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",[574,1090,1092,1111],{"className":1091},[577],[574,1093,1095],{"className":1094},[581],[583,1096,1097],{"xmlns":585},[587,1098,1099,1108],{},[590,1100,1101],{},[666,1102,1103,1105],{},[593,1104,682],{},[593,1106,1107],{},"n",[597,1109,1110],{"encoding":599},"x^n",[574,1112,1114],{"className":1113,"ariaHidden":604},[603],[574,1115,1117,1121],{"className":1116},[608],[574,1118],{"className":1119,"style":1120},[612],"height:0.6644em;",[574,1122,1124,1127],{"className":1123},[617],[574,1125,682],{"className":1126},[617,618],[574,1128,1130],{"className":1129},[719],[574,1131,1133],{"className":1132},[723],[574,1134,1136],{"className":1135},[727],[574,1137,1139],{"className":1138,"style":1120},[731],[574,1140,1141,1144],{"style":735},[574,1142],{"className":1143,"style":740},[739],[574,1145,1147],{"className":1146},[744,745,746,747],[574,1148,1107],{"className":1149},[617,618,747]," an der Stelle ",[574,1152,1154,1168],{"className":1153},[577],[574,1155,1157],{"className":1156},[581],[583,1158,1159],{"xmlns":585},[587,1160,1161,1166],{},[590,1162,1163],{},[817,1164,1165],{},"0",[597,1167,1165],{"encoding":599},[574,1169,1171],{"className":1170,"ariaHidden":604},[603],[574,1172,1174,1177],{"className":1173},[608],[574,1175],{"className":1176,"style":831},[612],[574,1178,1165],{"className":1179},[617]," nicht definiert. Ein bestimmtes Integral darf dann die ",[574,1182,1184,1197],{"className":1183},[577],[574,1185,1187],{"className":1186},[581],[583,1188,1189],{"xmlns":585},[587,1190,1191,1195],{},[590,1192,1193],{},[817,1194,1165],{},[597,1196,1165],{"encoding":599},[574,1198,1200],{"className":1199,"ariaHidden":604},[603],[574,1201,1203,1206],{"className":1202},[608],[574,1204],{"className":1205,"style":831},[612],[574,1207,1165],{"className":1208},[617]," nicht im Intervall enthalten: ",[574,1211,1213,1259],{"className":1212},[577],[574,1214,1216],{"className":1215},[581],[583,1217,1218],{"xmlns":585},[587,1219,1220,1256],{},[590,1221,1222,1237,1247,1251,1254],{},[1223,1224,1225,1228,1235],"msubsup",{},[671,1226,1227],{},"∫",[590,1229,1230,1233],{},[671,1231,1232],{},"−",[817,1234,819],{},[817,1236,819],{},[666,1238,1239,1241],{},[593,1240,682],{},[590,1242,1243,1245],{},[671,1244,1232],{},[817,1246,865],{},[1248,1249,1250],"mtext",{}," ",[593,1252,1253],{},"d",[593,1255,682],{},[597,1257,1258],{"encoding":599},"\\int_{-1}^{1} x^{-2}\\,dx",[574,1260,1262],{"className":1261,"ariaHidden":604},[603],[574,1263,1265,1269,1337,1341,1377,1380,1383],{"className":1264},[608],[574,1266],{"className":1267,"style":1268},[612],"height:1.4232em;vertical-align:-0.4142em;",[574,1270,1273,1279],{"className":1271},[1272],"mop",[574,1274,1227],{"className":1275,"style":1278},[1272,1276,1277],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[574,1280,1282],{"className":1281},[719],[574,1283,1285,1328],{"className":1284},[723,892],[574,1286,1288,1325],{"className":1287},[727],[574,1289,1292,1310],{"className":1290,"style":1291},[731],"height:1.009em;",[574,1293,1295,1298],{"style":1294},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[574,1296],{"className":1297,"style":740},[739],[574,1299,1301],{"className":1300},[744,745,746,747],[574,1302,1304,1307],{"className":1303},[617,747],[574,1305,1232],{"className":1306},[617,747],[574,1308,819],{"className":1309},[617,747],[574,1311,1313,1316],{"style":1312},"top:-3.2579em;margin-right:0.05em;",[574,1314],{"className":1315,"style":740},[739],[574,1317,1319],{"className":1318},[744,745,746,747],[574,1320,1322],{"className":1321},[617,747],[574,1323,819],{"className":1324},[617,747],[574,1326,977],{"className":1327},[976],[574,1329,1331],{"className":1330},[727],[574,1332,1335],{"className":1333,"style":1334},[731],"height:0.4142em;",[574,1336],{},[574,1338],{"className":1339,"style":1340},[768],"margin-right:0.1667em;",[574,1342,1344,1347],{"className":1343},[617],[574,1345,682],{"className":1346},[617,618],[574,1348,1350],{"className":1349},[719],[574,1351,1353],{"className":1352},[723],[574,1354,1356],{"className":1355},[727],[574,1357,1360],{"className":1358,"style":1359},[731],"height:0.8141em;",[574,1361,1362,1365],{"style":735},[574,1363],{"className":1364,"style":740},[739],[574,1366,1368],{"className":1367},[744,745,746,747],[574,1369,1371,1374],{"className":1370},[617,747],[574,1372,1232],{"className":1373},[617,747],[574,1375,865],{"className":1376},[617,747],[574,1378],{"className":1379,"style":1340},[768],[574,1381,1253],{"className":1382},[617,618],[574,1384,682],{"className":1385},[617,618]," lässt sich nicht mit der Regel berechnen. Für gebrochene Exponenten braucht man meist ",[574,1388,1390,1409],{"className":1389},[577],[574,1391,1393],{"className":1392},[581],[583,1394,1395],{"xmlns":585},[587,1396,1397,1406],{},[590,1398,1399,1401,1404],{},[593,1400,682],{},[671,1402,1403],{},"≥",[817,1405,1165],{},[597,1407,1408],{"encoding":599},"x \\geq 0",[574,1410,1412,1431],{"className":1411,"ariaHidden":604},[603],[574,1413,1415,1419,1422,1425,1428],{"className":1414},[608],[574,1416],{"className":1417,"style":1418},[612],"height:0.7719em;vertical-align:-0.136em;",[574,1420,682],{"className":1421},[617,618],[574,1423],{"className":1424,"style":769},[768],[574,1426,1403],{"className":1427},[773],[574,1429],{"className":1430,"style":769},[768],[574,1432,1434,1437],{"className":1433},[608],[574,1435],{"className":1436,"style":831},[612],[574,1438,1165],{"className":1439},[617],".",[565,1442,1443,1444,1502,1503,1531,1532,1692,1693,1440],{},"Einzige Ausnahme beim Exponenten ist ",[574,1445,1447,1467],{"className":1446},[577],[574,1448,1450],{"className":1449},[581],[583,1451,1452],{"xmlns":585},[587,1453,1454,1464],{},[590,1455,1456,1458,1460,1462],{},[593,1457,1107],{},[671,1459,688],{},[671,1461,1232],{},[817,1463,819],{},[597,1465,1466],{"encoding":599},"n = -1",[574,1468,1470,1489],{"className":1469,"ariaHidden":604},[603],[574,1471,1473,1477,1480,1483,1486],{"className":1472},[608],[574,1474],{"className":1475,"style":1476},[612],"height:0.4306em;",[574,1478,1107],{"className":1479},[617,618],[574,1481],{"className":1482,"style":769},[768],[574,1484,688],{"className":1485},[773],[574,1487],{"className":1488,"style":769},[768],[574,1490,1492,1496,1499],{"className":1491},[608],[574,1493],{"className":1494,"style":1495},[612],"height:0.7278em;vertical-align:-0.0833em;",[574,1497,1232],{"className":1498},[617],[574,1500,819],{"className":1501},[617],", denn dann stünde im Nenner eine ",[574,1504,1506,1519],{"className":1505},[577],[574,1507,1509],{"className":1508},[581],[583,1510,1511],{"xmlns":585},[587,1512,1513,1517],{},[590,1514,1515],{},[817,1516,1165],{},[597,1518,1165],{"encoding":599},[574,1520,1522],{"className":1521,"ariaHidden":604},[603],[574,1523,1525,1528],{"className":1524},[608],[574,1526],{"className":1527,"style":831},[612],[574,1529,1165],{"className":1530},[617],". Für ",[574,1533,1535,1565],{"className":1534},[577],[574,1536,1538],{"className":1537},[581],[583,1539,1540],{"xmlns":585},[587,1541,1542,1562],{},[590,1543,1544,1550,1552],{},[855,1545,1546,1548],{},[817,1547,819],{},[593,1549,682],{},[671,1551,688],{},[666,1553,1554,1556],{},[593,1555,682],{},[590,1557,1558,1560],{},[671,1559,1232],{},[817,1561,819],{},[597,1563,1564],{"encoding":599},"\\frac{1}{x} = x^{-1}",[574,1566,1568,1651],{"className":1567,"ariaHidden":604},[603],[574,1569,1571,1574,1642,1645,1648],{"className":1570},[608],[574,1572],{"className":1573,"style":878},[612],[574,1575,1577,1580,1639],{"className":1576},[617],[574,1578],{"className":1579},[757,885],[574,1581,1583],{"className":1582},[855],[574,1584,1586,1631],{"className":1585},[723,892],[574,1587,1589,1628],{"className":1588},[727],[574,1590,1592,1606,1614],{"className":1591,"style":899},[731],[574,1593,1594,1597],{"style":902},[574,1595],{"className":1596,"style":906},[739],[574,1598,1600],{"className":1599},[744,745,746,747],[574,1601,1603],{"className":1602},[617,747],[574,1604,682],{"className":1605},[617,618,747],[574,1607,1608,1611],{"style":949},[574,1609],{"className":1610,"style":906},[739],[574,1612],{"className":1613,"style":957},[956],[574,1615,1616,1619],{"style":960},[574,1617],{"className":1618,"style":906},[739],[574,1620,1622],{"className":1621},[744,745,746,747],[574,1623,1625],{"className":1624},[617,747],[574,1626,819],{"className":1627},[617,747],[574,1629,977],{"className":1630},[976],[574,1632,1634],{"className":1633},[727],[574,1635,1637],{"className":1636,"style":984},[731],[574,1638],{},[574,1640],{"className":1641},[764,885],[574,1643],{"className":1644,"style":769},[768],[574,1646,688],{"className":1647},[773],[574,1649],{"className":1650,"style":769},[768],[574,1652,1654,1657],{"className":1653},[608],[574,1655],{"className":1656,"style":1359},[612],[574,1658,1660,1663],{"className":1659},[617],[574,1661,682],{"className":1662},[617,618],[574,1664,1666],{"className":1665},[719],[574,1667,1669],{"className":1668},[723],[574,1670,1672],{"className":1671},[727],[574,1673,1675],{"className":1674,"style":1359},[731],[574,1676,1677,1680],{"style":735},[574,1678],{"className":1679,"style":740},[739],[574,1681,1683],{"className":1682},[744,745,746,747],[574,1684,1686,1689],{"className":1685},[617,747],[574,1687,1232],{"className":1688},[617,747],[574,1690,819],{"className":1691},[617,747]," ist die Stammfunktion ",[574,1694,1696,1721],{"className":1695},[577],[574,1697,1699],{"className":1698},[581],[583,1700,1701],{"xmlns":585},[587,1702,1703,1718],{},[590,1704,1705,1708,1711,1714,1716],{},[593,1706,1707],{},"ln",[671,1709,1710],{},"⁡",[593,1712,1713],{"mathvariant":673},"∣",[593,1715,682],{},[593,1717,1713],{"mathvariant":673},[597,1719,1720],{"encoding":599},"\\ln|x|",[574,1722,1724],{"className":1723,"ariaHidden":604},[603],[574,1725,1727,1730,1733,1736,1739,1742],{"className":1726},[608],[574,1728],{"className":1729,"style":783},[612],[574,1731,1707],{"className":1732},[1272],[574,1734],{"className":1735,"style":1340},[768],[574,1737,1713],{"className":1738},[617],[574,1740,682],{"className":1741},[617,618],[574,1743,1713],{"className":1744},[617],[565,1746,1747,1748,572,1751,1781],{},"Weil die Ableitung einer Konstanten null ist, unterscheiden sich alle Stammfunktionen nur um eine Konstante. Deshalb schreibt man beim unbestimmten Integral die ",[569,1749,1750],{},"Integrationskonstante",[574,1752,1754,1768],{"className":1753},[577],[574,1755,1757],{"className":1756},[581],[583,1758,1759],{"xmlns":585},[587,1760,1761,1766],{},[590,1762,1763],{},[593,1764,1765],{},"C",[597,1767,1765],{"encoding":599},[574,1769,1771],{"className":1770,"ariaHidden":604},[603],[574,1772,1774,1777],{"className":1773},[608],[574,1775],{"className":1776,"style":613},[612],[574,1778,1765],{"className":1779,"style":1780},[617,618],"margin-right:0.0715em;"," dazu.",[560,1783,1785],{"id":1784},"herleitung","Herleitung",[565,1787,1788],{},"Man prüft das Ergebnis durch Ableiten. Mit der Potenzregel der Ableitung gilt",[574,1790,1793],{"className":1791},[1792],"katex-display",[574,1794,1796,1891],{"className":1795},[577],[574,1797,1799],{"className":1798},[581],[583,1800,1802],{"xmlns":585,"display":1801},"block",[587,1803,1804,1888],{},[590,1805,1806,1843,1845,1876,1878,1880,1882],{},[666,1807,1808,1841],{},[590,1809,1810,1812,1835,1837,1839],{},[671,1811,679],{"fence":604},[855,1813,1814,1827],{},[666,1815,1816,1818],{},[593,1817,682],{},[590,1819,1820,1822,1825],{},[593,1821,1107],{},[671,1823,1824],{},"+",[817,1826,819],{},[590,1828,1829,1831,1833],{},[593,1830,1107],{},[671,1832,1824],{},[817,1834,819],{},[671,1836,1824],{},[593,1838,1765],{},[671,1840,685],{"fence":604},[671,1842,675],{"mathvariant":673,"lspace":674,"rspace":674},[671,1844,688],{},[855,1846,1847,1868],{},[590,1848,1849,1851,1853,1855,1857,1859,1862],{},[671,1850,679],{"stretchy":678},[593,1852,1107],{},[671,1854,1824],{},[817,1856,819],{},[671,1858,685],{"stretchy":678},[671,1860,1861],{},"⋅",[666,1863,1864,1866],{},[593,1865,682],{},[593,1867,1107],{},[590,1869,1870,1872,1874],{},[593,1871,1107],{},[671,1873,1824],{},[817,1875,819],{},[671,1877,1824],{},[817,1879,1165],{},[671,1881,688],{},[666,1883,1884,1886],{},[593,1885,682],{},[593,1887,1107],{},[597,1889,1890],{"encoding":599},"\\left(\\frac{x^{n+1}}{n+1} + C\\right)' = \\frac{(n+1) \\cdot x^n}{n+1} + 0 = x^n",[574,1892,1894,2087,2234,2252],{"className":1893,"ariaHidden":604},[603],[574,1895,1897,1901,2078,2081,2084],{"className":1896},[608],[574,1898],{"className":1899,"style":1900},[612],"height:2.5829em;vertical-align:-0.95em;",[574,1902,1905,2050],{"className":1903},[1904],"minner",[574,1906,1908,1917,2032,2035,2038,2041,2044],{"className":1907},[1904],[574,1909,1913],{"className":1910,"style":1912},[757,1911],"delimcenter","top:0em;",[574,1914,679],{"className":1915},[1916,746],"delimsizing",[574,1918,1920,1923,2029],{"className":1919},[617],[574,1921],{"className":1922},[757,885],[574,1924,1926],{"className":1925},[855],[574,1927,1929,2020],{"className":1928},[723,892],[574,1930,1932,2017],{"className":1931},[727],[574,1933,1936,1962,1970],{"className":1934,"style":1935},[731],"height:1.4911em;",[574,1937,1939,1942],{"style":1938},"top:-2.314em;",[574,1940],{"className":1941,"style":906},[739],[574,1943,1945,1948,1952,1956,1959],{"className":1944},[617],[574,1946,1107],{"className":1947},[617,618],[574,1949],{"className":1950,"style":1951},[768],"margin-right:0.2222em;",[574,1953,1824],{"className":1954},[1955],"mbin",[574,1957],{"className":1958,"style":1951},[768],[574,1960,819],{"className":1961},[617],[574,1963,1964,1967],{"style":949},[574,1965],{"className":1966,"style":906},[739],[574,1968],{"className":1969,"style":957},[956],[574,1971,1973,1976],{"style":1972},"top:-3.677em;",[574,1974],{"className":1975,"style":906},[739],[574,1977,1979],{"className":1978},[617],[574,1980,1982,1985],{"className":1981},[617],[574,1983,682],{"className":1984},[617,618],[574,1986,1988],{"className":1987},[719],[574,1989,1991],{"className":1990},[723],[574,1992,1994],{"className":1993},[727],[574,1995,1997],{"className":1996,"style":1359},[731],[574,1998,1999,2002],{"style":735},[574,2000],{"className":2001,"style":740},[739],[574,2003,2005],{"className":2004},[744,745,746,747],[574,2006,2008,2011,2014],{"className":2007},[617,747],[574,2009,1107],{"className":2010},[617,618,747],[574,2012,1824],{"className":2013},[1955,747],[574,2015,819],{"className":2016},[617,747],[574,2018,977],{"className":2019},[976],[574,2021,2023],{"className":2022},[727],[574,2024,2027],{"className":2025,"style":2026},[731],"height:0.7693em;",[574,2028],{},[574,2030],{"className":2031},[764,885],[574,2033],{"className":2034,"style":1951},[768],[574,2036,1824],{"className":2037},[1955],[574,2039],{"className":2040,"style":1951},[768],[574,2042,1765],{"className":2043,"style":1780},[617,618],[574,2045,2047],{"className":2046,"style":1912},[764,1911],[574,2048,685],{"className":2049},[1916,746],[574,2051,2053],{"className":2052},[719],[574,2054,2056],{"className":2055},[723],[574,2057,2059],{"className":2058},[727],[574,2060,2063],{"className":2061,"style":2062},[731],"height:1.6329em;",[574,2064,2066,2069],{"style":2065},"top:-3.944em;margin-right:0.05em;",[574,2067],{"className":2068,"style":740},[739],[574,2070,2072],{"className":2071},[744,745,746,747],[574,2073,2075],{"className":2074},[617,747],[574,2076,675],{"className":2077},[617,747],[574,2079],{"className":2080,"style":769},[768],[574,2082,688],{"className":2083},[773],[574,2085],{"className":2086,"style":769},[768],[574,2088,2090,2094,2225,2228,2231],{"className":2089},[608],[574,2091],{"className":2092,"style":2093},[612],"height:2.1963em;vertical-align:-0.7693em;",[574,2095,2097,2100,2222],{"className":2096},[617],[574,2098],{"className":2099},[757,885],[574,2101,2103],{"className":2102},[855],[574,2104,2106,2214],{"className":2105},[723,892],[574,2107,2109,2211],{"className":2108},[727],[574,2110,2113,2136,2144],{"className":2111,"style":2112},[731],"height:1.427em;",[574,2114,2115,2118],{"style":1938},[574,2116],{"className":2117,"style":906},[739],[574,2119,2121,2124,2127,2130,2133],{"className":2120},[617],[574,2122,1107],{"className":2123},[617,618],[574,2125],{"className":2126,"style":1951},[768],[574,2128,1824],{"className":2129},[1955],[574,2131],{"className":2132,"style":1951},[768],[574,2134,819],{"className":2135},[617],[574,2137,2138,2141],{"style":949},[574,2139],{"className":2140,"style":906},[739],[574,2142],{"className":2143,"style":957},[956],[574,2145,2146,2149],{"style":1972},[574,2147],{"className":2148,"style":906},[739],[574,2150,2152,2155,2158,2161,2164,2167,2170,2173,2176,2179,2182],{"className":2151},[617],[574,2153,679],{"className":2154},[757],[574,2156,1107],{"className":2157},[617,618],[574,2159],{"className":2160,"style":1951},[768],[574,2162,1824],{"className":2163},[1955],[574,2165],{"className":2166,"style":1951},[768],[574,2168,819],{"className":2169},[617],[574,2171,685],{"className":2172},[764],[574,2174],{"className":2175,"style":1951},[768],[574,2177,1861],{"className":2178},[1955],[574,2180],{"className":2181,"style":1951},[768],[574,2183,2185,2188],{"className":2184},[617],[574,2186,682],{"className":2187},[617,618],[574,2189,2191],{"className":2190},[719],[574,2192,2194],{"className":2193},[723],[574,2195,2197],{"className":2196},[727],[574,2198,2200],{"className":2199,"style":1120},[731],[574,2201,2202,2205],{"style":735},[574,2203],{"className":2204,"style":740},[739],[574,2206,2208],{"className":2207},[744,745,746,747],[574,2209,1107],{"className":2210},[617,618,747],[574,2212,977],{"className":2213},[976],[574,2215,2217],{"className":2216},[727],[574,2218,2220],{"className":2219,"style":2026},[731],[574,2221],{},[574,2223],{"className":2224},[764,885],[574,2226],{"className":2227,"style":1951},[768],[574,2229,1824],{"className":2230},[1955],[574,2232],{"className":2233,"style":1951},[768],[574,2235,2237,2240,2243,2246,2249],{"className":2236},[608],[574,2238],{"className":2239,"style":831},[612],[574,2241,1165],{"className":2242},[617],[574,2244],{"className":2245,"style":769},[768],[574,2247,688],{"className":2248},[773],[574,2250],{"className":2251,"style":769},[768],[574,2253,2255,2259],{"className":2254},[608],[574,2256],{"className":2257,"style":2258},[612],"height:0.7144em;",[574,2260,2262,2265],{"className":2261},[617],[574,2263,682],{"className":2264},[617,618],[574,2266,2268],{"className":2267},[719],[574,2269,2271],{"className":2270},[723],[574,2272,2274],{"className":2273},[727],[574,2275,2277],{"className":2276,"style":2258},[731],[574,2278,2280,2283],{"style":2279},"top:-3.113em;margin-right:0.05em;",[574,2281],{"className":2282,"style":740},[739],[574,2284,2286],{"className":2285},[744,745,746,747],[574,2287,1107],{"className":2288},[617,618,747],[565,2290,2291,2292,2344,2345,2442],{},"Das Kürzen durch ",[574,2293,2295,2313],{"className":2294},[577],[574,2296,2298],{"className":2297},[581],[583,2299,2300],{"xmlns":585},[587,2301,2302,2310],{},[590,2303,2304,2306,2308],{},[593,2305,1107],{},[671,2307,1824],{},[817,2309,819],{},[597,2311,2312],{"encoding":599},"n + 1",[574,2314,2316,2335],{"className":2315,"ariaHidden":604},[603],[574,2317,2319,2323,2326,2329,2332],{"className":2318},[608],[574,2320],{"className":2321,"style":2322},[612],"height:0.6667em;vertical-align:-0.0833em;",[574,2324,1107],{"className":2325},[617,618],[574,2327],{"className":2328,"style":1951},[768],[574,2330,1824],{"className":2331},[1955],[574,2333],{"className":2334,"style":1951},[768],[574,2336,2338,2341],{"className":2337},[608],[574,2339],{"className":2340,"style":831},[612],[574,2342,819],{"className":2343},[617]," ist nur für ",[574,2346,2348,2369],{"className":2347},[577],[574,2349,2351],{"className":2350},[581],[583,2352,2353],{"xmlns":585},[587,2354,2355,2366],{},[590,2356,2357,2359,2362,2364],{},[593,2358,1107],{},[671,2360,2361],{"mathvariant":673},"≠",[671,2363,1232],{},[817,2365,819],{},[597,2367,2368],{"encoding":599},"n \\neq -1",[574,2370,2372,2430],{"className":2371,"ariaHidden":604},[603],[574,2373,2375,2378,2381,2384,2427],{"className":2374},[608],[574,2376],{"className":2377,"style":647},[612],[574,2379,1107],{"className":2380},[617,618],[574,2382],{"className":2383,"style":769},[768],[574,2385,2387,2420,2424],{"className":2386},[773],[574,2388,2390],{"className":2389},[773],[574,2391,2394],{"className":2392},[617,2393],"vbox",[574,2395,2398],{"className":2396},[2397],"thinbox",[574,2399,2402,2405,2416],{"className":2400},[2401],"rlap",[574,2403],{"className":2404,"style":647},[612],[574,2406,2409],{"className":2407},[2408],"inner",[574,2410,2412],{"className":2411},[617],[574,2413,2415],{"className":2414},[773],"",[574,2417],{"className":2418},[2419],"fix",[574,2421],{"className":2422},[768,2423],"nobreak",[574,2425,688],{"className":2426},[773],[574,2428],{"className":2429,"style":769},[768],[574,2431,2433,2436,2439],{"className":2432},[608],[574,2434],{"className":2435,"style":1495},[612],[574,2437,1232],{"className":2438},[617],[574,2440,819],{"className":2441},[617]," erlaubt.",[560,2444,2446],{"id":2445},"beispiele","Beispiele",[574,2448,2450],{"className":2449},[1792],[574,2451,2453,2497],{"className":2452},[577],[574,2454,2456],{"className":2455},[581],[583,2457,2458],{"xmlns":585,"display":1801},[587,2459,2460,2494],{},[590,2461,2462,2464,2471,2473,2475,2477,2479,2490,2492],{},[671,2463,1227],{},[666,2465,2466,2468],{},[593,2467,682],{},[817,2469,2470],{},"3",[1248,2472,1250],{},[593,2474,1253],{},[593,2476,682],{},[671,2478,688],{},[855,2480,2481,2488],{},[666,2482,2483,2485],{},[593,2484,682],{},[817,2486,2487],{},"4",[817,2489,2487],{},[671,2491,1824],{},[593,2493,1765],{},[597,2495,2496],{"encoding":599},"\\int x^3 \\, dx = \\frac{x^4}{4} + C",[574,2498,2500,2563,2668],{"className":2499,"ariaHidden":604},[603],[574,2501,2503,2507,2512,2515,2545,2548,2551,2554,2557,2560],{"className":2502},[608],[574,2504],{"className":2505,"style":2506},[612],"height:2.2222em;vertical-align:-0.8622em;",[574,2508,1227],{"className":2509,"style":2511},[1272,1276,2510],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[574,2513],{"className":2514,"style":1340},[768],[574,2516,2518,2521],{"className":2517},[617],[574,2519,682],{"className":2520},[617,618],[574,2522,2524],{"className":2523},[719],[574,2525,2527],{"className":2526},[723],[574,2528,2530],{"className":2529},[727],[574,2531,2534],{"className":2532,"style":2533},[731],"height:0.8641em;",[574,2535,2536,2539],{"style":2279},[574,2537],{"className":2538,"style":740},[739],[574,2540,2542],{"className":2541},[744,745,746,747],[574,2543,2470],{"className":2544},[617,747],[574,2546],{"className":2547,"style":1340},[768],[574,2549,1253],{"className":2550},[617,618],[574,2552,682],{"className":2553},[617,618],[574,2555],{"className":2556,"style":769},[768],[574,2558,688],{"className":2559},[773],[574,2561],{"className":2562,"style":769},[768],[574,2564,2566,2570,2659,2662,2665],{"className":2565},[608],[574,2567],{"className":2568,"style":2569},[612],"height:2.1771em;vertical-align:-0.686em;",[574,2571,2573,2576,2656],{"className":2572},[617],[574,2574],{"className":2575},[757,885],[574,2577,2579],{"className":2578},[855],[574,2580,2582,2647],{"className":2581},[723,892],[574,2583,2585,2644],{"className":2584},[727],[574,2586,2588,2599,2607],{"className":2587,"style":1935},[731],[574,2589,2590,2593],{"style":1938},[574,2591],{"className":2592,"style":906},[739],[574,2594,2596],{"className":2595},[617],[574,2597,2487],{"className":2598},[617],[574,2600,2601,2604],{"style":949},[574,2602],{"className":2603,"style":906},[739],[574,2605],{"className":2606,"style":957},[956],[574,2608,2609,2612],{"style":1972},[574,2610],{"className":2611,"style":906},[739],[574,2613,2615],{"className":2614},[617],[574,2616,2618,2621],{"className":2617},[617],[574,2619,682],{"className":2620},[617,618],[574,2622,2624],{"className":2623},[719],[574,2625,2627],{"className":2626},[723],[574,2628,2630],{"className":2629},[727],[574,2631,2633],{"className":2632,"style":1359},[731],[574,2634,2635,2638],{"style":735},[574,2636],{"className":2637,"style":740},[739],[574,2639,2641],{"className":2640},[744,745,746,747],[574,2642,2487],{"className":2643},[617,747],[574,2645,977],{"className":2646},[976],[574,2648,2650],{"className":2649},[727],[574,2651,2654],{"className":2652,"style":2653},[731],"height:0.686em;",[574,2655],{},[574,2657],{"className":2658},[764,885],[574,2660],{"className":2661,"style":1951},[768],[574,2663,1824],{"className":2664},[1955],[574,2666],{"className":2667,"style":1951},[768],[574,2669,2671,2674],{"className":2670},[608],[574,2672],{"className":2673,"style":613},[612],[574,2675,1765],{"className":2676,"style":1780},[617,618],[565,2678,2679],{},"Ein Bruch wird zuerst als Potenz mit negativem Exponenten geschrieben:",[574,2681,2683],{"className":2682},[1792],[574,2684,2686,2787],{"className":2685},[577],[574,2687,2689],{"className":2688},[581],[583,2690,2691],{"xmlns":585,"display":1801},[587,2692,2693,2784],{},[590,2694,2695,2697,2707,2709,2711,2713,2715,2717,2727,2729,2731,2733,2735,2753,2755,2757,2759,2761,2767,2769,2771,2774,2776,2778,2780,2782],{},[671,2696,1227],{},[855,2698,2699,2701],{},[817,2700,819],{},[666,2702,2703,2705],{},[593,2704,682],{},[817,2706,865],{},[1248,2708,1250],{},[593,2710,1253],{},[593,2712,682],{},[671,2714,688],{},[671,2716,1227],{},[666,2718,2719,2721],{},[593,2720,682],{},[590,2722,2723,2725],{},[671,2724,1232],{},[817,2726,865],{},[1248,2728,1250],{},[593,2730,1253],{},[593,2732,682],{},[671,2734,688],{},[855,2736,2737,2747],{},[666,2738,2739,2741],{},[593,2740,682],{},[590,2742,2743,2745],{},[671,2744,1232],{},[817,2746,819],{},[590,2748,2749,2751],{},[671,2750,1232],{},[817,2752,819],{},[671,2754,1824],{},[593,2756,1765],{},[671,2758,688],{},[671,2760,1232],{},[855,2762,2763,2765],{},[817,2764,819],{},[593,2766,682],{},[671,2768,1824],{},[593,2770,1765],{},[768,2772],{"width":2773},"2em",[671,2775,679],{"stretchy":678},[593,2777,682],{},[671,2779,2361],{"mathvariant":673},[817,2781,1165],{},[671,2783,685],{"stretchy":678},[597,2785,2786],{"encoding":599},"\\int \\frac{1}{x^2} \\, dx = \\int x^{-2} \\, dx = \\frac{x^{-1}}{-1} + C = -\\frac{1}{x} + C \\qquad (x \\neq 0)",[574,2788,2790,2911,2976,3089,3107,3188,3249],{"className":2789,"ariaHidden":604},[603],[574,2791,2793,2796,2799,2802,2893,2896,2899,2902,2905,2908],{"className":2792},[608],[574,2794],{"className":2795,"style":2506},[612],[574,2797,1227],{"className":2798,"style":2511},[1272,1276,2510],[574,2800],{"className":2801,"style":1340},[768],[574,2803,2805,2808,2890],{"className":2804},[617],[574,2806],{"className":2807},[757,885],[574,2809,2811],{"className":2810},[855],[574,2812,2814,2882],{"className":2813},[723,892],[574,2815,2817,2879],{"className":2816},[727],[574,2818,2821,2860,2868],{"className":2819,"style":2820},[731],"height:1.3214em;",[574,2822,2823,2826],{"style":1938},[574,2824],{"className":2825,"style":906},[739],[574,2827,2829],{"className":2828},[617],[574,2830,2832,2835],{"className":2831},[617],[574,2833,682],{"className":2834},[617,618],[574,2836,2838],{"className":2837},[719],[574,2839,2841],{"className":2840},[723],[574,2842,2844],{"className":2843},[727],[574,2845,2848],{"className":2846,"style":2847},[731],"height:0.7401em;",[574,2849,2851,2854],{"style":2850},"top:-2.989em;margin-right:0.05em;",[574,2852],{"className":2853,"style":740},[739],[574,2855,2857],{"className":2856},[744,745,746,747],[574,2858,865],{"className":2859},[617,747],[574,2861,2862,2865],{"style":949},[574,2863],{"className":2864,"style":906},[739],[574,2866],{"className":2867,"style":957},[956],[574,2869,2870,2873],{"style":1972},[574,2871],{"className":2872,"style":906},[739],[574,2874,2876],{"className":2875},[617],[574,2877,819],{"className":2878},[617],[574,2880,977],{"className":2881},[976],[574,2883,2885],{"className":2884},[727],[574,2886,2888],{"className":2887,"style":2653},[731],[574,2889],{},[574,2891],{"className":2892},[764,885],[574,2894],{"className":2895,"style":1340},[768],[574,2897,1253],{"className":2898},[617,618],[574,2900,682],{"className":2901},[617,618],[574,2903],{"className":2904,"style":769},[768],[574,2906,688],{"className":2907},[773],[574,2909],{"className":2910,"style":769},[768],[574,2912,2914,2917,2920,2923,2958,2961,2964,2967,2970,2973],{"className":2913},[608],[574,2915],{"className":2916,"style":2506},[612],[574,2918,1227],{"className":2919,"style":2511},[1272,1276,2510],[574,2921],{"className":2922,"style":1340},[768],[574,2924,2926,2929],{"className":2925},[617],[574,2927,682],{"className":2928},[617,618],[574,2930,2932],{"className":2931},[719],[574,2933,2935],{"className":2934},[723],[574,2936,2938],{"className":2937},[727],[574,2939,2941],{"className":2940,"style":2533},[731],[574,2942,2943,2946],{"style":2279},[574,2944],{"className":2945,"style":740},[739],[574,2947,2949],{"className":2948},[744,745,746,747],[574,2950,2952,2955],{"className":2951},[617,747],[574,2953,1232],{"className":2954},[617,747],[574,2956,865],{"className":2957},[617,747],[574,2959],{"className":2960,"style":1340},[768],[574,2962,1253],{"className":2963},[617,618],[574,2965,682],{"className":2966},[617,618],[574,2968],{"className":2969,"style":769},[768],[574,2971,688],{"className":2972},[773],[574,2974],{"className":2975,"style":769},[768],[574,2977,2979,2983,3080,3083,3086],{"className":2978},[608],[574,2980],{"className":2981,"style":2982},[612],"height:2.2604em;vertical-align:-0.7693em;",[574,2984,2986,2989,3077],{"className":2985},[617],[574,2987],{"className":2988},[757,885],[574,2990,2992],{"className":2991},[855],[574,2993,2995,3069],{"className":2994},[723,892],[574,2996,2998,3066],{"className":2997},[727],[574,2999,3001,3015,3023],{"className":3000,"style":1935},[731],[574,3002,3003,3006],{"style":1938},[574,3004],{"className":3005,"style":906},[739],[574,3007,3009,3012],{"className":3008},[617],[574,3010,1232],{"className":3011},[617],[574,3013,819],{"className":3014},[617],[574,3016,3017,3020],{"style":949},[574,3018],{"className":3019,"style":906},[739],[574,3021],{"className":3022,"style":957},[956],[574,3024,3025,3028],{"style":1972},[574,3026],{"className":3027,"style":906},[739],[574,3029,3031],{"className":3030},[617],[574,3032,3034,3037],{"className":3033},[617],[574,3035,682],{"className":3036},[617,618],[574,3038,3040],{"className":3039},[719],[574,3041,3043],{"className":3042},[723],[574,3044,3046],{"className":3045},[727],[574,3047,3049],{"className":3048,"style":1359},[731],[574,3050,3051,3054],{"style":735},[574,3052],{"className":3053,"style":740},[739],[574,3055,3057],{"className":3056},[744,745,746,747],[574,3058,3060,3063],{"className":3059},[617,747],[574,3061,1232],{"className":3062},[617,747],[574,3064,819],{"className":3065},[617,747],[574,3067,977],{"className":3068},[976],[574,3070,3072],{"className":3071},[727],[574,3073,3075],{"className":3074,"style":2026},[731],[574,3076],{},[574,3078],{"className":3079},[764,885],[574,3081],{"className":3082,"style":1951},[768],[574,3084,1824],{"className":3085},[1955],[574,3087],{"className":3088,"style":1951},[768],[574,3090,3092,3095,3098,3101,3104],{"className":3091},[608],[574,3093],{"className":3094,"style":613},[612],[574,3096,1765],{"className":3097,"style":1780},[617,618],[574,3099],{"className":3100,"style":769},[768],[574,3102,688],{"className":3103},[773],[574,3105],{"className":3106,"style":769},[768],[574,3108,3110,3114,3117,3179,3182,3185],{"className":3109},[608],[574,3111],{"className":3112,"style":3113},[612],"height:2.0074em;vertical-align:-0.686em;",[574,3115,1232],{"className":3116},[617],[574,3118,3120,3123,3176],{"className":3119},[617],[574,3121],{"className":3122},[757,885],[574,3124,3126],{"className":3125},[855],[574,3127,3129,3168],{"className":3128},[723,892],[574,3130,3132,3165],{"className":3131},[727],[574,3133,3135,3146,3154],{"className":3134,"style":2820},[731],[574,3136,3137,3140],{"style":1938},[574,3138],{"className":3139,"style":906},[739],[574,3141,3143],{"className":3142},[617],[574,3144,682],{"className":3145},[617,618],[574,3147,3148,3151],{"style":949},[574,3149],{"className":3150,"style":906},[739],[574,3152],{"className":3153,"style":957},[956],[574,3155,3156,3159],{"style":1972},[574,3157],{"className":3158,"style":906},[739],[574,3160,3162],{"className":3161},[617],[574,3163,819],{"className":3164},[617],[574,3166,977],{"className":3167},[976],[574,3169,3171],{"className":3170},[727],[574,3172,3174],{"className":3173,"style":2653},[731],[574,3175],{},[574,3177],{"className":3178},[764,885],[574,3180],{"className":3181,"style":1951},[768],[574,3183,1824],{"className":3184},[1955],[574,3186],{"className":3187,"style":1951},[768],[574,3189,3191,3194,3197,3201,3204,3207,3210,3246],{"className":3190},[608],[574,3192],{"className":3193,"style":783},[612],[574,3195,1765],{"className":3196,"style":1780},[617,618],[574,3198],{"className":3199,"style":3200},[768],"margin-right:2em;",[574,3202,679],{"className":3203},[757],[574,3205,682],{"className":3206},[617,618],[574,3208],{"className":3209,"style":769},[768],[574,3211,3213,3240,3243],{"className":3212},[773],[574,3214,3216],{"className":3215},[773],[574,3217,3219],{"className":3218},[617,2393],[574,3220,3222],{"className":3221},[2397],[574,3223,3225,3228,3237],{"className":3224},[2401],[574,3226],{"className":3227,"style":647},[612],[574,3229,3231],{"className":3230},[2408],[574,3232,3234],{"className":3233},[617],[574,3235,2415],{"className":3236},[773],[574,3238],{"className":3239},[2419],[574,3241],{"className":3242},[768,2423],[574,3244,688],{"className":3245},[773],[574,3247],{"className":3248,"style":769},[768],[574,3250,3252,3255,3258],{"className":3251},[608],[574,3253],{"className":3254,"style":783},[612],[574,3256,1165],{"className":3257},[617],[574,3259,685],{"className":3260},[764],[565,3262,3263],{},"Eine Wurzel wird als Potenz mit Bruch im Exponenten geschrieben:",[574,3265,3267],{"className":3266},[1792],[574,3268,3270,3372],{"className":3269},[577],[574,3271,3273],{"className":3272},[581],[583,3274,3275],{"xmlns":585,"display":1801},[587,3276,3277,3369],{},[590,3278,3279,3281,3285,3287,3289,3291,3293,3295,3305,3307,3309,3311,3313,3331,3333,3335,3337,3343,3353,3355,3357,3359,3361,3363,3365,3367],{},[671,3280,1227],{},[1004,3282,3283],{},[593,3284,682],{},[1248,3286,1250],{},[593,3288,1253],{},[593,3290,682],{},[671,3292,688],{},[671,3294,1227],{},[666,3296,3297,3299],{},[593,3298,682],{},[855,3300,3301,3303],{},[817,3302,819],{},[817,3304,865],{},[1248,3306,1250],{},[593,3308,1253],{},[593,3310,682],{},[671,3312,688],{},[855,3314,3315,3325],{},[666,3316,3317,3319],{},[593,3318,682],{},[855,3320,3321,3323],{},[817,3322,2470],{},[817,3324,865],{},[855,3326,3327,3329],{},[817,3328,2470],{},[817,3330,865],{},[671,3332,1824],{},[593,3334,1765],{},[671,3336,688],{},[855,3338,3339,3341],{},[817,3340,865],{},[817,3342,2470],{},[666,3344,3345,3347],{},[593,3346,682],{},[855,3348,3349,3351],{},[817,3350,2470],{},[817,3352,865],{},[671,3354,1824],{},[593,3356,1765],{},[768,3358],{"width":2773},[671,3360,679],{"stretchy":678},[593,3362,682],{},[671,3364,1403],{},[817,3366,1165],{},[671,3368,685],{"stretchy":678},[597,3370,3371],{"encoding":599},"\\int \\sqrt{x} \\, dx = \\int x^{\\frac{1}{2}} \\, dx = \\frac{x^{\\frac{3}{2}}}{\\frac{3}{2}} + C = \\frac{2}{3} x^{\\frac{3}{2}} + C \\qquad (x \\geq 0)",[574,3373,3375,3455,3591,3833,3851,4025,4052],{"className":3374,"ariaHidden":604},[603],[574,3376,3378,3381,3384,3387,3437,3440,3443,3446,3449,3452],{"className":3377},[608],[574,3379],{"className":3380,"style":2506},[612],[574,3382,1227],{"className":3383,"style":2511},[1272,1276,2510],[574,3385],{"className":3386,"style":1340},[768],[574,3388,3390],{"className":3389},[617,1024],[574,3391,3393,3428],{"className":3392},[723,892],[574,3394,3396,3425],{"className":3395},[727],[574,3397,3400,3412],{"className":3398,"style":3399},[731],"height:0.8492em;",[574,3401,3403,3406],{"className":3402,"style":1039},[1038],[574,3404],{"className":3405,"style":906},[739],[574,3407,3409],{"className":3408,"style":1046},[617],[574,3410,682],{"className":3411},[617,618],[574,3413,3415,3418],{"style":3414},"top:-2.8092em;",[574,3416],{"className":3417,"style":906},[739],[574,3419,3421],{"className":3420,"style":1060},[1059],[1062,3422,3423],{"xmlns":1064,"width":1065,"height":1066,"viewBox":1067,"preserveAspectRatio":1068},[1070,3424],{"d":1072},[574,3426,977],{"className":3427},[976],[574,3429,3431],{"className":3430},[727],[574,3432,3435],{"className":3433,"style":3434},[731],"height:0.1908em;",[574,3436],{},[574,3438],{"className":3439,"style":1340},[768],[574,3441,1253],{"className":3442},[617,618],[574,3444,682],{"className":3445},[617,618],[574,3447],{"className":3448,"style":769},[768],[574,3450,688],{"className":3451},[773],[574,3453],{"className":3454,"style":769},[768],[574,3456,3458,3461,3464,3467,3573,3576,3579,3582,3585,3588],{"className":3457},[608],[574,3459],{"className":3460,"style":2506},[612],[574,3462,1227],{"className":3463,"style":2511},[1272,1276,2510],[574,3465],{"className":3466,"style":1340},[768],[574,3468,3470,3473],{"className":3469},[617],[574,3471,682],{"className":3472},[617,618],[574,3474,3476],{"className":3475},[719],[574,3477,3479],{"className":3478},[723],[574,3480,3482],{"className":3481},[727],[574,3483,3486],{"className":3484,"style":3485},[731],"height:1.004em;",[574,3487,3489,3492],{"style":3488},"top:-3.413em;margin-right:0.05em;",[574,3490],{"className":3491,"style":906},[739],[574,3493,3495],{"className":3494},[744,745,746,747],[574,3496,3498],{"className":3497},[617,747],[574,3499,3501,3505,3570],{"className":3500},[617,747],[574,3502],{"className":3503},[757,885,744,942,3504],"size6",[574,3506,3508],{"className":3507},[855],[574,3509,3511,3561],{"className":3510},[723,892],[574,3512,3514,3558],{"className":3513},[727],[574,3515,3518,3533,3543],{"className":3516,"style":3517},[731],"height:0.8443em;",[574,3519,3521,3524],{"style":3520},"top:-2.656em;",[574,3522],{"className":3523,"style":906},[739],[574,3525,3527],{"className":3526},[744,942,943,747],[574,3528,3530],{"className":3529},[617,747],[574,3531,865],{"className":3532},[617,747],[574,3534,3536,3539],{"style":3535},"top:-3.2255em;",[574,3537],{"className":3538,"style":906},[739],[574,3540],{"className":3541,"style":3542},[956,747],"border-bottom-width:0.049em;",[574,3544,3546,3549],{"style":3545},"top:-3.384em;",[574,3547],{"className":3548,"style":906},[739],[574,3550,3552],{"className":3551},[744,942,943,747],[574,3553,3555],{"className":3554},[617,747],[574,3556,819],{"className":3557},[617,747],[574,3559,977],{"className":3560},[976],[574,3562,3564],{"className":3563},[727],[574,3565,3568],{"className":3566,"style":3567},[731],"height:0.344em;",[574,3569],{},[574,3571],{"className":3572},[764,885,744,942,3504],[574,3574],{"className":3575,"style":1340},[768],[574,3577,1253],{"className":3578},[617,618],[574,3580,682],{"className":3581},[617,618],[574,3583],{"className":3584,"style":769},[768],[574,3586,688],{"className":3587},[773],[574,3589],{"className":3590,"style":769},[768],[574,3592,3594,3598,3824,3827,3830],{"className":3593},[608],[574,3595],{"className":3596,"style":3597},[612],"height:2.7111em;vertical-align:-1.0801em;",[574,3599,3601,3604,3821],{"className":3600},[617],[574,3602],{"className":3603},[757,885],[574,3605,3607],{"className":3606},[855],[574,3608,3610,3812],{"className":3609},[723,892],[574,3611,3613,3809],{"className":3612},[727],[574,3614,3617,3694,3702],{"className":3615,"style":3616},[731],"height:1.631em;",[574,3618,3620,3623],{"style":3619},"top:-2.2649em;",[574,3621],{"className":3622,"style":906},[739],[574,3624,3626],{"className":3625},[617],[574,3627,3629,3632,3691],{"className":3628},[617],[574,3630],{"className":3631},[757,885],[574,3633,3635],{"className":3634},[855],[574,3636,3638,3683],{"className":3637},[723,892],[574,3639,3641,3680],{"className":3640},[727],[574,3642,3644,3658,3666],{"className":3643,"style":899},[731],[574,3645,3646,3649],{"style":902},[574,3647],{"className":3648,"style":906},[739],[574,3650,3652],{"className":3651},[744,745,746,747],[574,3653,3655],{"className":3654},[617,747],[574,3656,865],{"className":3657},[617,747],[574,3659,3660,3663],{"style":949},[574,3661],{"className":3662,"style":906},[739],[574,3664],{"className":3665,"style":957},[956],[574,36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dem Hauptsatz folgt daraus ein bestimmtes Integral:",[574,4068,4070],{"className":4069},[1792],[574,4071,4073,4148],{"className":4072},[577],[574,4074,4076],{"className":4075},[581],[583,4077,4078],{"xmlns":585,"display":1801},[587,4079,4080,4145],{},[590,4081,4082,4090,4096,4098,4100,4102,4104,4128,4130,4137,4139,4141,4143],{},[1223,4083,4084,4086,4088],{},[671,4085,1227],{},[817,4087,1165],{},[817,4089,865],{},[666,4091,4092,4094],{},[593,4093,682],{},[817,4095,2470],{},[1248,4097,1250],{},[593,4099,1253],{},[593,4101,682],{},[671,4103,688],{},[1223,4105,4106,4124,4126],{},[590,4107,4108,4111,4121],{},[671,4109,4110],{"fence":604},"[",[855,4112,4113,4119],{},[666,4114,4115,4117],{},[593,4116,682],{},[817,4118,2487],{},[817,4120,2487],{},[671,4122,4123],{"fence":604},"]",[817,4125,1165],{},[817,4127,865],{},[671,4129,688],{},[855,4131,4132,4135],{},[817,4133,4134],{},"16",[817,4136,2487],{},[671,4138,1232],{},[817,4140,1165],{},[671,4142,688],{},[817,4144,2487],{},[597,4146,4147],{"encoding":599},"\\int_0^2 x^3 \\, dx = \\left[\\frac{x^4}{4}\\right]_0^2 = \\frac{16}{4} - 0 = 4",[574,4149,4151,4263,4433,4510,4528],{"className":4150,"ariaHidden":604},[603],[574,4152,4154,4158,4213,4216,4245,4248,4251,4254,4257,4260],{"className":4153},[608],[574,4155],{"className":4156,"style":4157},[612],"height:2.476em;vertical-align:-0.9119em;",[574,4159,4161,4164],{"className":4160},[1272],[574,4162,1227],{"className":4163,"style":2511},[1272,1276,2510],[574,4165,4167],{"className":4166},[719],[574,4168,4170,4204],{"className":4169},[723,892],[574,4171,4173,4201],{"className":4172},[727],[574,4174,4177,4189],{"className":4175,"style":4176},[731],"height:1.564em;",[574,4178,4180,4183],{"style":4179},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[574,4181],{"className":4182,"style":740},[739],[574,4184,4186],{"className":4185},[744,745,746,747],[574,4187,1165],{"className":4188},[617,747],[574,4190,4192,4195],{"style":4191},"top:-3.8129em;margin-right:0.05em;",[574,4193],{"className":4194,"style":740},[739],[574,4196,4198],{"className":4197},[744,745,746,747],[574,4199,865],{"className":4200},[617,747],[574,4202,977],{"className":4203},[976],[574,4205,4207],{"className":4206},[727],[574,4208,4211],{"className":4209,"style":4210},[731],"height:0.9119em;",[574,4212],{},[574,4214],{"className":4215,"style":1340},[768],[574,4217,4219,4222],{"className":4218},[617],[574,4220,682],{"className":4221},[617,618],[574,4223,4225],{"className":4224},[719],[574,4226,4228],{"className":4227},[723],[574,4229,4231],{"className":4230},[727],[574,4232,4234],{"className":4233,"style":2533},[731],[574,4235,4236,4239],{"style":2279},[574,4237],{"className":4238,"style":740},[739],[574,4240,4242],{"className":4241},[744,745,746,747],[574,4243,2470],{"className":4244},[617,747],[574,4246],{"className":4247,"style":1340},[768],[574,4249,1253],{"className":4250},[617,618],[574,4252,682],{"className":4253},[617,618],[574,4255],{"className":4256,"style":769},[768],[574,4258,688],{"className":4259},[773],[574,4261],{"className":4262,"style":769},[768],[574,4264,4266,4270,4424,4427,4430],{"className":4265},[608],[574,4267],{"className":4268,"style":4269},[612],"height:2.6948em;vertical-align:-0.9997em;",[574,4271,4273,4376],{"className":4272},[1904],[574,4274,4276,4282,4370],{"className":4275},[1904],[574,4277,4279],{"className":4278,"style":1912},[757,1911],[574,4280,4110],{"className":4281},[1916,746],[574,4283,4285,4288,4367],{"className":4284},[617],[574,4286],{"className":4287},[757,885],[574,4289,4291],{"className":4290},[855],[574,4292,4294,4359],{"className":4293},[723,892],[574,4295,4297,4356],{"className":4296},[727],[574,4298,4300,4311,4319],{"className":4299,"style":1935},[731],[574,4301,4302,4305],{"style":1938},[574,4303],{"className":4304,"style":906},[739],[574,4306,4308],{"className":4307},[617],[574,4309,2487],{"className":4310},[617],[574,4312,4313,4316],{"style":949},[574,4314],{"className":4315,"style":906},[739],[574,4317],{"className":4318,"style":957},[956],[574,4320,4321,4324],{"style":1972},[574,4322],{"className":4323,"style":906},[739],[574,4325,4327],{"className":4326},[617],[574,4328,4330,4333],{"className":4329},[617],[574,4331,682],{"className":4332},[617,618],[574,4334,4336],{"className":4335},[719],[574,4337,4339],{"className":4338},[723],[574,4340,4342],{"className":4341},[727],[574,4343,4345],{"className":4344,"style":1359},[731],[574,4346,4347,4350],{"style":735},[574,4348],{"className":4349,"style":740},[739],[574,4351,4353],{"className":4352},[744,745,746,747],[574,4354,2487],{"className":4355},[617,747],[574,4357,977],{"className":4358},[976],[574,4360,4362],{"className":4361},[727],[574,4363,4365],{"className":4364,"style":2653},[731],[574,4366],{},[574,4368],{"className":4369},[764,885],[574,4371,4373],{"className":4372,"style":1912},[764,1911],[574,4374,4123],{"className":4375},[1916,746],[574,4377,4379],{"className":4378},[719],[574,4380,4382,4415],{"className":4381},[723,892],[574,4383,4385,4412],{"className":4384},[727],[574,4386,4389,4401],{"className":4387,"style":4388},[731],"height:1.6951em;",[574,4390,4392,4395],{"style":4391},"top:-1.7003em;margin-right:0.05em;",[574,4393],{"className":4394,"style":740},[739],[574,4396,4398],{"className":4397},[744,745,746,747],[574,4399,1165],{"className":4400},[617,747],[574,4402,4403,4406],{"style":2065},[574,4404],{"className":4405,"style":740},[739],[574,4407,4409],{"className":4408},[744,745,746,747],[574,4410,865],{"className":4411},[617,747],[574,4413,977],{"className":4414},[976],[574,4416,4418],{"className":4417},[727],[574,4419,4422],{"className":4420,"style":4421},[731],"height:0.9997em;",[574,4423],{},[574,4425],{"className":4426,"style":769},[768],[574,4428,688],{"className":4429},[773],[574,4431],{"className":4432,"style":769},[768],[574,4434,4436,4439,4501,4504,4507],{"className":4435},[608],[574,4437],{"className":4438,"style":3113},[612],[574,4440,4442,4445,4498],{"className":4441},[617],[574,4443],{"className":4444},[757,885],[574,4446,4448],{"className":4447},[855],[574,4449,4451,4490],{"className":4450},[723,892],[574,4452,4454,4487],{"className":4453},[727],[574,4455,4457,4468,4476],{"className":4456,"style":2820},[731],[574,4458,4459,4462],{"style":1938},[574,4460],{"className":4461,"style":906},[739],[574,4463,4465],{"className":4464},[617],[574,4466,2487],{"className":4467},[617],[574,4469,4470,4473],{"style":949},[574,4471],{"className":4472,"style":906},[739],[574,4474],{"className":4475,"style":957},[956],[574,4477,4478,4481],{"style":1972},[574,4479],{"className":4480,"style":906},[739],[574,4482,4484],{"className":4483},[617],[574,4485,4134],{"className":4486},[617],[574,4488,977],{"className":4489},[976],[574,4491,4493],{"className":4492},[727],[574,4494,4496],{"className":4495,"style":2653},[731],[574,4497],{},[574,4499],{"className":4500},[764,885],[574,4502],{"className":4503,"style":1951},[768],[574,4505,1232],{"className":4506},[1955],[574,4508],{"className":4509,"style":1951},[768],[574,4511,4513,4516,4519,4522,4525],{"className":4512},[608],[574,4514],{"className":4515,"style":831},[612],[574,4517,1165],{"className":4518},[617],[574,4520],{"className":4521,"style":769},[768],[574,4523,688],{"className":4524},[773],[574,4526],{"className":4527,"style":769},[768],[574,4529,4531,4534],{"className":4530},[608],[574,4532],{"className":4533,"style":831},[612],[574,4535,2487],{"className":4536},[617],[560,4538,4540],{"id":4539},"typische-fehler","Typische Fehler",[4542,4543,4544,4841,4973,5175],"ul",{},[801,4545,4546,4547,4682,4683,4686,4687,1440],{},"Nur den Exponenten erhöhen und das Teilen vergessen: ",[574,4548,4550,4584],{"className":4549},[577],[574,4551,4553],{"className":4552},[581],[583,4554,4555],{"xmlns":585},[587,4556,4557,4581],{},[590,4558,4559,4561,4567,4569,4571,4573,4575],{},[671,4560,1227],{},[666,4562,4563,4565],{},[593,4564,682],{},[817,4566,2470],{},[1248,4568,1250],{},[593,4570,1253],{},[593,4572,682],{},[671,4574,688],{},[666,4576,4577,4579],{},[593,4578,682],{},[817,4580,2487],{},[597,4582,4583],{"encoding":599},"\\int x^3 \\, dx = x^4",[574,4585,4587,4647],{"className":4586,"ariaHidden":604},[603],[574,4588,4590,4594,4597,4600,4629,4632,4635,4638,4641,4644],{"className":4589},[608],[574,4591],{"className":4592,"style":4593},[612],"height:1.1202em;vertical-align:-0.3061em;",[574,4595,1227],{"className":4596,"style":1278},[1272,1276,1277],[574,4598],{"className":4599,"style":1340},[768],[574,4601,4603,4606],{"className":4602},[617],[574,4604,682],{"className":4605},[617,618],[574,4607,4609],{"className":4608},[719],[574,4610,4612],{"className":4611},[723],[574,4613,4615],{"className":4614},[727],[574,4616,4618],{"className":4617,"style":1359},[731],[574,4619,4620,4623],{"style":735},[574,4621],{"className":4622,"style":740},[739],[574,4624,4626],{"className":4625},[744,745,746,747],[574,4627,2470],{"className":4628},[617,747],[574,4630],{"className":4631,"style":1340},[768],[574,4633,1253],{"className":4634},[617,618],[574,4636,682],{"className":4637},[617,618],[574,4639],{"className":4640,"style":769},[768],[574,4642,688],{"className":4643},[773],[574,4645],{"className":4646,"style":769},[768],[574,4648,4650,4653],{"className":4649},[608],[574,4651],{"className":4652,"style":1359},[612],[574,4654,4656,4659],{"className":4655},[617],[574,4657,682],{"className":4658},[617,618],[574,4660,4662],{"className":4661},[719],[574,4663,4665],{"className":4664},[723],[574,4666,4668],{"className":4667},[727],[574,4669,4671],{"className":4670,"style":1359},[731],[574,4672,4673,4676],{"style":735},[574,4674],{"className":4675,"style":740},[739],[574,4677,4679],{"className":4678},[744,745,746,747],[574,4680,2487],{"className":4681},[617,747]," ist ",[569,4684,4685],{},"falsch",", richtig ist ",[574,4688,4690,4716],{"className":4689},[577],[574,4691,4693],{"className":4692},[581],[583,4694,4695],{"xmlns":585},[587,4696,4697,4713],{},[590,4698,4699,4709,4711],{},[855,4700,4701,4707],{},[666,4702,4703,4705],{},[593,4704,682],{},[817,4706,2487],{},[817,4708,2487],{},[671,4710,1824],{},[593,4712,1765],{},[597,4714,4715],{"encoding":599},"\\frac{x^4}{4} + C",[574,4717,4719,4832],{"className":4718,"ariaHidden":604},[603],[574,4720,4722,4726,4823,4826,4829],{"className":4721},[608],[574,4723],{"className":4724,"style":4725},[612],"height:1.3629em;vertical-align:-0.345em;",[574,4727,4729,4732,4820],{"className":4728},[617],[574,4730],{"className":4731},[757,885],[574,4733,4735],{"className":4734},[855],[574,4736,4738,4812],{"className":4737},[723,892],[574,4739,4741,4809],{"className":4740},[727],[574,4742,4745,4759,4767],{"className":4743,"style":4744},[731],"height:1.0179em;",[574,4746,4747,4750],{"style":902},[574,4748],{"className":4749,"style":906},[739],[574,4751,4753],{"className":4752},[744,745,746,747],[574,4754,4756],{"className":4755},[617,747],[574,4757,2487],{"className":4758},[617,747],[574,4760,4761,4764],{"style":949},[574,4762],{"className":4763,"style":906},[739],[574,4765],{"className":4766,"style":957},[956],[574,4768,4769,4772],{"style":960},[574,4770],{"className":4771,"style":906},[739],[574,4773,4775],{"className":4774},[744,745,746,747],[574,4776,4778],{"className":4777},[617,747],[574,4779,4781,4784],{"className":4780},[617,747],[574,4782,682],{"className":4783},[617,618,747],[574,4785,4787],{"className":4786},[719],[574,4788,4790],{"className":4789},[723],[574,4791,4793],{"className":4792},[727],[574,4794,4797],{"className":4795,"style":4796},[731],"height:0.8913em;",[574,4798,4800,4803],{"style":4799},"top:-2.931em;margin-right:0.0714em;",[574,4801],{"className":4802,"style":938},[739],[574,4804,4806],{"className":4805},[744,942,943,747],[574,4807,2487],{"className":4808},[617,747],[574,4810,977],{"className":4811},[976],[574,4813,4815],{"className":4814},[727],[574,4816,4818],{"className":4817,"style":984},[731],[574,4819],{},[574,4821],{"className":4822},[764,885],[574,4824],{"className":4825,"style":1951},[768],[574,4827,1824],{"className":4828},[1955],[574,4830],{"className":4831,"style":1951},[768],[574,4833,4835,4838],{"className":4834},[608],[574,4836],{"className":4837,"style":613},[612],[574,4839,1765],{"className":4840,"style":1780},[617,618],[801,4842,4843,4844,4972],{},"Durch den alten statt durch den neuen Exponenten teilen: ",[574,4845,4847,4869],{"className":4846},[577],[574,4848,4850],{"className":4849},[581],[583,4851,4852],{"xmlns":585},[587,4853,4854,4866],{},[590,4855,4856],{},[855,4857,4858,4864],{},[666,4859,4860,4862],{},[593,4861,682],{},[817,4863,2487],{},[817,4865,2470],{},[597,4867,4868],{"encoding":599},"\\frac{x^4}{3}",[574,4870,4872],{"className":4871,"ariaHidden":604},[603],[574,4873,4875,4878],{"className":4874},[608],[574,4876],{"className":4877,"style":4725},[612],[574,4879,4881,4884,4969],{"className":4880},[617],[574,4882],{"className":4883},[757,885],[574,4885,4887],{"className":4886},[855],[574,4888,4890,4961],{"className":4889},[723,892],[574,4891,4893,4958],{"className":4892},[727],[574,4894,4896,4910,4918],{"className":4895,"style":4744},[731],[574,4897,4898,4901],{"style":902},[574,4899],{"className":4900,"style":906},[739],[574,4902,4904],{"className":4903},[744,745,746,747],[574,4905,4907],{"className":4906},[617,747],[574,4908,2470],{"className":4909},[617,747],[574,4911,4912,4915],{"style":949},[574,4913],{"className":4914,"style":906},[739],[574,4916],{"className":4917,"style":957},[956],[574,4919,4920,4923],{"style":960},[574,4921],{"className":4922,"style":906},[739],[574,4924,4926],{"className":4925},[744,745,746,747],[574,4927,4929],{"className":4928},[617,747],[574,4930,4932,4935],{"className":4931},[617,747],[574,4933,682],{"className":4934},[617,618,747],[574,4936,4938],{"className":4937},[719],[574,4939,4941],{"className":4940},[723],[574,4942,4944],{"className":4943},[727],[574,4945,4947],{"className":4946,"style":4796},[731],[574,4948,4949,4952],{"style":4799},[574,4950],{"className":4951,"style":938},[739],[574,4953,4955],{"className":4954},[744,942,943,747],[574,4956,2487],{"className":4957},[617,747],[574,4959,977],{"className":4960},[976],[574,4962,4964],{"className":4963},[727],[574,4965,4967],{"className":4966,"style":984},[731],[574,4968],{},[574,4970],{"className":4971},[764,885]," ist falsch.",[801,4974,4975,4976,5074,5075,5103,5104,1440],{},"Die Regel auf ",[574,4977,4979,4997],{"className":4978},[577],[574,4980,4982],{"className":4981},[581],[583,4983,4984],{"xmlns":585},[587,4985,4986,4994],{},[590,4987,4988],{},[855,4989,4990,4992],{},[817,4991,819],{},[593,4993,682],{},[597,4995,4996],{"encoding":599},"\\frac{1}{x}",[574,4998,5000],{"className":4999,"ariaHidden":604},[603],[574,5001,5003,5006],{"className":5002},[608],[574,5004],{"className":5005,"style":878},[612],[574,5007,5009,5012,5071],{"className":5008},[617],[574,5010],{"className":5011},[757,885],[574,5013,5015],{"className":5014},[855],[574,5016,5018,5063],{"className":5017},[723,892],[574,5019,5021,5060],{"className":5020},[727],[574,5022,5024,5038,5046],{"className":5023,"style":899},[731],[574,5025,5026,5029],{"style":902},[574,5027],{"className":5028,"style":906},[739],[574,5030,5032],{"className":5031},[744,745,746,747],[574,5033,5035],{"className":5034},[617,747],[574,5036,682],{"className":5037},[617,618,747],[574,5039,5040,5043],{"style":949},[574,5041],{"className":5042,"style":906},[739],[574,5044],{"className":5045,"style":957},[956],[574,5047,5048,5051],{"style":960},[574,5049],{"className":5050,"style":906},[739],[574,5052,5054],{"className":5053},[744,745,746,747],[574,5055,5057],{"className":5056},[617,747],[574,5058,819],{"className":5059},[617,747],[574,5061,977],{"className":5062},[976],[574,5064,5066],{"className":5065},[727],[574,5067,5069],{"className":5068,"style":984},[731],[574,5070],{},[574,5072],{"className":5073},[764,885]," anwenden. Das ergibt eine Division durch ",[574,5076,5078,5091],{"className":5077},[577],[574,5079,5081],{"className":5080},[581],[583,5082,5083],{"xmlns":585},[587,5084,5085,5089],{},[590,5086,5087],{},[817,5088,1165],{},[597,5090,1165],{"encoding":599},[574,5092,5094],{"className":5093,"ariaHidden":604},[603],[574,5095,5097,5100],{"className":5096},[608],[574,5098],{"className":5099,"style":831},[612],[574,5101,1165],{"className":5102},[617],"; richtig ist ",[574,5105,5107,5133],{"className":5106},[577],[574,5108,5110],{"className":5109},[581],[583,5111,5112],{"xmlns":585},[587,5113,5114,5130],{},[590,5115,5116,5118,5120,5122,5124,5126,5128],{},[593,5117,1707],{},[671,5119,1710],{},[593,5121,1713],{"mathvariant":673},[593,5123,682],{},[593,5125,1713],{"mathvariant":673},[671,5127,1824],{},[593,5129,1765],{},[597,5131,5132],{"encoding":599},"\\ln|x| + C",[574,5134,5136,5166],{"className":5135,"ariaHidden":604},[603],[574,5137,5139,5142,5145,5148,5151,5154,5157,5160,5163],{"className":5138},[608],[574,5140],{"className":5141,"style":783},[612],[574,5143,1707],{"className":5144},[1272],[574,5146],{"className":5147,"style":1340},[768],[574,5149,1713],{"className":5150},[617],[574,5152,682],{"className":5153},[617,618],[574,5155,1713],{"className":5156},[617],[574,5158],{"className":5159,"style":1951},[768],[574,5161,1824],{"className":5162},[1955],[574,5164],{"className":5165,"style":1951},[768],[574,5167,5169,5172],{"className":5168},[608],[574,5170],{"className":5171,"style":613},[612],[574,5173,1765],{"className":5174,"style":1780},[617,618],[801,5176,5177,5304,5305,5374,5375,5452],{},[574,5178,5180,5201],{"className":5179},[577],[574,5181,5183],{"className":5182},[581],[583,5184,5185],{"xmlns":585},[587,5186,5187,5199],{},[590,5188,5189],{},[855,5190,5191,5193],{},[817,5192,819],{},[666,5194,5195,5197],{},[593,5196,682],{},[817,5198,865],{},[597,5200,868],{"encoding":599},[574,5202,5204],{"className":5203,"ariaHidden":604},[603],[574,5205,5207,5210],{"className":5206},[608],[574,5208],{"className":5209,"style":878},[612],[574,5211,5213,5216,5301],{"className":5212},[617],[574,5214],{"className":5215},[757,885],[574,5217,5219],{"className":5218},[855],[574,5220,5222,5293],{"className":5221},[723,892],[574,5223,5225,5290],{"className":5224},[727],[574,5226,5228,5268,5276],{"className":5227,"style":899},[731],[574,5229,5230,5233],{"style":902},[574,5231],{"className":5232,"style":906},[739],[574,5234,5236],{"className":5235},[744,745,746,747],[574,5237,5239],{"className":5238},[617,747],[574,5240,5242,5245],{"className":5241},[617,747],[574,5243,682],{"className":5244},[617,618,747],[574,5246,5248],{"className":5247},[719],[574,5249,5251],{"className":5250},[723],[574,5252,5254],{"className":5253},[727],[574,5255,5257],{"className":5256,"style":931},[731],[574,5258,5259,5262],{"style":934},[574,5260],{"className":5261,"style":938},[739],[574,5263,5265],{"className":5264},[744,942,943,747],[574,5266,865],{"className":5267},[617,747],[574,5269,5270,5273],{"style":949},[574,5271],{"className":5272,"style":906},[739],[574,5274],{"className":5275,"style":957},[956],[574,5277,5278,5281],{"style":960},[574,5279],{"className":5280,"style":906},[739],[574,5282,5284],{"className":5283},[744,745,746,747],[574,5285,5287],{"className":5286},[617,747],[574,5288,819],{"className":5289},[617,747],[574,5291,977],{"className":5292},[976],[574,5294,5296],{"className":5295},[727],[574,5297,5299],{"className":5298,"style":984},[731],[574,5300],{},[574,5302],{"className":5303},[764,885]," nicht als ",[574,5306,5308,5330],{"className":5307},[577],[574,5309,5311],{"className":5310},[581],[583,5312,5313],{"xmlns":585},[587,5314,5315,5327],{},[590,5316,5317],{},[666,5318,5319,5321],{},[593,5320,682],{},[590,5322,5323,5325],{},[671,5324,1232],{},[817,5326,865],{},[597,5328,5329],{"encoding":599},"x^{-2}",[574,5331,5333],{"className":5332,"ariaHidden":604},[603],[574,5334,5336,5339],{"className":5335},[608],[574,5337],{"className":5338,"style":1359},[612],[574,5340,5342,5345],{"className":5341},[617],[574,5343,682],{"className":5344},[617,618],[574,5346,5348],{"className":5347},[719],[574,5349,5351],{"className":5350},[723],[574,5352,5354],{"className":5353},[727],[574,5355,5357],{"className":5356,"style":1359},[731],[574,5358,5359,5362],{"style":735},[574,5360],{"className":5361,"style":740},[739],[574,5363,5365],{"className":5364},[744,745,746,747],[574,5366,5368,5371],{"className":5367},[617,747],[574,5369,1232],{"className":5370},[617,747],[574,5372,865],{"className":5373},[617,747]," umschreiben und stattdessen ",[574,5376,5378,5404],{"className":5377},[577],[574,5379,5381],{"className":5380},[581],[583,5382,5383],{"xmlns":585},[587,5384,5385,5401],{},[590,5386,5387,5389,5391,5393,5399],{},[593,5388,1707],{},[671,5390,1710],{},[671,5392,679],{"stretchy":678},[666,5394,5395,5397],{},[593,5396,682],{},[817,5398,865],{},[671,5400,685],{"stretchy":678},[597,5402,5403],{"encoding":599},"\\ln(x^2)",[574,5405,5407],{"className":5406,"ariaHidden":604},[603],[574,5408,5410,5414,5417,5420,5449],{"className":5409},[608],[574,5411],{"className":5412,"style":5413},[612],"height:1.0641em;vertical-align:-0.25em;",[574,5415,1707],{"className":5416},[1272],[574,5418,679],{"className":5419},[757],[574,5421,5423,5426],{"className":5422},[617],[574,5424,682],{"className":5425},[617,618],[574,5427,5429],{"className":5428},[719],[574,5430,5432],{"className":5431},[723],[574,5433,5435],{"className":5434},[727],[574,5436,5438],{"className":5437,"style":1359},[731],[574,5439,5440,5443],{"style":735},[574,5441],{"className":5442,"style":740},[739],[574,5444,5446],{"className":5445},[744,745,746,747],[574,5447,865],{"className":5448},[617,747],[574,5450,685],{"className":5451},[764]," ansetzen.",{"title":5454,"searchDepth":5455,"depth":5455,"links":5456},"",2,[5457,5458,5459,5460],{"id":562,"depth":5455,"text":563},{"id":1784,"depth":5455,"text":1785},{"id":2445,"depth":5455,"text":2446},{"id":4539,"depth":5455,"text":4540},[5462,5465,5467,5470,5473,5476,5478],{"lhs":5463,"rhs":5464},"round(sum(map(0:999, f(k) = (1 + (k + 0.5) \u002F 1000)^(-2))) \u002F 1000, 4)","0.5",{"lhs":5466,"rhs":5464},"(2^(-2 + 1) - 1^(-2 + 1)) \u002F (-2 + 1)",{"lhs":5468,"rhs":5469},"x^(3 + 1) \u002F (3 + 1)","x^4 \u002F 4",{"lhs":5471,"rhs":5472},"x^(-2 + 1) \u002F (-2 + 1)","-1 \u002F x",{"lhs":5474,"rhs":5475},"x^(1\u002F2 + 1) \u002F (1\u002F2 + 1)","2\u002F3 * x^(3\u002F2)",{"lhs":5477,"rhs":2487},"2^4 \u002F 4 - 0^4 \u002F 4",{"lhs":5479,"rhs":2487},"round(sum(map(0:999, f(k) = ((k + 0.5) * 2 \u002F 1000)^3)) * 2 \u002F 1000, 4)","n \\neq -1,\\ x^n \\text{ definiert; für } n \u003C 0: x \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\neq -1,\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\">n\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\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x^n\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:0.6644em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\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 mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">definiert; für\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>:\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n < 0: x \\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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\">x\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","antiderivative-power","\\int x^n \\, dx = \\frac{x^{n+1}}{n+1} + 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>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int x^n \\, dx = \\frac{x^{n+1}}{n+1} + 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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:2.2604em;vertical-align:-0.7693em;\">\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:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\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>\u003Cspan class=\"mord\">1\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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\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 mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin 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