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\\frac{f'(x)}{f(x)}\\,dx = \\ln|f(x)| + C",[569,1034,1036,1195,1237],{"className":1035,"ariaHidden":674},[673],[569,1037,1039,1043,1049,1052,1177,1180,1183,1186,1189,1192],{"className":1038},[678],[569,1040],{"className":1041,"style":1042},[682],"height:1.5845em;vertical-align:-0.52em;",[569,1044,967],{"className":1045,"style":1048},[687,1046,1047],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[569,1050],{"className":1051,"style":692},[691],[569,1053,1055,1058,1174],{"className":1054},[696],[569,1056],{"className":1057},[722,723],[569,1059,1061],{"className":1060},[607],[569,1062,1064,1165],{"className":1063},[730,731],[569,1065,1067,1162],{"className":1066},[735],[569,1068,1071,1096,1104],{"className":1069,"style":1070},[739],"height:1.0645em;",[569,1072,1074,1077],{"style":1073},"top:-2.655em;",[569,1075],{"className":1076,"style":748},[747],[569,1078,1080],{"className":1079},[921,922,923,924],[569,1081,1083,1087,1090,1093],{"className":1082},[696,924],[569,1084,976],{"className":1085,"style":1086},[696,697,924],"margin-right:0.1076em;",[569,1088,639],{"className":1089},[722,924],[569,1091,602],{"className":1092},[696,697,924],[569,1094,651],{"className":1095},[807,924],[569,1097,1098,1101],{"style":763},[569,1099],{"className":1100,"style":748},[747],[569,1102],{"className":1103,"style":771},[770],[569,1105,1107,1110],{"style":1106},"top:-3.485em;",[569,1108],{"className":1109,"style":748},[747],[569,1111,1113],{"className":1112},[921,922,923,924],[569,1114,1116,1153,1156,1159],{"className":1115},[696,924],[569,1117,1119,1122],{"className":1118},[696,924],[569,1120,976],{"className":1121,"style":1086},[696,697,924],[569,1123,1125],{"className":1124},[900],[569,1126,1128],{"className":1127},[730],[569,1129,1131],{"className":1130},[735],[569,1132,1135],{"className":1133,"style":1134},[739],"height:0.8278em;",[569,1136,1138,1142],{"style":1137},"top:-2.931em;margin-right:0.0714em;",[569,1139],{"className":1140,"style":1141},[747],"height:2.5em;",[569,1143,1147],{"className":1144},[921,1145,1146,924],"reset-size3","size1",[569,1148,1150],{"className":1149},[696,924],[569,1151,656],{"className":1152},[696,924],[569,1154,639],{"className":1155},[722,924],[569,1157,602],{"className":1158},[696,697,924],[569,1160,651],{"className":1161},[807,924],[569,1163,794],{"className":1164},[793],[569,1166,1168],{"className":1167},[735],[569,1169,1172],{"className":1170,"style":1171},[739],"height:0.52em;",[569,1173],{},[569,1175],{"className":1176},[807,723],[569,1178],{"className":1179,"style":692},[691],[569,1181,1001],{"className":1182},[696,697],[569,1184,602],{"className":1185},[696,697],[569,1187],{"className":1188,"style":701},[691],[569,1190,605],{"className":1191},[705],[569,1193],{"className":1194,"style":701},[691],[569,1196,1198,1202,1205,1208,1211,1214,1217,1220,1223,1226,1230,1234],{"className":1197},[678],[569,1199],{"className":1200,"style":1201},[682],"height:1em;vertical-align:-0.25em;",[569,1203,1008],{"className":1204},[687],[569,1206],{"className":1207,"style":692},[691],[569,1209,1013],{"className":1210},[696],[569,1212,976],{"className":1213,"style":1086},[696,697],[569,1215,639],{"className":1216},[722],[569,1218,602],{"className":1219},[696,697],[569,1221,651],{"className":1222},[807],[569,1224,1013],{"className":1225},[696],[569,1227],{"className":1228,"style":1229},[691],"margin-right:0.2222em;",[569,1231,1026],{"className":1232},[1233],"mbin",[569,1235],{"className":1236,"style":1229},[691],[569,1238,1240,1244],{"className":1239},[678],[569,1241],{"className":1242,"style":1243},[682],"height:0.6833em;",[569,1245,1029],{"className":1246,"style":1247},[696,697],"margin-right:0.0715em;",".",[565,1250,1251,1252,1318,1319,1375,1376,1534],{},"Die Betragsstriche sind wichtig: Auf Intervallen, auf denen ",[569,1253,1255,1280],{"className":1254},[576],[569,1256,1258],{"className":1257},[580],[582,1259,1260],{"xmlns":584},[587,1261,1262,1277],{},[590,1263,1264,1266,1268,1270,1273],{},[593,1265,622],{},[597,1267,599],{},[593,1269,602],{},[597,1271,1272],{},"\u003C",[1274,1275,1276],"mn",{},"0",[666,1278,1279],{"encoding":668},"\\cos x \u003C 0",[569,1281,1283,1308],{"className":1282,"ariaHidden":674},[673],[569,1284,1286,1290,1293,1296,1299,1302,1305],{"className":1285},[678],[569,1287],{"className":1288,"style":1289},[682],"height:0.5782em;vertical-align:-0.0391em;",[569,1291,622],{"className":1292},[687],[569,1294],{"className":1295,"style":692},[691],[569,1297,602],{"className":1298},[696,697],[569,1300],{"className":1301,"style":701},[691],[569,1303,1272],{"className":1304},[705],[569,1306],{"className":1307,"style":701},[691],[569,1309,1311,1315],{"className":1310},[678],[569,1312],{"className":1313,"style":1314},[682],"height:0.6444em;",[569,1316,1276],{"className":1317},[696]," ist, wäre ",[569,1320,1322,1348],{"className":1321},[576],[569,1323,1325],{"className":1324},[580],[582,1326,1327],{"xmlns":584},[587,1328,1329,1345],{},[590,1330,1331,1333,1335,1337,1339,1341,1343],{},[593,1332,1008],{},[597,1334,599],{},[597,1336,639],{"stretchy":638},[593,1338,622],{},[597,1340,599],{},[593,1342,602],{},[597,1344,651],{"stretchy":638},[666,1346,1347],{"encoding":668},"\\ln(\\cos x)",[569,1349,1351],{"className":1350,"ariaHidden":674},[673],[569,1352,1354,1357,1360,1363,1366,1369,1372],{"className":1353},[678],[569,1355],{"className":1356,"style":1201},[682],[569,1358,1008],{"className":1359},[687],[569,1361,639],{"className":1362},[722],[569,1364,622],{"className":1365},[687],[569,1367],{"className":1368,"style":692},[691],[569,1370,602],{"className":1371},[696,697],[569,1373,651],{"className":1374},[807]," nicht definiert. Ein bestimmtes Integral darf keine Polstelle ",[569,1377,1379,1410],{"className":1378},[576],[569,1380,1382],{"className":1381},[580],[582,1383,1384],{"xmlns":584},[587,1385,1386,1407],{},[590,1387,1388,1390,1392,1400,1402,1405],{},[593,1389,602],{},[597,1391,605],{},[607,1393,1394,1397],{},[593,1395,1396],{},"π",[1274,1398,1399],{},"2",[597,1401,1026],{},[593,1403,1404],{},"k",[593,1406,1396],{},[666,1408,1409],{"encoding":668},"x = \\frac{\\pi}{2} + k\\pi",[569,1411,1413,1432,1520],{"className":1412,"ariaHidden":674},[673],[569,1414,1416,1420,1423,1426,1429],{"className":1415},[678],[569,1417],{"className":1418,"style":1419},[682],"height:0.4306em;",[569,1421,602],{"className":1422},[696,697],[569,1424],{"className":1425,"style":701},[691],[569,1427,605],{"className":1428},[705],[569,1430],{"className":1431,"style":701},[691],[569,1433,1435,1439,1511,1514,1517],{"className":1434},[678],[569,1436],{"className":1437,"style":1438},[682],"height:1.0404em;vertical-align:-0.345em;",[569,1440,1442,1445,1508],{"className":1441},[696],[569,1443],{"className":1444},[722,723],[569,1446,1448],{"className":1447},[607],[569,1449,1451,1499],{"className":1450},[730,731],[569,1452,1454,1496],{"className":1453},[735],[569,1455,1458,1472,1480],{"className":1456,"style":1457},[739],"height:0.6954em;",[569,1459,1460,1463],{"style":1073},[569,1461],{"className":1462,"style":748},[747],[569,1464,1466],{"className":1465},[921,922,923,924],[569,1467,1469],{"className":1468},[696,924],[569,1470,1399],{"className":1471},[696,924],[569,1473,1474,1477],{"style":763},[569,1475],{"className":1476,"style":748},[747],[569,1478],{"className":1479,"style":771},[770],[569,1481,1483,1486],{"style":1482},"top:-3.394em;",[569,1484],{"className":1485,"style":748},[747],[569,1487,1489],{"className":1488},[921,922,923,924],[569,1490,1492],{"className":1491},[696,924],[569,1493,1396],{"className":1494,"style":1495},[696,697,924],"margin-right:0.0359em;",[569,1497,794],{"className":1498},[793],[569,1500,1502],{"className":1501},[735],[569,1503,1506],{"className":1504,"style":1505},[739],"height:0.345em;",[569,1507],{},[569,1509],{"className":1510},[807,723],[569,1512],{"className":1513,"style":1229},[691],[569,1515,1026],{"className":1516},[1233],[569,1518],{"className":1519,"style":1229},[691],[569,1521,1523,1527,1531],{"className":1522},[678],[569,1524],{"className":1525,"style":1526},[682],"height:0.6944em;",[569,1528,1404],{"className":1529,"style":1530},[696,697],"margin-right:0.0315em;",[569,1532,1396],{"className":1533,"style":1495},[696,697]," einschließen.",[565,1536,1537,1538,1750,1751,1836],{},"Wegen ",[569,1539,1541,1592],{"className":1540},[576],[569,1542,1544],{"className":1543},[580],[582,1545,1546],{"xmlns":584},[587,1547,1548,1589],{},[590,1549,1550,1552,1554,1556,1558,1560,1562,1564,1566,1568,1570,1572],{},[597,1551,631],{},[593,1553,1008],{},[597,1555,599],{},[593,1557,1013],{"mathvariant":654},[593,1559,622],{},[597,1561,599],{},[593,1563,602],{},[593,1565,1013],{"mathvariant":654},[597,1567,605],{},[593,1569,1008],{},[597,1571,599],{},[607,1573,1574,1577],{},[1274,1575,1576],{},"1",[590,1578,1579,1581,1583,1585,1587],{},[593,1580,1013],{"mathvariant":654},[593,1582,622],{},[597,1584,599],{},[593,1586,602],{},[593,1588,1013],{"mathvariant":654},[666,1590,1591],{"encoding":668},"-\\ln|\\cos x| = \\ln\\frac{1}{|\\cos x|}",[569,1593,1595,1640],{"className":1594,"ariaHidden":674},[673],[569,1596,1598,1601,1604,1607,1610,1613,1616,1619,1622,1625,1628,1631,1634,1637],{"className":1597},[678],[569,1599],{"className":1600,"style":1201},[682],[569,1602,631],{"className":1603},[696],[569,1605],{"className":1606,"style":692},[691],[569,1608,1008],{"className":1609},[687],[569,1611],{"className":1612,"style":692},[691],[569,1614,1013],{"className":1615},[696],[569,1617],{"className":1618,"style":692},[691],[569,1620,622],{"className":1621},[687],[569,1623],{"className":1624,"style":692},[691],[569,1626,602],{"className":1627},[696,697],[569,1629,1013],{"className":1630},[696],[569,1632],{"className":1633,"style":701},[691],[569,1635,605],{"className":1636},[705],[569,1638],{"className":1639,"style":701},[691],[569,1641,1643,1647,1650,1653],{"className":1642},[678],[569,1644],{"className":1645,"style":1646},[682],"height:1.3651em;vertical-align:-0.52em;",[569,1648,1008],{"className":1649},[687],[569,1651],{"className":1652,"style":692},[691],[569,1654,1656,1659,1747],{"className":1655},[696],[569,1657],{"className":1658},[722,723],[569,1660,1662],{"className":1661},[607],[569,1663,1665,1739],{"className":1664},[730,731],[569,1666,1668,1736],{"className":1667},[735],[569,1669,1672,1714,1722],{"className":1670,"style":1671},[739],"height:0.8451em;",[569,1673,1674,1677],{"style":1073},[569,1675],{"className":1676,"style":748},[747],[569,1678,1680],{"className":1679},[921,922,923,924],[569,1681,1683,1686,1690,1705,1708,1711],{"className":1682},[696,924],[569,1684,1013],{"className":1685},[696,924],[569,1687],{"className":1688,"style":1689},[691,924],"margin-right:0.1952em;",[569,1691,1693,1697,1701],{"className":1692},[687,924],[569,1694,1696],{"className":1695},[924],"c",[569,1698,1700],{"className":1699},[924],"o",[569,1702,1704],{"className":1703},[924],"s",[569,1706],{"className":1707,"style":1689},[691,924],[569,1709,602],{"className":1710},[696,697,924],[569,1712,1013],{"className":1713},[696,924],[569,1715,1716,1719],{"style":763},[569,1717],{"className":1718,"style":748},[747],[569,1720],{"className":1721,"style":771},[770],[569,1723,1724,1727],{"style":1482},[569,1725],{"className":1726,"style":748},[747],[569,1728,1730],{"className":1729},[921,922,923,924],[569,1731,1733],{"className":1732},[696,924],[569,1734,1576],{"className":1735},[696,924],[569,1737,794],{"className":1738},[793],[569,1740,1742],{"className":1741},[735],[569,1743,1745],{"className":1744,"style":1171},[739],[569,1746],{},[569,1748],{"className":1749},[807,723]," findet man die Stammfunktion auch als ",[569,1752,1754,1785],{"className":1753},[576],[569,1755,1757],{"className":1756},[580],[582,1758,1759],{"xmlns":584},[587,1760,1761,1782],{},[590,1762,1763,1765,1767,1769,1772,1774,1776,1778,1780],{},[593,1764,1008],{},[597,1766,599],{},[593,1768,1013],{"mathvariant":654},[593,1770,1771],{},"sec",[597,1773,599],{},[593,1775,602],{},[593,1777,1013],{"mathvariant":654},[597,1779,1026],{},[593,1781,1029],{},[666,1783,1784],{"encoding":668},"\\ln|\\sec x| + C",[569,1786,1788,1827],{"className":1787,"ariaHidden":674},[673],[569,1789,1791,1794,1797,1800,1803,1806,1809,1812,1815,1818,1821,1824],{"className":1790},[678],[569,1792],{"className":1793,"style":1201},[682],[569,1795,1008],{"className":1796},[687],[569,1798],{"className":1799,"style":692},[691],[569,1801,1013],{"className":1802},[696],[569,1804],{"className":1805,"style":692},[691],[569,1807,1771],{"className":1808},[687],[569,1810],{"className":1811,"style":692},[691],[569,1813,602],{"className":1814},[696,697],[569,1816,1013],{"className":1817},[696],[569,1819],{"className":1820,"style":1229},[691],[569,1822,1026],{"className":1823},[1233],[569,1825],{"className":1826,"style":1229},[691],[569,1828,1830,1833],{"className":1829},[678],[569,1831],{"className":1832,"style":1243},[682],[569,1834,1029],{"className":1835,"style":1247},[696,697]," geschrieben.",[565,1838,1839],{},"Genauso erhält man für den Kotangens:",[569,1841,1843],{"className":1842},[572],[569,1844,1846,1908],{"className":1845},[576],[569,1847,1849],{"className":1848},[580],[582,1850,1851],{"xmlns":584,"display":585},[587,1852,1853,1905],{},[590,1854,1855,1857,1860,1862,1864,1866,1868,1870,1872,1874,1876,1878,1880,1882,1884,1886,1888,1890,1893,1896,1898,1901,1903],{},[597,1856,967],{},[593,1858,1859],{},"cot",[597,1861,599],{},[593,1863,602],{},[996,1865,998],{},[593,1867,1001],{},[593,1869,602],{},[597,1871,605],{},[593,1873,1008],{},[597,1875,599],{},[593,1877,1013],{"mathvariant":654},[593,1879,613],{},[597,1881,599],{},[593,1883,602],{},[593,1885,1013],{"mathvariant":654},[597,1887,1026],{},[593,1889,1029],{},[597,1891,1892],{"separator":674},",",[691,1894],{"width":1895},"2em",[593,1897,602],{},[597,1899,1900],{"mathvariant":654},"≠",[593,1902,1404],{},[593,1904,1396],{},[666,1906,1907],{"encoding":668},"\\int \\cot x\\,dx = \\ln|\\sin x| + C, \\qquad x \\neq k\\pi",[569,1909,1911,1953,1992,2065],{"className":1910,"ariaHidden":674},[673],[569,1912,1914,1918,1923,1926,1929,1932,1935,1938,1941,1944,1947,1950],{"className":1913},[678],[569,1915],{"className":1916,"style":1917},[682],"height:2.2222em;vertical-align:-0.8622em;",[569,1919,967],{"className":1920,"style":1922},[687,1046,1921],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[569,1924],{"className":1925,"style":692},[691],[569,1927,1859],{"className":1928},[687],[569,1930],{"className":1931,"style":692},[691],[569,1933,602],{"className":1934},[696,697],[569,1936],{"className":1937,"style":692},[691],[569,1939,1001],{"className":1940},[696,697],[569,1942,602],{"className":1943},[696,697],[569,1945],{"className":1946,"style":701},[691],[569,1948,605],{"className":1949},[705],[569,1951],{"className":1952,"style":701},[691],[569,1954,1956,1959,1962,1965,1968,1971,1974,1977,1980,1983,1986,1989],{"className":1955},[678],[569,1957],{"className":1958,"style":1201},[682],[569,1960,1008],{"className":1961},[687],[569,1963],{"className":1964,"style":692},[691],[569,1966,1013],{"className":1967},[696],[569,1969],{"className":1970,"style":692},[691],[569,1972,613],{"className":1973},[687],[569,1975],{"className":1976,"style":692},[691],[569,1978,602],{"className":1979},[696,697],[569,1981,1013],{"className":1982},[696],[569,1984],{"className":1985,"style":1229},[691],[569,1987,1026],{"className":1988},[1233],[569,1990],{"className":1991,"style":1229},[691],[569,1993,1995,1999,2002,2006,2010,2013,2016,2019,2062],{"className":1994},[678],[569,1996],{"className":1997,"style":1998},[682],"height:0.8889em;vertical-align:-0.1944em;",[569,2000,1029],{"className":2001,"style":1247},[696,697],[569,2003,1892],{"className":2004},[2005],"mpunct",[569,2007],{"className":2008,"style":2009},[691],"margin-right:2em;",[569,2011],{"className":2012,"style":692},[691],[569,2014,602],{"className":2015},[696,697],[569,2017],{"className":2018,"style":701},[691],[569,2020,2022,2055,2059],{"className":2021},[705],[569,2023,2025],{"className":2024},[705],[569,2026,2029],{"className":2027},[696,2028],"vbox",[569,2030,2033],{"className":2031},[2032],"thinbox",[569,2034,2037,2040,2051],{"className":2035},[2036],"rlap",[569,2038],{"className":2039,"style":1998},[682],[569,2041,2044],{"className":2042},[2043],"inner",[569,2045,2047],{"className":2046},[696],[569,2048,2050],{"className":2049},[705],"",[569,2052],{"className":2053},[2054],"fix",[569,2056],{"className":2057},[691,2058],"nobreak",[569,2060,605],{"className":2061},[705],[569,2063],{"className":2064,"style":701},[691],[569,2066,2068,2071,2074],{"className":2067},[678],[569,2069],{"className":2070,"style":1526},[682],[569,2072,1404],{"className":2073,"style":1530},[696,697],[569,2075,1396],{"className":2076,"style":1495},[696,697],[560,2078,2080],{"id":2079},"beispiele","Beispiele",[565,2082,2083,2084,2112,2113,2212,2213,2479,2480,2541],{},"Von 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mit ",[569,2214,2216,2249],{"className":2215},[576],[569,2217,2219],{"className":2218},[580],[582,2220,2221],{"xmlns":584},[587,2222,2223,2246],{},[590,2224,2225,2227,2229,2235,2237],{},[593,2226,622],{},[597,2228,599],{},[607,2230,2231,2233],{},[593,2232,1396],{},[1274,2234,2131],{},[597,2236,605],{},[607,2238,2239,2241],{},[1274,2240,1576],{},[2242,2243,2244],"msqrt",{},[1274,2245,1399],{},[666,2247,2248],{"encoding":668},"\\cos\\frac{\\pi}{4} = 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0 400000 1080","xMinYMin slice",[2427,2428],"path",{"d":2429},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 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",[569,2481,2483,2505],{"className":2482},[576],[569,2484,2486],{"className":2485},[580],[582,2487,2488],{"xmlns":584},[587,2489,2490,2502],{},[590,2491,2492,2494,2496,2498,2500],{},[593,2493,622],{},[597,2495,599],{},[1274,2497,1276],{},[597,2499,605],{},[1274,2501,1576],{},[666,2503,2504],{"encoding":668},"\\cos 0 = 1",[569,2506,2508,2532],{"className":2507,"ariaHidden":674},[673],[569,2509,2511,2514,2517,2520,2523,2526,2529],{"className":2510},[678],[569,2512],{"className":2513,"style":1314},[682],[569,2515,622],{"className":2516},[687],[569,2518],{"className":2519,"style":692},[691],[569,2521,1276],{"className":2522},[696],[569,2524],{"className":2525,"style":701},[691],[569,2527,605],{"className":2528},[705],[569,2530],{"className":2531,"style":701},[691],[569,2533,2535,2538],{"className":2534},[678],[569,2536],{"className":2537,"style":1314},[682],[569,2539,1576],{"className":2540},[696],":",[569,2543,2545],{"className":2544},[572],[569,2546,2548,2629],{"className":2547},[576],[569,2549,2551],{"className":2550},[580],[582,2552,2553],{"xmlns":584,"display":585},[587,2554,2555,2626],{},[590,2556,2557,2570,2572,2574,2576,2578,2580,2582,2584,2586,2588,2590,2598,2600,2602,2604,2606,2608,2614,2616,2618,2620,2623],{},[2558,2559,2560,2562,2564],"msubsup",{},[597,2561,967],{},[1274,2563,1276],{},[607,2565,2566,2568],{},[593,2567,1396],{},[1274,2569,2131],{},[593,2571,595],{},[597,2573,599],{},[593,2575,602],{},[996,2577,998],{},[593,2579,1001],{},[593,2581,602],{},[597,2583,605],{},[597,2585,631],{},[593,2587,1008],{},[597,2589,599],{},[607,2591,2592,2594],{},[1274,2593,1576],{},[2242,2595,2596],{},[1274,2597,1399],{},[597,2599,1026],{},[593,2601,1008],{},[597,2603,599],{},[1274,2605,1576],{},[597,2607,605],{},[607,2609,2610,2612],{},[1274,2611,1576],{},[1274,2613,1399],{},[593,2615,1008],{},[597,2617,599],{},[1274,2619,1399],{},[597,2621,2622],{},"≈",[1274,2624,2625],{},"0,3466",[666,2627,2628],{"encoding":668},"\\int_0^{\\frac{\\pi}{4}} \\tan x\\,dx = -\\ln\\frac{1}{\\sqrt{2}} + \\ln 1 = \\frac{1}{2}\\ln 2 \\approx 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= \\frac{1}{2}",[569,3236,3238,3327],{"className":3237,"ariaHidden":674},[673],[569,3239,3241,3244,3247,3250,3318,3321,3324],{"className":3240},[678],[569,3242],{"className":3243,"style":1438},[682],[569,3245,622],{"className":3246},[687],[569,3248],{"className":3249,"style":692},[691],[569,3251,3253,3256,3315],{"className":3252},[696],[569,3254],{"className":3255},[722,723],[569,3257,3259],{"className":3258},[607],[569,3260,3262,3307],{"className":3261},[730,731],[569,3263,3265,3304],{"className":3264},[735],[569,3266,3268,3282,3290],{"className":3267,"style":1457},[739],[569,3269,3270,3273],{"style":1073},[569,3271],{"className":3272,"style":748},[747],[569,3274,3276],{"className":3275},[921,922,923,924],[569,3277,3279],{"className":3278},[696,924],[569,3280,3121],{"className":3281},[696,924],[569,3283,3284,3287],{"style":763},[569,3285],{"className":3286,"style":748},[747],[569,3288],{"className":3289,"style":771},[770],[569,3291,3292,3295],{"style":1482},[569,3293],{"className":3294,"style":748},[747],[569,3296,3298],{"className":3297},[921,922,923,924],[569,3299,3301],{"className":3300},[696,924],[569,3302,1396],{"className":3303,"style":1495},[696,697,924],[569,3305,794],{"className":3306},[793],[569,3308,3310],{"className":3309},[735],[569,3311,3313],{"className":3312,"style":1505},[739],[569,3314],{},[569,3316],{"className":3317},[807,723],[569,3319],{"className":3320,"style":701},[691],[569,3322,605],{"className":3323},[705],[569,3325],{"className":3326,"style":701},[691],[569,3328,3330,3334],{"className":3329},[678],[569,3331],{"className":3332,"style":3333},[682],"height:1.1901em;vertical-align:-0.345em;",[569,3335,3337,3340,3399],{"className":3336},[696],[569,3338],{"className":3339},[722,723],[569,3341,3343],{"className":3342},[607],[569,3344,3346,3391],{"className":3345},[730,731],[569,3347,3349,3388],{"className":3348},[735],[569,3350,3352,3366,3374],{"className":3351,"style":1671},[739],[569,3353,3354,3357],{"style":1073},[569,3355],{"className":3356,"style":748},[747],[569,3358,3360],{"className":3359},[921,922,923,924],[569,3361,3363],{"className":3362},[696,924],[569,3364,1399],{"className":3365},[696,924],[569,3367,3368,3371],{"style":763},[569,3369],{"className":3370,"style":748},[747],[569,3372],{"className":3373,"style":771},[770],[569,3375,3376,3379],{"style":1482},[569,3377],{"className":3378,"style":748},[747],[569,3380,3382],{"className":3381},[921,922,923,924],[569,3383,3385],{"className":3384},[696,924],[569,3386,1576],{"className":3387},[696,924],[569,3389,794],{"className":3390},[793],[569,3392,3394],{"className":3393},[735],[569,3395,3397],{"className":3396,"style":1505},[739],[569,3398],{},[569,3400],{"className":3401},[807,723],[569,3403,3405],{"className":3404},[572],[569,3406,3408,3479],{"className":3407},[576],[569,3409,3411],{"className":3410},[580],[582,3412,3413],{"xmlns":584,"display":585},[587,3414,3415,3476],{},[590,3416,3417,3429,3431,3433,3435,3437,3439,3441,3443,3445,3447,3449,3455,3457,3459,3461,3463,3465,3467,3469,3471,3473],{},[2558,3418,3419,3421,3423],{},[597,3420,967],{},[1274,3422,1276],{},[607,3424,3425,3427],{},[593,3426,1396],{},[1274,3428,3121],{},[593,3430,595],{},[597,3432,599],{},[593,3434,602],{},[996,3436,998],{},[593,3438,1001],{},[593,3440,602],{},[597,3442,605],{},[597,3444,631],{},[593,3446,1008],{},[597,3448,599],{},[607,3450,3451,3453],{},[1274,3452,1576],{},[1274,3454,1399],{},[597,3456,1026],{},[593,3458,1008],{},[597,3460,599],{},[1274,3462,1576],{},[597,3464,605],{},[593,3466,1008],{},[597,3468,599],{},[1274,3470,1399],{},[597,3472,2622],{},[1274,3474,3475],{},"0,6931",[666,3477,3478],{"encoding":668},"\\int_0^{\\frac{\\pi}{3}} \\tan x\\,dx = -\\ln\\frac{1}{2} + \\ln 1 = \\ln 2 \\approx 0{,}6931",[569,3480,3482,3637,3726,3750,3774],{"className":3481,"ariaHidden":674},[673],[569,3483,3485,3488,3607,3610,3613,3616,3619,3622,3625,3628,3631,3634],{"className":3484},[678],[569,3486],{"className":3487,"style":2638},[682],[569,3489,3491,3494],{"className":3490},[687],[569,3492,967],{"className":3493,"style":1922},[687,1046,1921],[569,3495,3497],{"className":3496},[900],[569,3498,3500,3599],{"className":3499},[730,731],[569,3501,3503,3596],{"className":3502},[735],[569,3504,3506,3517],{"className":3505,"style":2657},[739],[569,3507,3508,3511],{"style":2660},[569,3509],{"className":3510,"style":748},[747],[569,3512,3514],{"className":3513},[921,922,923,924],[569,3515,1276],{"className":3516},[696,924],[569,3518,3519,3522],{"style":2672},[569,3520],{"className":3521,"style":748},[747],[569,3523,3525],{"className":3524},[921,922,923,924],[569,3526,3528],{"className":3527},[696,924],[569,3529,3531,3534,3593],{"className":3530},[696,924],[569,3532],{"className":3533},[722,723,921,1145,2688],[569,3535,3537],{"className":3536},[607],[569,3538,3540,3585],{"className":3539},[730,731],[569,3541,3543,3582],{"className":3542},[735],[569,3544,3546,3560,3568],{"className":3545,"style":2701},[739],[569,3547,3548,3551],{"style":2704},[569,3549],{"className":3550,"style":748},[747],[569,3552,3554],{"className":3553},[921,1145,1146,924],[569,3555,3557],{"className":3556},[696,924],[569,3558,3121],{"className":3559},[696,924],[569,3561,3562,3565],{"style":2719},[569,3563],{"className":3564,"style":748},[747],[569,3566],{"className":3567,"style":2726},[770,924],[569,3569,3570,3573],{"style":2729},[569,3571],{"className":3572,"style":748},[747],[569,3574,3576],{"className":3575},[921,1145,1146,924],[569,3577,3579],{"className":3578},[696,924],[569,3580,1396],{"className":3581,"style":1495},[696,697,924],[569,3583,794],{"className":3584},[793],[569,3586,3588],{"className":3587},[735],[569,3589,3591],{"className":3590,"style":2751},[739],[569,3592],{},[569,3594],{"className":3595},[807,723,921,1145,2688],[569,3597,794],{"className":3598},[793],[569,3600,3602],{"className":3601},[735],[569,3603,3605],{"className":3604,"style":2766},[739],[569,3606],{},[569,3608],{"className":3609,"style":692},[691],[569,3611,595],{"className":3612},[687],[569,3614],{"className":3615,"style":692},[691],[569,3617,602],{"className":3618},[696,697],[569,3620],{"className":3621,"style":692},[691],[569,3623,1001],{"className":3624},[696,697],[569,3626,602],{"className":3627},[696,697],[569,3629],{"className":3630,"style":701},[691],[569,3632,605],{"className":3633},[705],[569,3635],{"className":3636,"style":701},[691],[569,3638,3640,3643,3646,3649,3652,3655,3717,3720,3723],{"className":3639},[678],[569,3641],{"className":3642,"style":2969},[682],[569,3644,631],{"className":3645},[696],[569,3647],{"className":3648,"style":692},[691],[569,3650,1008],{"className":3651},[687],[569,3653],{"className":3654,"style":692},[691],[569,3656,3658,3661,3714],{"className":3657},[696],[569,3659],{"className":3660},[722,723],[569,3662,3664],{"className":3663},[607],[569,3665,3667,3706],{"className":3666},[730,731],[569,3668,3670,3703],{"className":3669},[735],[569,3671,3673,3684,3692],{"className":3672,"style":2836},[739],[569,3674,3675,3678],{"style":743},[569,3676],{"className":3677,"style":748},[747],[569,3679,3681],{"className":3680},[696],[569,3682,1399],{"className":3683},[696],[569,3685,3686,3689],{"style":763},[569,3687],{"className":3688,"style":748},[747],[569,3690],{"className":3691,"style":771},[770],[569,3693,3694,3697],{"style":774},[569,3695],{"className":3696,"style":748},[747],[569,3698,3700],{"className":3699},[696],[569,3701,1576],{"className":3702},[696],[569,3704,794],{"className":3705},[793],[569,3707,3709],{"className":3708},[735],[569,3710,3712],{"className":3711,"style":801},[739],[569,3713],{},[569,3715],{"className":3716},[807,723],[569,3718],{"className":3719,"style":1229},[691],[569,3721,1026],{"className":3722},[1233],[569,3724],{"className":3725,"style":1229},[691],[569,3727,3729,3732,3735,3738,3741,3744,3747],{"className":3728},[678],[569,3730],{"className":3731,"style":1526},[682],[569,3733,1008],{"className":3734},[687],[569,3736],{"className":3737,"style":692},[691],[569,3739,1576],{"className":3740},[696],[569,3742],{"className":3743,"style":701},[691],[569,3745,605],{"className":3746},[705],[569,3748],{"className":3749,"style":701},[691],[569,3751,3753,3756,3759,3762,3765,3768,3771],{"className":3752},[678],[569,3754],{"className":3755,"style":1526},[682],[569,3757,1008],{"className":3758},[687],[569,3760],{"className":3761,"style":692},[691],[569,3763,1399],{"className":3764},[696],[569,3766],{"className":3767,"style":701},[691],[569,3769,2622],{"className":3770},[705],[569,3772],{"className":3773,"style":701},[691],[569,3775,3777,3780,3783,3789],{"className":3776},[678],[569,3778],{"className":3779,"style":3059},[682],[569,3781,1276],{"className":3782},[696],[569,3784,3786],{"className":3785},[696],[569,3787,1892],{"className":3788},[2005],[569,3790,3792],{"className":3791},[696],"6931",[560,3794,3796],{"id":3795},"typische-fehler","Typische Fehler",[3798,3799,3800,3915,4130,4191],"ul",{},[3801,3802,3803,3804,3866,3867,1248],"li",{},"Das Minuszeichen vergessen. ",[569,3805,3807,3833],{"className":3806},[576],[569,3808,3810],{"className":3809},[580],[582,3811,3812],{"xmlns":584},[587,3813,3814,3830],{},[590,3815,3816,3818,3820,3822,3824,3826,3828],{},[593,3817,1008],{},[597,3819,599],{},[593,3821,1013],{"mathvariant":654},[593,3823,622],{},[597,3825,599],{},[593,3827,602],{},[593,3829,1013],{"mathvariant":654},[666,3831,3832],{"encoding":668},"\\ln|\\cos x|",[569,3834,3836],{"className":3835,"ariaHidden":674},[673],[569,3837,3839,3842,3845,3848,3851,3854,3857,3860,3863],{"className":3838},[678],[569,3840],{"className":3841,"style":1201},[682],[569,3843,1008],{"className":3844},[687],[569,3846],{"className":3847,"style":692},[691],[569,3849,1013],{"className":3850},[696],[569,3852],{"className":3853,"style":692},[691],[569,3855,622],{"className":3856},[687],[569,3858],{"className":3859,"style":692},[691],[569,3861,602],{"className":3862},[696,697],[569,3864,1013],{"className":3865},[696]," abgeleitet ergibt ",[569,3868,3870,3890],{"className":3869},[576],[569,3871,3873],{"className":3872},[580],[582,3874,3875],{"xmlns":584},[587,3876,3877,3887],{},[590,3878,3879,3881,3883,3885],{},[597,3880,631],{},[593,3882,595],{},[597,3884,599],{},[593,3886,602],{},[666,3888,3889],{"encoding":668},"-\\tan x",[569,3891,3893],{"className":3892,"ariaHidden":674},[673],[569,3894,3896,3900,3903,3906,3909,3912],{"className":3895},[678],[569,3897],{"className":3898,"style":3899},[682],"height:0.6984em;vertical-align:-0.0833em;",[569,3901,631],{"className":3902},[696],[569,3904],{"className":3905,"style":692},[691],[569,3907,595],{"className":3908},[687],[569,3910],{"className":3911,"style":692},[691],[569,3913,602],{"className":3914},[696,697],[3801,3916,3917,3918,4129],{},"Die Betragsstriche weglassen. Dann ist die Stammfunktion z.B. auf ",[569,3919,3921,3955],{"className":3920},[576],[569,3922,3924],{"className":3923},[580],[582,3925,3926],{"xmlns":584},[587,3927,3928,3952],{},[590,3929,3930,3932,3938,3940,3950],{},[597,3931,639],{"fence":674},[607,3933,3934,3936],{},[593,3935,1396],{},[1274,3937,1399],{},[597,3939,1892],{"separator":674},[607,3941,3942,3948],{},[590,3943,3944,3946],{},[1274,3945,3121],{},[593,3947,1396],{},[1274,3949,1399],{},[597,3951,651],{"fence":674},[666,3953,3954],{"encoding":668},"\\left(\\frac{\\pi}{2}, \\frac{3\\pi}{2}\\right)",[569,3956,3958],{"className":3957,"ariaHidden":674},[673],[569,3959,3961,3965],{"className":3960},[678],[569,3962],{"className":3963,"style":3964},[682],"height:1.2em;vertical-align:-0.35em;",[569,3966,3969,3978,4046,4049,4052,4123],{"className":3967},[3968],"minner",[569,3970,3974],{"className":3971,"style":3973},[722,3972],"delimcenter","top:0em;",[569,3975,639],{"className":3976},[3977,1146],"delimsizing",[569,3979,3981,3984,4043],{"className":3980},[696],[569,3982],{"className":3983},[722,723],[569,3985,3987],{"className":3986},[607],[569,3988,3990,4035],{"className":3989},[730,731],[569,3991,3993,4032],{"className":3992},[735],[569,3994,3996,4010,4018],{"className":3995,"style":1457},[739],[569,3997,3998,4001],{"style":1073},[569,3999],{"className":4000,"style":748},[747],[569,4002,4004],{"className":4003},[921,922,923,924],[569,4005,4007],{"className":4006},[696,924],[569,4008,1399],{"className":4009},[696,924],[569,4011,4012,4015],{"style":763},[569,4013],{"className":4014,"style":748},[747],[569,4016],{"className":4017,"style":771},[770],[569,4019,4020,4023],{"style":1482},[569,4021],{"className":4022,"style":748},[747],[569,4024,4026],{"className":4025},[921,922,923,924],[569,4027,4029],{"className":4028},[696,924],[569,4030,1396],{"className":4031,"style":1495},[696,697,924],[569,4033,794],{"className":4034},[793],[569,4036,4038],{"className":4037},[735],[569,4039,4041],{"className":4040,"style":1505},[739],[569,4042],{},[569,4044],{"className":4045},[807,723],[569,4047,1892],{"className":4048},[2005],[569,4050],{"className":4051,"style":692},[691],[569,4053,4055,4058,4120],{"className":4054},[696],[569,4056],{"className":4057},[722,723],[569,4059,4061],{"className":4060},[607],[569,4062,4064,4112],{"className":4063},[730,731],[569,4065,4067,4109],{"className":4066},[735],[569,4068,4070,4084,4092],{"className":4069,"style":1671},[739],[569,4071,4072,4075],{"style":1073},[569,4073],{"className":4074,"style":748},[747],[569,4076,4078],{"className":4077},[921,922,923,924],[569,4079,4081],{"className":4080},[696,924],[569,4082,1399],{"className":4083},[696,924],[569,4085,4086,4089],{"style":763},[569,4087],{"className":4088,"style":748},[747],[569,4090],{"className":4091,"style":771},[770],[569,4093,4094,4097],{"style":1482},[569,4095],{"className":4096,"style":748},[747],[569,4098,4100],{"className":4099},[921,922,923,924],[569,4101,4103,4106],{"className":4102},[696,924],[569,4104,3121],{"className":4105},[696,924],[569,4107,1396],{"className":4108,"style":1495},[696,697,924],[569,4110,794],{"className":4111},[793],[569,4113,4115],{"className":4114},[735],[569,4116,4118],{"className":4117,"style":1505},[739],[569,4119],{},[569,4121],{"className":4122},[807,723],[569,4124,4126],{"className":4125,"style":3973},[807,3972],[569,4127,651],{"className":4128},[3977,1146]," nicht definiert.",[3801,4131,4132,4133,2112,4161,4190],{},"Über eine Polstelle hinweg integrieren, z.B. von ",[569,4134,4136,4149],{"className":4135},[576],[569,4137,4139],{"className":4138},[580],[582,4140,4141],{"xmlns":584},[587,4142,4143,4147],{},[590,4144,4145],{},[1274,4146,1276],{},[666,4148,1276],{"encoding":668},[569,4150,4152],{"className":4151,"ariaHidden":674},[673],[569,4153,4155,4158],{"className":4154},[678],[569,4156],{"className":4157,"style":1314},[682],[569,4159,1276],{"className":4160},[696],[569,4162,4164,4178],{"className":4163},[576],[569,4165,4167],{"className":4166},[580],[582,4168,4169],{"xmlns":584},[587,4170,4171,4175],{},[590,4172,4173],{},[593,4174,1396],{},[666,4176,4177],{"encoding":668},"\\pi",[569,4179,4181],{"className":4180,"ariaHidden":674},[673],[569,4182,4184,4187],{"className":4183},[678],[569,4185],{"className":4186,"style":1419},[682],[569,4188,1396],{"className":4189,"style":1495},[696,697],". Das Integral existiert dort nicht, auch wenn das Einsetzen der Grenzen eine Zahl liefert.",[3801,4192,4193,4194,4347],{},"Die Stammfunktion mit der Ableitung ",[569,4195,4197,4227],{"className":4196},[576],[569,4198,4200],{"className":4199},[580],[582,4201,4202],{"xmlns":584},[587,4203,4204,4224],{},[590,4205,4206],{},[607,4207,4208,4210],{},[1274,4209,1576],{},[590,4211,4212,4222],{},[647,4213,4214,4220],{},[590,4215,4216,4218],{},[593,4217,622],{},[597,4219,599],{},[1274,4221,1399],{},[593,4223,602],{},[666,4225,4226],{"encoding":668},"\\frac{1}{\\cos^2 x}",[569,4228,4230],{"className":4229,"ariaHidden":674},[673],[569,4231,4233,4236],{"className":4232},[678],[569,4234],{"className":4235,"style":3333},[682],[569,4237,4239,4242,4344],{"className":4238},[696],[569,4240],{"className":4241},[722,723],[569,4243,4245],{"className":4244},[607],[569,4246,4248,4336],{"className":4247},[730,731],[569,4249,4251,4333],{"className":4250},[735],[569,4252,4254,4311,4319],{"className":4253,"style":1671},[739],[569,4255,4256,4259],{"style":1073},[569,4257],{"className":4258,"style":748},[747],[569,4260,4262],{"className":4261},[921,922,923,924],[569,4263,4265,4305,4308],{"className":4264},[696,924],[569,4266,4268,4280],{"className":4267},[687,924],[569,4269,4271,4274,4277],{"className":4270},[687,924],[569,4272,1696],{"className":4273},[924],[569,4275,1700],{"className":4276},[924],[569,4278,1704],{"className":4279},[924],[569,4281,4283],{"className":4282},[900],[569,4284,4286],{"className":4285},[730],[569,4287,4289],{"className":4288},[735],[569,4290,4293],{"className":4291,"style":4292},[739],"height:0.7463em;",[569,4294,4296,4299],{"style":4295},"top:-2.786em;margin-right:0.0714em;",[569,4297],{"className":4298,"style":1141},[747],[569,4300,4302],{"className":4301},[921,1145,1146,924],[569,4303,1399],{"className":4304},[696,924],[569,4306],{"className":4307,"style":1689},[691,924],[569,4309,602],{"className":4310},[696,697,924],[569,4312,4313,4316],{"style":763},[569,4314],{"className":4315,"style":748},[747],[569,4317],{"className":4318,"style":771},[770],[569,4320,4321,4324],{"style":1482},[569,4322],{"className":4323,"style":748},[747],[569,4325,4327],{"className":4326},[921,922,923,924],[569,4328,4330],{"className":4329},[696,924],[569,4331,1576],{"className":4332},[696,924],[569,4334,794],{"className":4335},[793],[569,4337,4339],{"className":4338},[735],[569,4340,4342],{"className":4341,"style":1505},[739],[569,4343],{},[569,4345],{"className":4346},[807,723]," verwechseln.",{"title":4349,"searchDepth":4350,"depth":4350,"links":4351},"",2,[4352,4353,4354],{"id":562,"depth":4350,"text":563},{"id":2079,"depth":4350,"text":2080},{"id":3795,"depth":4350,"text":3796},[4356,4359,4363,4365,4368,4371,4373,4376,4379],{"lhs":4357,"rhs":4358},"-(-sin(x))\u002Fcos(x)","tan(x)",{"lhs":4360,"rhs":1276,"where":4361},"round((-log(abs(cos(x+1e-5))) + log(abs(cos(x-1e-5))))\u002F(2e-5) - tan(x), 6)",{"x":4362},0.5,{"lhs":4360,"rhs":1276,"where":4364},{"x":4350},{"lhs":4366,"rhs":4367},"-log(cos(pi\u002F4)) + log(cos(0))","log(2)\u002F2",{"lhs":4369,"rhs":4370},"round(log(2)\u002F2, 4)","0.3466",{"lhs":4372,"rhs":4370},"round(sum(map(0:999, f(k) = tan((k + 0.5) * pi\u002F4 \u002F 1000))) * pi\u002F4 \u002F 1000, 4)",{"lhs":4374,"rhs":4375},"-log(cos(pi\u002F3)) + log(cos(0))","log(2)",{"lhs":4377,"rhs":4378},"round(sum(map(0:999, f(k) = tan((k + 0.5) * pi\u002F3 \u002F 1000))) * pi\u002F3 \u002F 1000, 4)","round(log(2), 4)",{"lhs":4380,"rhs":1276,"where":4381},"round((log(abs(sin(x+1e-5))) - log(abs(sin(x-1e-5))))\u002F(2e-5) - cos(x)\u002Fsin(x), 6)",{"x":4382},-1,"x \\neq \\frac{\\pi}{2} + k\\pi,\\ k \\in \\mathbb{Z},\\ x \\text{ im Bogenmaß}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq \\frac{\\pi}{2} + k\\pi,\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\">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:1.0404em;vertical-align:-0.345em;\">\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:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\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:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\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>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\mathbb{Z},\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\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>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","integral-tangent","\\int \\tan x\\,dx = -\\ln|\\cos x| + C","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>ln\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int \\tan x\\,dx = -\\ln|\\cos x| + C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2222em;vertical-align:-0.8622em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">tan\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">ln\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-tangens",[],[4396,4397,4398,4399],"logarithmic-integration","tangent-quotient","derivative-ln","integral-sine",{"title":548,"description":4349},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-tangens","Eine Stammfunktion des Tangens ist minus der natürliche Logarithmus vom Betrag des Kosinus.",[4404,4405,4406,4407],"integral","stammfunktion","tangens","logarithmische integration",[4409,4412,4415],{"symbol":602,"meaning":4410,"symbolHtml":4411},"Integrationsvariable, ein Winkel im Bogenmaß","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1404,"meaning":4413,"symbolHtml":4414},"beliebige ganze Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1029,"meaning":4416,"symbolHtml":4417},"Integrationskonstante","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","h3C9cBD_sUmC9DbZO-0D0HXPn9cgZejvoeVKCfy6cC8",[4420,4423,4426,4429],{"stem":4421,"title":4422,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-ln","Ableitung des natürlichen Logarithmus",{"stem":4424,"title":4425,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-sinus","Integral des Sinus",{"stem":4427,"title":4428,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Flogarithmische-integration","Logarithmische Integration",{"stem":4430,"title":4431,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Ftangens-als-quotient","Tangens als Quotient von Sinus und Kosinus",1793824282153]