;",[569,1316,1318],{"className":1317},[678],[569,1319,1248],{"className":1320},[1321,843],"delimsizing",[569,1323],{"className":1324,"style":674},[673],[569,1326,1006],{"className":1327},[666],[569,1329,1248],{"className":1330},[751],[569,1332,914],{"className":1333},[678],[569,1335,597],{"className":1336},[678,682],[569,1338,1261],{"className":1339},[873],[569,1341,1343,1349],{"className":1342},[678],[569,1344,1346],{"className":1345},[678],[569,1347,1261],{"className":1348},[1321,843],[569,1350,1352],{"className":1351},[686],[569,1353,1355],{"className":1354},[690],[569,1356,1358],{"className":1357},[694],[569,1359,1362],{"className":1360,"style":1361},[698],"height:0.9918em;",[569,1363,1365,1368],{"style":1364},"top:-3.3029em;margin-right:0.05em;",[569,1366],{"className":1367,"style":707},[706],[569,1369,1371],{"className":1370},[711,712,713,714],[569,1372,1374],{"className":1373},[678,714],[569,1375,1270],{"className":1376},[678,714],[569,1378],{"className":1379,"style":730},[673],[569,1381,612],{"className":1382},[734],[569,1384],{"className":1385,"style":730},[673],[569,1387,1389,1393,1462,1465,1468],{"className":1388},[657],[569,1390],{"className":1391,"style":1392},[661],"height:2.0908em;vertical-align:-0.7693em;",[569,1394,1396,1399,1459],{"className":1395},[678],[569,1397],{"className":1398},[751,752],[569,1400,1402],{"className":1401},[614],[569,1403,1405,1450],{"className":1404},[690,759],[569,1406,1408,1447],{"className":1407},[694],[569,1409,1412,1427,1435],{"className":1410,"style":1411},[698],"height:1.3214em;",[569,1413,1415,1418],{"style":1414},"top:-2.314em;",[569,1416],{"className":1417,"style":773},[706],[569,1419,1421,1424],{"className":1420},[678],[569,1422,914],{"className":1423},[678],[569,1425,597],{"className":1426},[678,682],[569,1428,1429,1432],{"style":792},[569,1430],{"className":1431,"style":773},[706],[569,1433],{"className":1434,"style":800},[799],[569,1436,1438,1441],{"style":1437},"top:-3.677em;",[569,1439],{"className":1440,"style":773},[706],[569,1442,1444],{"className":1443},[678],[569,1445,630],{"className":1446},[678],[569,1448,860],{"className":1449},[859],[569,1451,1453],{"className":1452},[694],[569,1454,1457],{"className":1455,"style":1456},[698],"height:0.7693em;",[569,1458],{},[569,1460],{"className":1461},[873,752],[569,1463],{"className":1464,"style":877},[673],[569,1466,1285],{"className":1467},[786],[569,1469],{"className":1470,"style":877},[673],[569,1472,1474,1478,1481,1484,1487,1490,1493,1496],{"className":1473},[657],[569,1475],{"className":1476,"style":1477},[661],"height:1em;vertical-align:-0.25em;",[569,1479,1248],{"className":1480},[751],[569,1482,914],{"className":1483},[678],[569,1485,630],{"className":1486},[678],[569,1488,1261],{"className":1489},[873],[569,1491],{"className":1492,"style":730},[673],[569,1494,612],{"className":1495},[734],[569,1497],{"className":1498,"style":730},[673],[569,1500,1502,1506],{"className":1501},[657],[569,1503],{"className":1504,"style":1505},[661],"height:2.0074em;vertical-align:-0.686em;",[569,1507,1509,1512,1566],{"className":1508},[678],[569,1510],{"className":1511},[751,752],[569,1513,1515],{"className":1514},[614],[569,1516,1518,1557],{"className":1517},[690,759],[569,1519,1521,1554],{"className":1520},[694],[569,1522,1524,1535,1543],{"className":1523,"style":1411},[698],[569,1525,1526,1529],{"style":1414},[569,1527],{"className":1528,"style":773},[706],[569,1530,1532],{"className":1531},[678],[569,1533,597],{"className":1534},[678,682],[569,1536,1537,1540],{"style":792},[569,1538],{"className":1539,"style":773},[706],[569,1541],{"className":1542,"style":800},[799],[569,1544,1545,1548],{"style":1437},[569,1546],{"className":1547,"style":773},[706],[569,1549,1551],{"className":1550},[678],[569,1552,630],{"className":1553},[678],[569,1555,860],{"className":1556},[859],[569,1558,1560],{"className":1559},[694],[569,1561,1564],{"className":1562,"style":1563},[698],"height:0.686em;",[569,1565],{},[569,1567],{"className":1568},[873,752],[565,1570,1571,1572,1669,1670,1698],{},"Ein bestimmtes Integral über ",[569,1573,1575,1592],{"className":1574},[572],[569,1576,1578],{"className":1577},[576],[578,1579,1580],{"xmlns":580},[582,1581,1582,1590],{},[585,1583,1584],{},[614,1585,1586,1588],{},[628,1587,630],{},[595,1589,597],{},[645,1591,1055],{"encoding":647},[569,1593,1595],{"className":1594,"ariaHidden":653},[652],[569,1596,1598,1601],{"className":1597},[657],[569,1599],{"className":1600,"style":1065},[661],[569,1602,1604,1607,1666],{"className":1603},[678],[569,1605],{"className":1606},[751,752],[569,1608,1610],{"className":1609},[614],[569,1611,1613,1658],{"className":1612},[690,759],[569,1614,1616,1655],{"className":1615},[694],[569,1617,1619,1633,1641],{"className":1618,"style":1084},[698],[569,1620,1621,1624],{"style":769},[569,1622],{"className":1623,"style":773},[706],[569,1625,1627],{"className":1626},[711,712,713,714],[569,1628,1630],{"className":1629},[678,714],[569,1631,597],{"className":1632},[678,682,714],[569,1634,1635,1638],{"style":792},[569,1636],{"className":1637,"style":773},[706],[569,1639],{"className":1640,"style":800},[799],[569,1642,1643,1646],{"style":803},[569,1644],{"className":1645,"style":773},[706],[569,1647,1649],{"className":1648},[711,712,713,714],[569,1650,1652],{"className":1651},[678,714],[569,1653,630],{"className":1654},[678,714],[569,1656,860],{"className":1657},[859],[569,1659,1661],{"className":1660},[694],[569,1662,1664],{"className":1663,"style":1130},[698],[569,1665],{},[569,1667],{"className":1668},[873,752]," darf die Stelle ",[569,1671,1673,1686],{"className":1672},[572],[569,1674,1676],{"className":1675},[576],[578,1677,1678],{"xmlns":580},[582,1679,1680,1684],{},[585,1681,1682],{},[628,1683,970],{},[645,1685,970],{"encoding":647},[569,1687,1689],{"className":1688,"ariaHidden":653},[652],[569,1690,1692,1695],{"className":1691},[657],[569,1693],{"className":1694,"style":982},[661],[569,1696,970],{"className":1697},[678]," nicht enthalten. Beide Grenzen müssen also positiv oder beide negativ sein.",[560,1700,1702],{"id":1701},"beispiele","Beispiele",[569,1704,1706],{"className":1705},[1230],[569,1707,1709,1798],{"className":1708},[572],[569,1710,1712],{"className":1711},[576],[578,1713,1714],{"xmlns":580,"display":1239},[582,1715,1716,1795],{},[585,1717,1718,1728,1734,1736,1738,1740,1742,1767,1769,1771,1773,1775,1777,1779,1781,1783,1785,1787,1789,1791,1793],{},[1719,1720,1721,1723,1725],"msubsup",{},[588,1722,590],{},[628,1724,630],{},[595,1726,1727],{},"e",[614,1729,1730,1732],{},[628,1731,630],{},[595,1733,597],{},[602,1735,604],{},[595,1737,607],{},[595,1739,597],{},[588,1741,612],{},[1719,1743,1744,1763,1765],{},[585,1745,1746,1749,1751,1753,1756,1758,1760],{},[588,1747,1748],{"fence":653},"[",[595,1750,1006],{},[588,1752,1009],{},[595,1754,1755],{"mathvariant":1268},"∣",[595,1757,597],{},[595,1759,1755],{"mathvariant":1268},[588,1761,1762],{"fence":653},"]",[628,1764,630],{},[595,1766,1727],{},[588,1768,612],{},[595,1770,1006],{},[588,1772,1009],{},[595,1774,1727],{},[588,1776,914],{},[595,1778,1006],{},[588,1780,1009],{},[628,1782,630],{},[588,1784,612],{},[628,1786,630],{},[588,1788,914],{},[628,1790,970],{},[588,1792,612],{},[628,1794,630],{},[645,1796,1797],{"encoding":647},"\\int_1^e \\frac{1}{x} \\, dx = \\left[\\ln|x|\\right]_1^e = \\ln e - \\ln 1 = 1 - 0 = 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,2104,2107],{"className":2094},[657],[569,2096],{"className":2097,"style":948},[661],[569,2099,630],{"className":2100},[678],[569,2102],{"className":2103,"style":877},[673],[569,2105,914],{"className":2106},[786],[569,2108],{"className":2109,"style":877},[673],[569,2111,2113,2116,2119,2122,2125],{"className":2112},[657],[569,2114],{"className":2115,"style":982},[661],[569,2117,970],{"className":2118},[678],[569,2120],{"className":2121,"style":730},[673],[569,2123,612],{"className":2124},[734],[569,2126],{"className":2127,"style":730},[673],[569,2129,2131,2134],{"className":2130},[657],[569,2132],{"className":2133,"style":982},[661],[569,2135,630],{"className":2136},[678],[569,2138,2140],{"className":2139},[1230],[569,2141,2143,2208],{"className":2142},[572],[569,2144,2146],{"className":2145},[576],[578,2147,2148],{"xmlns":580,"display":1239},[582,2149,2150,2205],{},[585,2151,2152,2162,2168,2170,2172,2174,2176,2178,2180,2182,2184,2186,2188,2190,2192,2194,2196,2199,2202],{},[1719,2153,2154,2156,2159],{},[588,2155,590],{},[628,2157,2158],{},"2",[628,2160,2161],{},"8",[614,2163,2164,2166],{},[628,2165,630],{},[595,2167,597],{},[602,2169,604],{},[595,2171,607],{},[595,2173,597],{},[588,2175,612],{},[595,2177,1006],{},[588,2179,1009],{},[628,2181,2161],{},[588,2183,914],{},[595,2185,1006],{},[588,2187,1009],{},[628,2189,2158],{},[588,2191,612],{},[595,2193,1006],{},[588,2195,1009],{},[628,2197,2198],{},"4",[588,2200,2201],{},"≈",[628,2203,2204],{},"1,3863",[645,2206,2207],{"encoding":647},"\\int_2^8 \\frac{1}{x} \\, dx = \\ln 8 - \\ln 2 = \\ln 4 \\approx 1{,}3863",[569,2209,2211,2353,2377,2401,2425],{"className":2210,"ariaHidden":653},[652],[569,2212,2214,2218,2270,2273,2335,2338,2341,2344,2347,2350],{"className":2213},[657],[569,2215],{"className":2216,"style":2217},[661],"height:2.476em;vertical-align:-0.9119em;",[569,2219,2221,2224],{"className":2220},[666],[569,2222,590],{"className":2223,"style":1815},[666,667,1814],[569,2225,2227],{"className":2226},[686],[569,2228,2230,2262],{"className":2229},[690,759],[569,2231,2233,2259],{"className":2232},[694],[569,2234,2237,2248],{"className":2235,"style":2236},[698],"height:1.564em;",[569,2238,2239,2242],{"style":1831},[569,2240],{"className":2241,"style":707},[706],[569,2243,2245],{"className":2244},[711,712,713,714],[569,2246,2158],{"className":2247},[678,714],[569,2249,2250,2253],{"style":1843},[569,2251],{"className":2252,"style":707},[706],[569,2254,2256],{"className":2255},[711,712,713,714],[569,2257,2161],{"className":2258},[678,714],[569,2260,860],{"className":2261},[859],[569,2263,2265],{"className":2264},[694],[569,2266,2268],{"className":2267,"style":1862},[698],[569,2269],{},[569,2271],{"className":2272,"style":674},[673],[569,2274,2276,2279,2332],{"className":2275},[678],[569,2277],{"className":2278},[751,752],[569,2280,2282],{"className":2281},[614],[569,2283,2285,2324],{"className":2284},[690,759],[569,2286,2288,2321],{"className":2287},[694],[569,2289,2291,2302,2310],{"className":2290,"style":1411},[698],[569,2292,2293,2296],{"style":1414},[569,2294],{"className":2295,"style":773},[706],[569,2297,2299],{"className":2298},[678],[569,2300,597],{"className":2301},[678,682],[569,2303,2304,2307],{"style":792},[569,2305],{"className":2306,"style":773},[706],[569,2308],{"className":2309,"style":800},[799],[569,2311,2312,2315],{"style":1437},[569,2313],{"className":2314,"style":773},[706],[569,2316,2318],{"className":2317},[678],[569,2319,630],{"className":2320},[678],[569,2322,860],{"className":2323},[859],[569,2325,2327],{"className":2326},[694],[569,2328,2330],{"className":2329,"style":1563},[698],[569,2331],{},[569,2333],{"className":2334},[873,752],[569,2336],{"className":2337,"style":674},[673],[569,2339,607],{"className":2340},[678,682],[569,2342,597],{"className":2343},[678,682],[569,2345],{"className":2346,"style":730},[673],[569,2348,612],{"className":2349},[734],[569,2351],{"className":2352,"style":730},[673],[569,2354,2356,2359,2362,2365,2368,2371,2374],{"className":2355},[657],[569,2357],{"className":2358,"style":2049},[661],[569,2360,1006],{"className":2361},[666],[569,2363],{"className":2364,"style":674},[673],[569,2366,2161],{"className":2367},[678],[569,2369],{"className":2370,"style":877},[673],[569,2372,914],{"className":2373},[786],[569,2375],{"className":2376,"style":877},[673],[569,2378,2380,2383,2386,2389,2392,2395,2398],{"className":2379},[657],[569,2381],{"className":2382,"style":1024},[661],[569,2384,1006],{"className":2385},[666],[569,2387],{"className":2388,"style":674},[673],[569,2390,2158],{"className":2391},[678],[569,2393],{"className":2394,"style":730},[673],[569,2396,612],{"className":2397},[734],[569,2399],{"className":2400,"style":730},[673],[569,2402,2404,2407,2410,2413,2416,2419,2422],{"className":2403},[657],[569,2405],{"className":2406,"style":1024},[661],[569,2408,1006],{"className":2409},[666],[569,2411],{"className":2412,"style":674},[673],[569,2414,2198],{"className":2415},[678],[569,2417],{"className":2418,"style":730},[673],[569,2420,2201],{"className":2421},[734],[569,2423],{"className":2424,"style":730},[673],[569,2426,2428,2432,2435,2443],{"className":2427},[657],[569,2429],{"className":2430,"style":2431},[661],"height:0.8389em;vertical-align:-0.1944em;",[569,2433,630],{"className":2434},[678],[569,2436,2438],{"className":2437},[678],[569,2439,2442],{"className":2440},[2441],"mpunct",",",[569,2444,2446],{"className":2445},[678],"3863",[565,2448,2449,2450,2478],{},"Auf einem Intervall mit negativen Zahlen ist das Ergebnis negativ, weil der Graph dort unter der ",[569,2451,2453,2466],{"className":2452},[572],[569,2454,2456],{"className":2455},[576],[578,2457,2458],{"xmlns":580},[582,2459,2460,2464],{},[585,2461,2462],{},[595,2463,597],{},[645,2465,597],{"encoding":647},[569,2467,2469],{"className":2468,"ariaHidden":653},[652],[569,2470,2472,2475],{"className":2471},[657],[569,2473],{"className":2474,"style":929},[661],[569,2476,597],{"className":2477},[678,682],"-Achse liegt:",[569,2480,2482],{"className":2481},[1230],[569,2483,2485,2573],{"className":2484},[572],[569,2486,2488],{"className":2487},[576],[578,2489,2490],{"xmlns":580,"display":1239},[582,2491,2492,2570],{},[585,2493,2494,2511,2517,2519,2521,2523,2525,2527,2529,2531,2533,2535,2537,2539,2541,2543,2545,2547,2549,2551,2553,2555,2557,2559,2561,2563,2565,2567],{},[1719,2495,2496,2498,2505],{},[588,2497,590],{},[585,2499,2500,2502],{},[588,2501,914],{},[628,2503,2504],{},"3",[585,2506,2507,2509],{},[588,2508,914],{},[628,2510,630],{},[614,2512,2513,2515],{},[628,2514,630],{},[595,2516,597],{},[602,2518,604],{},[595,2520,607],{},[595,2522,597],{},[588,2524,612],{},[595,2526,1006],{},[588,2528,1009],{},[595,2530,1755],{"mathvariant":1268},[588,2532,914],{},[628,2534,630],{},[595,2536,1755],{"mathvariant":1268},[588,2538,914],{},[595,2540,1006],{},[588,2542,1009],{},[595,2544,1755],{"mathvariant":1268},[588,2546,914],{},[628,2548,2504],{},[595,2550,1755],{"mathvariant":1268},[588,2552,612],{},[628,2554,970],{},[588,2556,914],{},[595,2558,1006],{},[588,2560,1009],{},[628,2562,2504],{},[588,2564,2201],{},[588,2566,914],{},[628,2568,2569],{},"1,0986",[645,2571,2572],{"encoding":647},"\\int_{-3}^{-1} \\frac{1}{x} \\, dx = \\ln|-1| - \\ln|-3| = 0 - \\ln 3 \\approx -1{,}0986",[569,2574,2576,2730,2754,2773,2797,2816,2834,2858],{"className":2575,"ariaHidden":653},[652],[569,2577,2579,2583,2647,2650,2712,2715,2718,2721,2724,2727],{"className":2578},[657],[569,2580],{"className":2581,"style":2582},[661],"height:2.5343em;vertical-align:-0.9703em;",[569,2584,2586,2589],{"className":2585},[666],[569,2587,590],{"className":2588,"style":1815},[666,667,1814],[569,2590,2592],{"className":2591},[686],[569,2593,2595,2638],{"className":2594},[690,759],[569,2596,2598,2635],{"className":2597},[694],[569,2599,2601,2618],{"className":2600,"style":2236},[698],[569,2602,2603,2606],{"style":1831},[569,2604],{"className":2605,"style":707},[706],[569,2607,2609],{"className":2608},[711,712,713,714],[569,2610,2612,2615],{"className":2611},[678,714],[569,2613,914],{"className":2614},[678,714],[569,2616,2504],{"className":2617},[678,714],[569,2619,2620,2623],{"style":1843},[569,2621],{"className":2622,"style":707},[706],[569,2624,2626],{"className":2625},[711,712,713,714],[569,2627,2629,2632],{"className":2628},[678,714],[569,2630,914],{"className":2631},[678,714],[569,2633,630],{"className":2634},[678,714],[569,2636,860],{"className":2637},[859],[569,2639,2641],{"className":2640},[694],[569,2642,2645],{"className":2643,"style":2644},[698],"height:0.9703em;",[569,2646],{},[569,2648],{"className":2649,"style":674},[673],[569,2651,2653,2656,2709],{"className":2652},[678],[569,2654],{"className":2655},[751,752],[569,2657,2659],{"className":2658},[614],[569,2660,2662,2701],{"className":2661},[690,759],[569,2663,2665,2698],{"className":2664},[694],[569,2666,2668,2679,2687],{"className":2667,"style":1411},[698],[569,2669,2670,2673],{"style":1414},[569,2671],{"className":2672,"style":773},[706],[569,2674,2676],{"className":2675},[678],[569,2677,597],{"className":2678},[678,682],[569,2680,2681,2684],{"style":792},[569,2682],{"className":2683,"style":773},[706],[569,2685],{"className":2686,"style":800},[799],[569,2688,2689,2692],{"style":1437},[569,2690],{"className":2691,"style":773},[706],[569,2693,2695],{"className":2694},[678],[569,2696,630],{"className":2697},[678],[569,2699,860],{"className":2700},[859],[569,2702,2704],{"className":2703},[694],[569,2705,2707],{"className":2706,"style":1563},[698],[569,2708],{},[569,2710],{"className":2711},[873,752],[569,2713],{"className":2714,"style":674},[673],[569,2716,607],{"className":2717},[678,682],[569,2719,597],{"className":2720},[678,682],[569,2722],{"className":2723,"style":730},[673],[569,2725,612],{"className":2726},[734],[569,2728],{"className":2729,"style":730},[673],[569,2731,2733,2736,2739,2742,2745,2748,2751],{"className":2732},[657],[569,2734],{"className":2735,"style":1477},[661],[569,2737,1006],{"className":2738},[666],[569,2740],{"className":2741,"style":674},[673],[569,2743,1755],{"className":2744},[678],[569,2746],{"className":2747,"style":877},[673],[569,2749,914],{"className":2750},[786],[569,2752],{"className":2753,"style":877},[673],[569,2755,2757,2760,2764,2767,2770],{"className":2756},[657],[569,2758],{"className":2759,"style":1477},[661],[569,2761,2763],{"className":2762},[678],"1∣",[569,2765],{"className":2766,"style":877},[673],[569,2768,914],{"className":2769},[786],[569,2771],{"className":2772,"style":877},[673],[569,2774,2776,2779,2782,2785,2788,2791,2794],{"className":2775},[657],[569,2777],{"className":2778,"style":1477},[661],[569,2780,1006],{"className":2781},[666],[569,2783],{"className":2784,"style":674},[673],[569,2786,1755],{"className":2787},[678],[569,2789],{"className":2790,"style":877},[673],[569,2792,914],{"className":2793},[786],[569,2795],{"className":2796,"style":877},[673],[569,2798,2800,2803,2807,2810,2813],{"className":2799},[657],[569,2801],{"className":2802,"style":1477},[661],[569,2804,2806],{"className":2805},[678],"3∣",[569,2808],{"className":2809,"style":730},[673],[569,2811,612],{"className":2812},[734],[569,2814],{"className":2815,"style":730},[673],[569,2817,2819,2822,2825,2828,2831],{"className":2818},[657],[569,2820],{"className":2821,"style":948},[661],[569,2823,970],{"className":2824},[678],[569,2826],{"className":2827,"style":877},[673],[569,2829,914],{"className":2830},[786],[569,2832],{"className":2833,"style":877},[673],[569,2835,2837,2840,2843,2846,2849,2852,2855],{"className":2836},[657],[569,2838],{"className":2839,"style":1024},[661],[569,2841,1006],{"className":2842},[666],[569,2844],{"className":2845,"style":674},[673],[569,2847,2504],{"className":2848},[678],[569,2850],{"className":2851,"style":730},[673],[569,2853,2201],{"className":2854},[734],[569,2856],{"className":2857,"style":730},[673],[569,2859,2861,2864,2867,2870,2876],{"className":2860},[657],[569,2862],{"className":2863,"style":2431},[661],[569,2865,914],{"className":2866},[678],[569,2868,630],{"className":2869},[678],[569,2871,2873],{"className":2872},[678],[569,2874,2442],{"className":2875},[2441],[569,2877,2879],{"className":2878},[678],"0986",[560,2881,2883],{"id":2882},"typische-fehler","Typische Fehler",[2885,2886,2887,3021,3024,3348],"ul",{},[2888,2889,2890,2891,3020],"li",{},"Die Potenzregel anwenden: ",[569,2892,2894,2916],{"className":2893},[572],[569,2895,2897],{"className":2896},[576],[578,2898,2899],{"xmlns":580},[582,2900,2901,2913],{},[585,2902,2903],{},[614,2904,2905,2911],{},[592,2906,2907,2909],{},[595,2908,597],{},[628,2910,970],{},[628,2912,970],{},[645,2914,2915],{"encoding":647},"\\frac{x^0}{0}",[569,2917,2919],{"className":2918,"ariaHidden":653},[652],[569,2920,2922,2926],{"className":2921},[657],[569,2923],{"className":2924,"style":2925},[661],"height:1.3629em;vertical-align:-0.345em;",[569,2927,2929,2932,3017],{"className":2928},[678],[569,2930],{"className":2931},[751,752],[569,2933,2935],{"className":2934},[614],[569,2936,2938,3009],{"className":2937},[690,759],[569,2939,2941,3006],{"className":2940},[694],[569,2942,2944,2958,2966],{"className":2943,"style":766},[698],[569,2945,2946,2949],{"style":769},[569,2947],{"className":2948,"style":773},[706],[569,2950,2952],{"className":2951},[711,712,713,714],[569,2953,2955],{"className":2954},[678,714],[569,2956,970],{"className":2957},[678,714],[569,2959,2960,2963],{"style":792},[569,2961],{"className":2962,"style":773},[706],[569,2964],{"className":2965,"style":800},[799],[569,2967,2968,2971],{"style":803},[569,2969],{"className":2970,"style":773},[706],[569,2972,2974],{"className":2973},[711,712,713,714],[569,2975,2977],{"className":2976},[678,714],[569,2978,2980,2983],{"className":2979},[678,714],[569,2981,597],{"className":2982},[678,682,714],[569,2984,2986],{"className":2985},[686],[569,2987,2989],{"className":2988},[690],[569,2990,2992],{"className":2991},[694],[569,2993,2995],{"className":2994,"style":831},[698],[569,2996,2997,3000],{"style":834},[569,2998],{"className":2999,"style":838},[706],[569,3001,3003],{"className":3002},[711,842,843,714],[569,3004,970],{"className":3005},[678,714],[569,3007,860],{"className":3008},[859],[569,3010,3012],{"className":3011},[694],[569,3013,3015],{"className":3014,"style":1130},[698],[569,3016],{},[569,3018],{"className":3019},[873,752]," ist nicht definiert.",[2888,3022,3023],{},"Den Betrag weglassen und dann den Logarithmus einer negativen Zahl berechnen wollen.",[2888,3025,3026,3027,3055,3056,3249,3250,3347],{},"Über die Stelle ",[569,3028,3030,3043],{"className":3029},[572],[569,3031,3033],{"className":3032},[576],[578,3034,3035],{"xmlns":580},[582,3036,3037,3041],{},[585,3038,3039],{},[628,3040,970],{},[645,3042,970],{"encoding":647},[569,3044,3046],{"className":3045,"ariaHidden":653},[652],[569,3047,3049,3052],{"className":3048},[657],[569,3050],{"className":3051,"style":982},[661],[569,3053,970],{"className":3054},[678]," hinweg integrieren, z.B. ",[569,3057,3059,3095],{"className":3058},[572],[569,3060,3062],{"className":3061},[576],[578,3063,3064],{"xmlns":580},[582,3065,3066,3092],{},[585,3067,3068,3080,3086,3088,3090],{},[1719,3069,3070,3072,3078],{},[588,3071,590],{},[585,3073,3074,3076],{},[588,3075,914],{},[628,3077,630],{},[628,3079,630],{},[614,3081,3082,3084],{},[628,3083,630],{},[595,3085,597],{},[602,3087,604],{},[595,3089,607],{},[595,3091,597],{},[645,3093,3094],{"encoding":647},"\\int_{-1}^{1} \\frac{1}{x}\\,dx",[569,3096,3098],{"className":3097,"ariaHidden":653},[652],[569,3099,3101,3105,3169,3172,3240,3243,3246],{"className":3100},[657],[569,3102],{"className":3103,"style":3104},[661],"height:1.4232em;vertical-align:-0.4142em;",[569,3106,3108,3111],{"className":3107},[666],[569,3109,590],{"className":3110,"style":669},[666,667,668],[569,3112,3114],{"className":3113},[686],[569,3115,3117,3160],{"className":3116},[690,759],[569,3118,3120,3157],{"className":3119},[694],[569,3121,3124,3142],{"className":3122,"style":3123},[698],"height:1.009em;",[569,3125,3127,3130],{"style":3126},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[569,3128],{"className":3129,"style":707},[706],[569,3131,3133],{"className":3132},[711,712,713,714],[569,3134,3136,3139],{"className":3135},[678,714],[569,3137,914],{"className":3138},[678,714],[569,3140,630],{"className":3141},[678,714],[569,3143,3145,3148],{"style":3144},"top:-3.2579em;margin-right:0.05em;",[569,3146],{"className":3147,"style":707},[706],[569,3149,3151],{"className":3150},[711,712,713,714],[569,3152,3154],{"className":3153},[678,714],[569,3155,630],{"className":3156},[678,714],[569,3158,860],{"className":3159},[859],[569,3161,3163],{"className":3162},[694],[569,3164,3167],{"className":3165,"style":3166},[698],"height:0.4142em;",[569,3168],{},[569,3170],{"className":3171,"style":674},[673],[569,3173,3175,3178,3237],{"className":3174},[678],[569,3176],{"className":3177},[751,752],[569,3179,3181],{"className":3180},[614],[569,3182,3184,3229],{"className":3183},[690,759],[569,3185,3187,3226],{"className":3186},[694],[569,3188,3190,3204,3212],{"className":3189,"style":1084},[698],[569,3191,3192,3195],{"style":769},[569,3193],{"className":3194,"style":773},[706],[569,3196,3198],{"className":3197},[711,712,713,714],[569,3199,3201],{"className":3200},[678,714],[569,3202,597],{"className":3203},[678,682,714],[569,3205,3206,3209],{"style":792},[569,3207],{"className":3208,"style":773},[706],[569,3210],{"className":3211,"style":800},[799],[569,3213,3214,3217],{"style":803},[569,3215],{"className":3216,"style":773},[706],[569,3218,3220],{"className":3219},[711,712,713,714],[569,3221,3223],{"className":3222},[678,714],[569,3224,630],{"className":3225},[678,714],[569,3227,860],{"className":3228},[859],[569,3230,3232],{"className":3231},[694],[569,3233,3235],{"className":3234,"style":1130},[698],[569,3236],{},[569,3238],{"className":3239},[873,752],[569,3241],{"className":3242,"style":674},[673],[569,3244,607],{"className":3245},[678,682],[569,3247,597],{"className":3248},[678,682],". Dort ist ",[569,3251,3253,3270],{"className":3252},[572],[569,3254,3256],{"className":3255},[576],[578,3257,3258],{"xmlns":580},[582,3259,3260,3268],{},[585,3261,3262],{},[614,3263,3264,3266],{},[628,3265,630],{},[595,3267,597],{},[645,3269,1055],{"encoding":647},[569,3271,3273],{"className":3272,"ariaHidden":653},[652],[569,3274,3276,3279],{"className":3275},[657],[569,3277],{"className":3278,"style":1065},[661],[569,3280,3282,3285,3344],{"className":3281},[678],[569,3283],{"className":3284},[751,752],[569,3286,3288],{"className":3287},[614],[569,3289,3291,3336],{"className":3290},[690,759],[569,3292,3294,3333],{"className":3293},[694],[569,3295,3297,3311,3319],{"className":3296,"style":1084},[698],[569,3298,3299,3302],{"style":769},[569,3300],{"className":3301,"style":773},[706],[569,3303,3305],{"className":3304},[711,712,713,714],[569,3306,3308],{"className":3307},[678,714],[569,3309,597],{"className":3310},[678,682,714],[569,3312,3313,3316],{"style":792},[569,3314],{"className":3315,"style":773},[706],[569,3317],{"className":3318,"style":800},[799],[569,3320,3321,3324],{"style":803},[569,3322],{"className":3323,"style":773},[706],[569,3325,3327],{"className":3326},[711,712,713,714],[569,3328,3330],{"className":3329},[678,714],[569,3331,630],{"className":3332},[678,714],[569,3334,860],{"className":3335},[859],[569,3337,3339],{"className":3338},[694],[569,3340,3342],{"className":3341,"style":1130},[698],[569,3343],{},[569,3345],{"className":3346},[873,752]," nicht definiert, der Hauptsatz darf nicht angewendet werden.",[2888,3349,3350,1034,3574,3577,3578,1136],{},[569,3351,3353,3399],{"className":3352},[572],[569,3354,3356],{"className":3355},[576],[578,3357,3358],{"xmlns":580},[582,3359,3360,3396],{},[585,3361,3362,3364,3374,3376,3378,3380,3382,3384,3386,3388,3394],{},[588,3363,590],{},[614,3365,3366,3368],{},[628,3367,630],{},[592,3369,3370,3372],{},[595,3371,597],{},[628,3373,2158],{},[602,3375,604],{},[595,3377,607],{},[595,3379,597],{},[588,3381,612],{},[595,3383,1006],{},[588,3385,1009],{},[588,3387,1248],{"stretchy":1246},[592,3389,3390,3392],{},[595,3391,597],{},[628,3393,2158],{},[588,3395,1261],{"stretchy":1246},[645,3397,3398],{"encoding":647},"\\int \\frac{1}{x^2}\\,dx = \\ln(x^2)",[569,3400,3402,3528],{"className":3401,"ariaHidden":653},[652],[569,3403,3405,3408,3411,3414,3510,3513,3516,3519,3522,3525],{"className":3404},[657],[569,3406],{"className":3407,"style":1065},[661],[569,3409,590],{"className":3410,"style":669},[666,667,668],[569,3412],{"className":3413,"style":674},[673],[569,3415,3417,3420,3507],{"className":3416},[678],[569,3418],{"className":3419},[751,752],[569,3421,3423],{"className":3422},[614],[569,3424,3426,3499],{"className":3425},[690,759],[569,3427,3429,3496],{"className":3428},[694],[569,3430,3432,3474,3482],{"className":3431,"style":1084},[698],[569,3433,3434,3437],{"style":769},[569,3435],{"className":3436,"style":773},[706],[569,3438,3440],{"className":3439},[711,712,713,714],[569,3441,3443],{"className":3442},[678,714],[569,3444,3446,3449],{"className":3445},[678,714],[569,3447,597],{"className":3448},[678,682,714],[569,3450,3452],{"className":3451},[686],[569,3453,3455],{"className":3454},[690],[569,3456,3458],{"className":3457},[694],[569,3459,3462],{"className":3460,"style":3461},[698],"height:0.7463em;",[569,3463,3465,3468],{"style":3464},"top:-2.786em;margin-right:0.0714em;",[569,3466],{"className":3467,"style":838},[706],[569,3469,3471],{"className":3470},[711,842,843,714],[569,3472,2158],{"className":3473},[678,714],[569,3475,3476,3479],{"style":792},[569,3477],{"className":3478,"style":773},[706],[569,3480],{"className":3481,"style":800},[799],[569,3483,3484,3487],{"style":803},[569,3485],{"className":3486,"style":773},[706],[569,3488,3490],{"className":3489},[711,712,713,714],[569,3491,3493],{"className":3492},[678,714],[569,3494,630],{"className":3495},[678,714],[569,3497,860],{"className":3498},[859],[569,3500,3502],{"className":3501},[694],[569,3503,3505],{"className":3504,"style":1130},[698],[569,3506],{},[569,3508],{"className":3509},[873,752],[569,3511],{"className":3512,"style":674},[673],[569,3514,607],{"className":3515},[678,682],[569,3517,597],{"className":3518},[678,682],[569,3520],{"className":3521,"style":730},[673],[569,3523,612],{"className":3524},[734],[569,3526],{"className":3527,"style":730},[673],[569,3529,3531,3535,3538,3541,3571],{"className":3530},[657],[569,3532],{"className":3533,"style":3534},[661],"height:1.0641em;vertical-align:-0.25em;",[569,3536,1006],{"className":3537},[666],[569,3539,1248],{"className":3540},[751],[569,3542,3544,3547],{"className":3543},[678],[569,3545,597],{"className":3546},[678,682],[569,3548,3550],{"className":3549},[686],[569,3551,3553],{"className":3552},[690],[569,3554,3556],{"className":3555},[694],[569,3557,3560],{"className":3558,"style":3559},[698],"height:0.8141em;",[569,3561,3562,3565],{"style":702},[569,3563],{"className":3564,"style":707},[706],[569,3566,3568],{"className":3567},[711,712,713,714],[569,3569,2158],{"className":3570},[678,714],[569,3572,1261],{"className":3573},[873],[988,3575,3576],{},"falsch",". Hier hilft die Potenzregel: ",[569,3579,3581,3625],{"className":3580},[572],[569,3582,3584],{"className":3583},[576],[578,3585,3586],{"xmlns":580},[582,3587,3588,3622],{},[585,3589,3590,3592,3602,3604,3606,3608,3610,3612,3618,3620],{},[588,3591,590],{},[592,3593,3594,3596],{},[595,3595,597],{},[585,3597,3598,3600],{},[588,3599,914],{},[628,3601,2158],{},[602,3603,604],{},[595,3605,607],{},[595,3607,597],{},[588,3609,612],{},[588,3611,914],{},[614,3613,3614,3616],{},[628,3615,630],{},[595,3617,597],{},[588,3619,626],{},[595,3621,643],{},[645,3623,3624],{"encoding":647},"\\int x^{-2}\\,dx = -\\frac{1}{x} + 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