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C",[568,1175,1177,1324,1419,1449],{"className":1176,"ariaHidden":622},[621],[568,1178,1180,1184,1190,1193,1306,1309,1312,1315,1318,1321],{"className":1179},[626],[568,1181],{"className":1182,"style":1183},[630],"height:2.3649em;vertical-align:-0.936em;",[568,1185,1104],{"className":1186,"style":1189},[635,1187,1188],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,1191],{"className":1192,"style":640},[639],[568,1194,1196,1199,1303],{"className":1195},[644],[568,1197],{"className":1198},[653,731],[568,1200,1202],{"className":1201},[678],[568,1203,1205,1294],{"className":1204},[738,739],[568,1206,1208,1291],{"className":1207},[743],[568,1209,1212,1233,1241],{"className":1210,"style":1211},[747],"height:1.4289em;",[568,1213,1215,1218],{"style":1214},"top:-2.314em;",[568,1216],{"className":1217,"style":756},[755],[568,1219,1221,1224,1227,1230],{"className":1220},[644],[568,1222,600],{"className":1223,"style":649},[644,648],[568,1225,604],{"className":1226},[653],[568,1228,607],{"className":1229},[644,648],[568,1231,610],{"className":1232},[660],[568,1234,1235,1238],{"style":781},[568,1236],{"className":1237,"style":756},[755],[568,1239],{"className":1240,"style":789},[788],[568,1242,1244,1247],{"style":1243},"top:-3.677em;",[568,1245],{"className":1246,"style":756},[755],[568,1248,1250,1282,1285,1288],{"className":1249},[644],[568,1251,1253,1256],{"className":1252},[644],[568,1254,600],{"className":1255,"style":649},[644,648],[568,1257,1259],{"className":1258},[849],[568,1260,1262],{"className":1261},[738],[568,1263,1265],{"className":1264},[743],[568,1266,1268],{"className":1267,"style":859},[747],[568,1269,1270,1273],{"style":862},[568,1271],{"className":1272,"style":866},[755],[568,1274,1276],{"className":1275},[760,761,762,763],[568,1277,1279],{"className":1278},[644,763],[568,1280,705],{"className":1281},[644,763],[568,1283,604],{"className":1284},[653],[568,1286,607],{"className":1287},[644,648],[568,1289,610],{"className":1290},[660],[568,1292,809],{"className":1293},[808],[568,1295,1297],{"className":1296},[743],[568,1298,1301],{"className":1299,"style":1300},[747],"height:0.936em;",[568,1302],{},[568,1304],{"className":1305},[660,731],[568,1307],{"className":1308,"style":640},[639],[568,1310,975],{"className":1311},[644,648],[568,1313,607],{"className":1314},[644,648],[568,1316],{"className":1317,"style":934},[639],[568,1319,906],{"className":1320},[938],[568,1322],{"className":1323,"style":934},[639],[568,1325,1327,1331,1334,1337,1401,1404,1407,1410,1413,1416],{"className":1326},[626],[568,1328],{"className":1329,"style":1330},[630],"height:2.2222em;vertical-align:-0.8622em;",[568,1332,1104],{"className":1333,"style":1189},[635,1187,1188],[568,1335],{"className":1336,"style":640},[639],[568,1338,1340,1343,1398],{"className":1339},[644],[568,1341],{"className":1342},[653,731],[568,1344,1346],{"className":1345},[678],[568,1347,1349,1389],{"className":1348},[738,739],[568,1350,1352,1386],{"className":1351},[743],[568,1353,1356,1367,1375],{"className":1354,"style":1355},[747],"height:1.3214em;",[568,1357,1358,1361],{"style":1214},[568,1359],{"className":1360,"style":756},[755],[568,1362,1364],{"className":1363},[644],[568,1365,903],{"className":1366},[644,648],[568,1368,1369,1372],{"style":781},[568,1370],{"className":1371,"style":756},[755],[568,1373],{"className":1374,"style":789},[788],[568,1376,1377,1380],{"style":1243},[568,1378],{"className":1379,"style":756},[755],[568,1381,1383],{"className":1382},[644],[568,1384,683],{"className":1385},[644],[568,1387,809],{"className":1388},[808],[568,1390,1392],{"className":1391},[743],[568,1393,1396],{"className":1394,"style":1395},[747],"height:0.686em;",[568,1397],{},[568,1399],{"className":1400},[660,731],[568,1402],{"className":1403,"style":640},[639],[568,1405,975],{"className":1406},[644,648],[568,1408,903],{"className":1409},[644,648],[568,1411],{"className":1412,"style":934},[639],[568,1414,906],{"className":1415},[938],[568,1417],{"className":1418,"style":934},[639],[568,1420,1422,1425,1428,1431,1434,1437,1440,1443,1446],{"className":1421},[626],[568,1423],{"className":1424,"style":631},[630],[568,1426,589],{"className":1427},[635],[568,1429],{"className":1430,"style":640},[639],[568,1432,597],{"className":1433},[644],[568,1435,903],{"className":1436},[644,648],[568,1438,597],{"className":1439},[644],[568,1441],{"className":1442,"style":825},[639],[568,1444,1167],{"className":1445},[829],[568,1447],{"className":1448,"style":825},[639],[568,1450,1452,1456],{"className":1451},[626],[568,1453],{"className":1454,"style":1455},[630],"height:0.6833em;",[568,1457,1170],{"className":1458,"style":1459},[644,648],"margin-right:0.0715em;",[564,1461,1462,1463,1467,1468,1512,1513,1542],{},"Der ",[1464,1465,1466],"strong",{},"Betrag"," ist nötig, weil ",[568,1469,1471,1491],{"className":1470},[571],[568,1472,1474],{"className":1473},[575],[577,1475,1476],{"xmlns":579},[581,1477,1478,1488],{},[584,1479,1480,1482,1484,1486],{},[587,1481,600],{},[591,1483,604],{"stretchy":603},[587,1485,607],{},[591,1487,610],{"stretchy":603},[614,1489,1490],{"encoding":616},"f(x)",[568,1492,1494],{"className":1493,"ariaHidden":622},[621],[568,1495,1497,1500,1503,1506,1509],{"className":1496},[626],[568,1498],{"className":1499,"style":631},[630],[568,1501,600],{"className":1502,"style":649},[644,648],[568,1504,604],{"className":1505},[653],[568,1507,607],{"className":1508},[644,648],[568,1510,610],{"className":1511},[660]," negativ sein kann. Der Integrationsbereich darf keine Nullstelle von ",[568,1514,1516,1529],{"className":1515},[571],[568,1517,1519],{"className":1518},[575],[577,1520,1521],{"xmlns":579},[581,1522,1523,1527],{},[584,1524,1525],{},[587,1526,600],{},[614,1528,600],{"encoding":616},[568,1530,1532],{"className":1531,"ariaHidden":622},[621],[568,1533,1535,1539],{"className":1534},[626],[568,1536],{"className":1537,"style":1538},[630],"height:0.8889em;vertical-align:-0.1944em;",[568,1540,600],{"className":1541,"style":649},[644,648]," enthalten.",[564,1544,1545,1546,1549],{},"Passt der Zähler nur bis auf einen ",[1464,1547,1548],{},"konstanten"," Faktor, gleicht man ihn vor dem Integral aus.",[559,1551,1553],{"id":1552},"beispiele","Beispiele",[564,1555,1556,1557,1642,1643,1677],{},"Der Nenner ",[568,1558,1560,1583],{"className":1559},[571],[568,1561,1563],{"className":1562},[575],[577,1564,1565],{"xmlns":579},[581,1566,1567,1580],{},[584,1568,1569,1576,1578],{},[698,1570,1571,1573],{},[587,1572,607],{},[681,1574,1575],{},"2",[591,1577,1167],{},[681,1579,683],{},[614,1581,1582],{"encoding":616},"x^2 + 1",[568,1584,1586,1632],{"className":1585,"ariaHidden":622},[621],[568,1587,1589,1593,1623,1626,1629],{"className":1588},[626],[568,1590],{"className":1591,"style":1592},[630],"height:0.8974em;vertical-align:-0.0833em;",[568,1594,1596,1599],{"className":1595},[644],[568,1597,607],{"className":1598},[644,648],[568,1600,1602],{"className":1601},[849],[568,1603,1605],{"className":1604},[738],[568,1606,1608],{"className":1607},[743],[568,1609,1612],{"className":1610,"style":1611},[747],"height:0.8141em;",[568,1613,1614,1617],{"style":862},[568,1615],{"className":1616,"style":866},[755],[568,1618,1620],{"className":1619},[760,761,762,763],[568,1621,1575],{"className":1622},[644,763],[568,1624],{"className":1625,"style":825},[639],[568,1627,1167],{"className":1628},[829],[568,1630],{"className":1631,"style":825},[639],[568,1633,1635,1639],{"className":1634},[626],[568,1636],{"className":1637,"style":1638},[630],"height:0.6444em;",[568,1640,683],{"className":1641},[644]," hat die Ableitung ",[568,1644,1646,1662],{"className":1645},[571],[568,1647,1649],{"className":1648},[575],[577,1650,1651],{"xmlns":579},[581,1652,1653,1659],{},[584,1654,1655,1657],{},[681,1656,1575],{},[587,1658,607],{},[614,1660,1661],{"encoding":616},"2x",[568,1663,1665],{"className":1664,"ariaHidden":622},[621],[568,1666,1668,1671,1674],{"className":1667},[626],[568,1669],{"className":1670,"style":1638},[630],[568,1672,1575],{"className":1673},[644],[568,1675,607],{"className":1676},[644,648],", und er ist immer positiv:",[568,1679,1681],{"className":1680},[1088],[568,1682,1684,1780],{"className":1683},[571],[568,1685,1687],{"className":1686},[575],[577,1688,1689],{"xmlns":579,"display":1097},[581,1690,1691,1777],{},[584,1692,1693,1703,1723,1725,1727,1729,1731,1763,1765,1767,1769,1771,1774],{},[1694,1695,1696,1698,1701],"msubsup",{},[591,1697,1104],{},[681,1699,1700],{},"0",[681,1702,683],{},[678,1704,1705,1711],{},[584,1706,1707,1709],{},[681,1708,1575],{},[587,1710,607],{},[584,1712,1713,1719,1721],{},[698,1714,1715,1717],{},[587,1716,607],{},[681,1718,1575],{},[591,1720,1167],{},[681,1722,683],{},[993,1724,995],{},[587,1726,975],{},[587,1728,607],{},[591,1730,906],{},[1694,1732,1733,1759,1761],{},[584,1734,1735,1738,1740,1742,1744,1750,1752,1754,1756],{},[591,1736,1737],{"fence":622},"[",[587,1739,589],{},[591,1741,593],{},[591,1743,604],{"stretchy":603},[698,1745,1746,1748],{},[587,1747,607],{},[681,1749,1575],{},[591,1751,1167],{},[681,1753,683],{},[591,1755,610],{"stretchy":603},[591,1757,1758],{"fence":622},"]",[681,1760,1700],{},[681,1762,683],{},[591,1764,906],{},[587,1766,589],{},[591,1768,593],{},[681,1770,1575],{},[591,1772,1773],{},"≈",[681,1775,1776],{},"0,6931",[614,1778,1779],{"encoding":616},"\\int_0^1 \\frac{2x}{x^2 + 1}\\,dx = \\left[\\ln(x^2 + 1)\\right]_0^1 = \\ln 2 \\approx 0{,}6931",[568,1781,1783,1972,2112,2136],{"className":1782,"ariaHidden":622},[621],[568,1784,1786,1790,1845,1848,1954,1957,1960,1963,1966,1969],{"className":1785},[626],[568,1787],{"className":1788,"style":1789},[630],"height:2.476em;vertical-align:-0.9119em;",[568,1791,1793,1796],{"className":1792},[635],[568,1794,1104],{"className":1795,"style":1189},[635,1187,1188],[568,1797,1799],{"className":1798},[849],[568,1800,1802,1836],{"className":1801},[738,739],[568,1803,1805,1833],{"className":1804},[743],[568,1806,1809,1821],{"className":1807,"style":1808},[747],"height:1.564em;",[568,1810,1812,1815],{"style":1811},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,1813],{"className":1814,"style":866},[755],[568,1816,1818],{"className":1817},[760,761,762,763],[568,1819,1700],{"className":1820},[644,763],[568,1822,1824,1827],{"style":1823},"top:-3.8129em;margin-right:0.05em;",[568,1825],{"className":1826,"style":866},[755],[568,1828,1830],{"className":1829},[760,761,762,763],[568,1831,683],{"className":1832},[644,763],[568,1834,809],{"className":1835},[808],[568,1837,1839],{"className":1838},[743],[568,1840,1843],{"className":1841,"style":1842},[747],"height:0.9119em;",[568,1844],{},[568,1846],{"className":1847,"style":640},[639],[568,1849,1851,1854,1951],{"className":1850},[644],[568,1852],{"className":1853},[653,731],[568,1855,1857],{"className":1856},[678],[568,1858,1860,1942],{"className":1859},[738,739],[568,1861,1863,1939],{"className":1862},[743],[568,1864,1866,1917,1925],{"className":1865,"style":1355},[747],[568,1867,1868,1871],{"style":1214},[568,1869],{"className":1870,"style":756},[755],[568,1872,1874,1905,1908,1911,1914],{"className":1873},[644],[568,1875,1877,1880],{"className":1876},[644],[568,1878,607],{"className":1879},[644,648],[568,1881,1883],{"className":1882},[849],[568,1884,1886],{"className":1885},[738],[568,1887,1889],{"className":1888},[743],[568,1890,1893],{"className":1891,"style":1892},[747],"height:0.7401em;",[568,1894,1896,1899],{"style":1895},"top:-2.989em;margin-right:0.05em;",[568,1897],{"className":1898,"style":866},[755],[568,1900,1902],{"className":1901},[760,761,762,763],[568,1903,1575],{"className":1904},[644,763],[568,1906],{"className":1907,"style":825},[639],[568,1909,1167],{"className":1910},[829],[568,1912],{"className":1913,"style":825},[639],[568,1915,683],{"className":1916},[644],[568,1918,1919,1922],{"style":781},[568,1920],{"className":1921,"style":756},[755],[568,1923],{"className":1924,"style":789},[788],[568,1926,1927,1930],{"style":1243},[568,1928],{"className":1929,"style":756},[755],[568,1931,1933,1936],{"className":1932},[644],[568,1934,1575],{"className":1935},[644],[568,1937,607],{"className":1938},[644,648],[568,1940,809],{"className":1941},[808],[568,1943,1945],{"className":1944},[743],[568,1946,1949],{"className":1947,"style":1948},[747],"height:0.7693em;",[568,1950],{},[568,1952],{"className":1953},[660,731],[568,1955],{"className":1956,"style":640},[639],[568,1958,975],{"className":1959},[644,648],[568,1961,607],{"className":1962},[644,648],[568,1964],{"className":1965,"style":934},[639],[568,1967,906],{"className":1968},[938],[568,1970],{"className":1971,"style":934},[639],[568,1973,1975,1979,2103,2106,2109],{"className":1974},[626],[568,1976],{"className":1977,"style":1978},[630],"height:1.4678em;vertical-align:-0.3997em;",[568,1980,1983,2054],{"className":1981},[1982],"minner",[568,1984,1986,1996,1999,2002,2033,2036,2039,2042,2045,2048],{"className":1985},[1982],[568,1987,1991],{"className":1988,"style":1990},[653,1989],"delimcenter","top:0em;",[568,1992,1737],{"className":1993},[1994,1995],"delimsizing","size1",[568,1997,589],{"className":1998},[635],[568,2000,604],{"className":2001},[653],[568,2003,2005,2008],{"className":2004},[644],[568,2006,607],{"className":2007},[644,648],[568,2009,2011],{"className":2010},[849],[568,2012,2014],{"className":2013},[738],[568,2015,2017],{"className":2016},[743],[568,2018,2021],{"className":2019,"style":2020},[747],"height:0.8641em;",[568,2022,2024,2027],{"style":2023},"top:-3.113em;margin-right:0.05em;",[568,2025],{"className":2026,"style":866},[755],[568,2028,2030],{"className":2029},[760,761,762,763],[568,2031,1575],{"className":2032},[644,763],[568,2034],{"className":2035,"style":825},[639],[568,2037,1167],{"className":2038},[829],[568,2040],{"className":2041,"style":825},[639],[568,2043,683],{"className":2044},[644],[568,2046,610],{"className":2047},[660],[568,2049,2051],{"className":2050,"style":1990},[660,1989],[568,2052,1758],{"className":2053},[1994,1995],[568,2055,2057],{"className":2056},[849],[568,2058,2060,2094],{"className":2059},[738,739],[568,2061,2063,2091],{"className":2062},[743],[568,2064,2067,2079],{"className":2065,"style":2066},[747],"height:1.0681em;",[568,2068,2070,2073],{"style":2069},"top:-2.3003em;margin-right:0.05em;",[568,2071],{"className":2072,"style":866},[755],[568,2074,2076],{"className":2075},[760,761,762,763],[568,2077,1700],{"className":2078},[644,763],[568,2080,2082,2085],{"style":2081},"top:-3.317em;margin-right:0.05em;",[568,2083],{"className":2084,"style":866},[755],[568,2086,2088],{"className":2087},[760,761,762,763],[568,2089,683],{"className":2090},[644,763],[568,2092,809],{"className":2093},[808],[568,2095,2097],{"className":2096},[743],[568,2098,2101],{"className":2099,"style":2100},[747],"height:0.3997em;",[568,2102],{},[568,2104],{"className":2105,"style":934},[639],[568,2107,906],{"className":2108},[938],[568,2110],{"className":2111,"style":934},[639],[568,2113,2115,2118,2121,2124,2127,2130,2133],{"className":2114},[626],[568,2116],{"className":2117,"style":1012},[630],[568,2119,589],{"className":2120},[635],[568,2122],{"className":2123,"style":640},[639],[568,2125,1575],{"className":2126},[644],[568,2128],{"className":2129,"style":934},[639],[568,2131,1773],{"className":2132},[938],[568,2134],{"className":2135,"style":934},[639],[568,2137,2139,2143,2146,2154],{"className":2138},[626],[568,2140],{"className":2141,"style":2142},[630],"height:0.8389em;vertical-align:-0.1944em;",[568,2144,1700],{"className":2145},[644],[568,2147,2149],{"className":2148},[644],[568,2150,2153],{"className":2151},[2152],"mpunct",",",[568,2155,2157],{"className":2156},[644],"6931",[564,2159,2160,2161,2534,2535,2685,2686,1084],{},"Mit 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für ",[568,2687,2689,2712],{"className":2688},[571],[568,2690,2692],{"className":2691},[575],[577,2693,2694],{"xmlns":579},[581,2695,2696,2709],{},[584,2697,2698,2700,2702,2704,2707],{},[587,2699,2197],{},[591,2701,593],{},[587,2703,607],{},[591,2705,2706],{"mathvariant":596},"≠",[681,2708,1700],{},[614,2710,2711],{"encoding":616},"\\cos x \\neq 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\\tan x\\,dx = -\\ln\\left(\\cos \\frac{\\pi}{4}\\right) + \\ln(\\cos 0) = -\\ln \\frac{\\sqrt{2}}{2} = \\frac{1}{2}\\ln 2 \\approx 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ein konstanter Faktor, ergänzt man ihn:",[568,3489,3491],{"className":3490},[1088],[568,3492,3494,3596],{"className":3493},[571],[568,3495,3497],{"className":3496},[575],[577,3498,3499],{"xmlns":579,"display":1097},[581,3500,3501,3593],{},[584,3502,3503,3505,3521,3523,3525,3527,3529,3535,3537,3557,3559,3561,3563,3565,3571,3573,3575,3577,3583,3585,3587,3589,3591],{},[591,3504,1104],{},[678,3506,3507,3509],{},[587,3508,607],{},[584,3510,3511,3517,3519],{},[698,3512,3513,3515],{},[587,3514,607],{},[681,3516,1575],{},[591,3518,1167],{},[681,3520,2816],{},[993,3522,995],{},[587,3524,975],{},[587,3526,607],{},[591,3528,906],{},[678,3530,3531,3533],{},[681,3532,683],{},[681,3534,1575],{},[591,3536,1104],{},[678,3538,3539,3545],{},[584,3540,3541,3543],{},[681,3542,1575],{},[587,3544,607],{},[584,3546,3547,3553,3555],{},[698,3548,3549,3551],{},[587,3550,607],{},[681,3552,1575],{},[591,3554,1167],{},[681,3556,2816],{},[993,3558,995],{},[587,3560,975],{},[587,3562,607],{},[591,3564,906],{},[678,3566,3567,3569],{},[681,3568,683],{},[681,3570,1575],{},[587,3572,589],{},[591,3574,593],{},[591,3576,604],{"stretchy":603},[698,3578,3579,3581],{},[587,3580,607],{},[681,3582,1575],{},[591,3584,1167],{},[681,3586,2816],{},[591,3588,610],{"stretchy":603},[591,3590,1167],{},[587,3592,1170],{},[614,3594,3595],{"encoding":616},"\\int \\frac{x}{x^2 + 4}\\,dx = \\frac{1}{2} \\int \\frac{2x}{x^2 + 4}\\,dx = \\frac{1}{2}\\ln(x^2 + 4) + C",[568,3597,3599,3729,3927,4042,4063],{"className":3598,"ariaHidden":622},[621],[568,3600,3602,3605,3608,3611,3711,3714,3717,3720,3723,3726],{"className":3601},[626],[568,3603],{"className":3604,"style":1330},[630],[568,3606,1104],{"className":3607,"style":1189},[635,1187,1188],[568,3609],{"className":3610,"style":640},[639],[568,3612,3614,3617,3708],{"className":3613},[644],[568,3615],{"className":3616},[653,731],[568,3618,3620],{"className":3619},[678],[568,3621,3623,3700],{"className":3622},[738,739],[568,3624,3626,3697],{"className":3625},[743],[568,3627,3629,3678,3686],{"className":3628,"style":3131},[747],[568,3630,3631,3634],{"style":1214},[568,3632],{"className":3633,"style":756},[755],[568,3635,3637,3666,3669,3672,3675],{"className":3636},[644],[568,3638,3640,3643],{"className":3639},[644],[568,3641,607],{"className":3642},[644,648],[568,3644,3646],{"className":3645},[849],[568,3647,3649],{"className":3648},[738],[568,3650,3652],{"className":3651},[743],[568,3653,3655],{"className":3654,"style":1892},[747],[568,3656,3657,3660],{"style":1895},[568,3658],{"className":3659,"style":866},[755],[568,3661,3663],{"className":3662},[760,761,762,763],[568,3664,1575],{"className":3665},[644,763],[568,3667],{"className":3668,"style":825},[639],[568,3670,1167],{"className":3671},[829],[568,3673],{"className":3674,"style":825},[639],[568,3676,2816],{"className":3677},[644],[568,3679,3680,3683],{"style":781},[568,3681],{"className":3682,"style":756},[755],[568,3684],{"className":3685,"style":789},[788],[568,3687,3688,3691],{"style":1243},[568,3689],{"className":3690,"style":756},[755],[568,3692,3694],{"className":3693},[644],[568,3695,607],{"className":3696},[644,648],[568,3698,809],{"className":3699},[808],[568,3701,3703],{"className":3702},[743],[568,3704,3706],{"className":3705,"style":1948},[747],[568,3707],{},[568,3709],{"className":3710},[660,731],[568,3712],{"className":3713,"style":640},[639],[568,3715,975],{"className":3716},[644,648],[568,3718,607],{"className":3719},[644,648],[568,3721],{"className":3722,"style":934},[639],[568,3724,906],{"className":3725},[938],[568,3727],{"className":3728,"style":934},[639],[568,3730,3732,3735,3797,3800,3803,3806,3909,3912,3915,3918,3921,3924],{"className":3731},[626],[568,3733],{"className":3734,"style":1330},[630],[568,3736,3738,3741,3794],{"className":3737},[644],[568,3739],{"className":3740},[653,731],[568,3742,3744],{"className":3743},[678],[568,3745,3747,3786],{"className":3746},[738,739],[568,3748,3750,3783],{"className":3749},[743],[568,3751,3753,3764,3772],{"className":3752,"style":1355},[747],[568,3754,3755,3758],{"style":1214},[568,3756],{"className":3757,"style":756},[755],[568,3759,3761],{"className":3760},[644],[568,3762,1575],{"className":3763},[644],[568,3765,3766,3769],{"style":781},[568,3767],{"className":3768,"style":756},[755],[568,3770],{"className":3771,"style":789},[788],[568,3773,3774,3777],{"style":1243},[568,3775],{"className":3776,"style":756},[755],[568,3778,3780],{"className":3779},[644],[568,3781,683],{"className":3782},[644],[568,3784,809],{"className":3785},[808],[568,3787,3789],{"className":3788},[743],[568,3790,3792],{"className":3791,"style":1395},[747],[568,3793],{},[568,3795],{"className":3796},[660,731],[568,3798],{"className":3799,"style":640},[639],[568,3801,1104],{"className":3802,"style":1189},[635,1187,1188],[568,3804],{"className":3805,"style":640},[639],[568,3807,3809,3812,3906],{"className":3808},[644],[568,3810],{"className":3811},[653,731],[568,3813,3815],{"className":3814},[678],[568,3816,3818,3898],{"className":3817},[738,739],[568,3819,3821,3895],{"className":3820},[743],[568,3822,3824,3873,3881],{"className":3823,"style":1355},[747],[568,3825,3826,3829],{"style":1214},[568,3827],{"className":3828,"style":756},[755],[568,3830,3832,3861,3864,3867,3870],{"className":3831},[644],[568,3833,3835,3838],{"className":3834},[644],[568,3836,607],{"className":3837},[644,648],[568,3839,3841],{"className":3840},[849],[568,3842,3844],{"className":3843},[738],[568,3845,3847],{"className":3846},[743],[568,3848,3850],{"className":3849,"style":1892},[747],[568,3851,3852,3855],{"style":1895},[568,3853],{"className":3854,"style":866},[755],[568,3856,3858],{"className":3857},[760,761,762,763],[568,3859,1575],{"className":3860},[644,763],[568,3862],{"className":3863,"style":825},[639],[568,3865,1167],{"className":3866},[829],[568,3868],{"className":3869,"style":825},[639],[568,3871,2816],{"className":3872},[644],[568,3874,3875,3878],{"style":781},[568,3876],{"className":3877,"style":756},[755],[568,3879],{"className":3880,"style":789},[788],[568,3882,3883,3886],{"style":1243},[568,3884],{"className":3885,"style":756},[755],[568,3887,3889,3892],{"className":3888},[644],[568,3890,1575],{"className":3891},[644],[568,3893,607],{"className":3894},[644,648],[568,3896,809],{"className":3897},[808],[568,3899,3901],{"className":3900},[743],[568,3902,3904],{"className":3903,"style":1948},[747],[568,3905],{},[568,3907],{"className":3908},[660,731],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Fehler",[4077,4078,4079,4810,4813],"ul",{},[4080,4081,4082,4083,4397,4398,4461,4462,885],"li",{},"Die Regel anwenden, obwohl der Zähler nicht die Ableitung des Nenners ist: ",[568,4084,4086,4146],{"className":4085},[571],[568,4087,4089],{"className":4088},[575],[577,4090,4091],{"xmlns":579},[581,4092,4093,4143],{},[584,4094,4095,4097,4113,4115,4117,4119,4121,4123,4125,4127,4133,4135,4137,4139,4141],{},[591,4096,1104],{},[678,4098,4099,4101],{},[681,4100,683],{},[584,4102,4103,4109,4111],{},[698,4104,4105,4107],{},[587,4106,607],{},[681,4108,1575],{},[591,4110,1167],{},[681,4112,683],{},[993,4114,995],{},[587,4116,975],{},[587,4118,607],{},[591,4120,2706],{"mathvariant":596},[587,4122,589],{},[591,4124,593],{},[591,4126,604],{"stretchy":603},[698,4128,4129,4131],{},[587,4130,607],{},[681,4132,1575],{},[591,4134,1167],{},[681,4136,683],{},[591,4138,610],{"stretchy":603},[591,4140,1167],{},[587,4142,1170],{},[614,4144,4145],{"encoding":616},"\\int \\frac{1}{x^2 + 1}\\,dx \\neq \\ln(x^2 + 1) + C",[568,4147,4149,4316,4367,4388],{"className":4148,"ariaHidden":622},[621],[568,4150,4152,4156,4159,4162,4265,4268,4271,4274,4277,4313],{"className":4151},[626],[568,4153],{"className":4154,"style":4155},[630],"height:1.2484em;vertical-align:-0.4033em;",[568,4157,1104],{"className":4158,"style":2600},[635,1187,2599],[568,4160],{"className":4161,"style":640},[639],[568,4163,4165,4168,4262],{"className":4164},[644],[568,4166],{"className":4167},[653,731],[568,4169,4171],{"className":4170},[678],[568,4172,4174,4253],{"className":4173},[738,739],[568,4175,4177,4250],{"className":4176},[743],[568,4178,4180,4228,4236],{"className":4179,"style":748},[747],[568,4181,4182,4185],{"style":751},[568,4183],{"className":4184,"style":756},[755],[568,4186,4188],{"className":4187},[760,761,762,763],[568,4189,4191,4222,4225],{"className":4190},[644,763],[568,4192,4194,4197],{"className":4193},[644,763],[568,4195,607],{"className":4196},[644,648,763],[568,4198,4200],{"className":4199},[849],[568,4201,4203],{"className":4202},[738],[568,4204,4206],{"className":4205},[743],[568,4207,4210],{"className":4208,"style":4209},[747],"height:0.7463em;",[568,4211,4213,4216],{"style":4212},"top:-2.786em;margin-right:0.0714em;",[568,4214],{"className":4215,"style":2509},[755],[568,4217,4219],{"className":4218},[760,2513,1995,763],[568,4220,1575],{"className":4221},[644,763],[568,4223,1167],{"className":4224},[829,763],[568,4226,683],{"className":4227},[644,763],[568,4229,4230,4233],{"style":781},[568,4231],{"className":4232,"style":756},[755],[568,4234],{"className":4235,"style":789},[788],[568,4237,4238,4241],{"style":792},[568,4239],{"className":4240,"style":756},[755],[568,4242,4244],{"className":4243},[760,761,762,763],[568,4245,4247],{"className":4246},[644,763],[568,4248,683],{"className":4249},[644,763],[568,4251,809],{"className":4252},[808],[568,4254,4256],{"className":4255},[743],[568,4257,4260],{"className":4258,"style":4259},[747],"height:0.4033em;",[568,4261],{},[568,4263],{"className":4264},[660,731],[568,4266],{"className":4267,"style":640},[639],[568,4269,975],{"className":4270},[644,648],[568,4272,607],{"className":4273},[644,648],[568,4275],{"className":4276,"style":934},[639],[568,4278,4280,4307,4310],{"className":4279},[938],[568,4281,4283],{"className":4282},[938],[568,4284,4286],{"className":4285},[644,2742],[568,4287,4289],{"className":4288},[2746],[568,4290,4292,4295,4304],{"className":4291},[2750],[568,4293],{"className":4294,"style":1538},[630],[568,4296,4298],{"className":4297},[2757],[568,4299,4301],{"className":4300},[644],[568,4302,2764],{"className":4303},[938],[568,4305],{"className":4306},[2768],[568,4308],{"className":4309},[639,2772],[568,4311,906],{"className":4312},[938],[568,4314],{"className":4315,"style":934},[639],[568,4317,4319,4323,4326,4329,4358,4361,4364],{"className":4318},[626],[568,4320],{"className":4321,"style":4322},[630],"height:1.0641em;vertical-align:-0.25em;",[568,4324,589],{"className":4325},[635],[568,4327,604],{"className":4328},[653],[568,4330,4332,4335],{"className":4331},[644],[568,4333,607],{"className":4334},[644,648],[568,4336,4338],{"className":4337},[849],[568,4339,4341],{"className":4340},[738],[568,4342,4344],{"className":4343},[743],[568,4345,4347],{"className":4346,"style":1611},[747],[568,4348,4349,4352],{"style":862},[568,4350],{"className":4351,"style":866},[755],[568,4353,4355],{"className":4354},[760,761,762,763],[568,4356,1575],{"className":4357},[644,763],[568,4359],{"className":4360,"style":825},[639],[568,4362,1167],{"className":4363},[829],[568,4365],{"className":4366,"style":825},[639],[568,4368,4370,4373,4376,4379,4382,4385],{"className":4369},[626],[568,4371],{"className":4372,"style":631},[630],[568,4374,683],{"className":4375},[644],[568,4377,610],{"className":4378},[660],[568,4380],{"className":4381,"style":825},[639],[568,4383,1167],{"className":4384},[829],[568,4386],{"className":4387,"style":825},[639],[568,4389,4391,4394],{"className":4390},[626],[568,4392],{"className":4393,"style":1455},[630],[568,4395,1170],{"className":4396,"style":1459},[644,648],". Richtig ist ",[568,4399,4401,4424],{"className":4400},[571],[568,4402,4404],{"className":4403},[575],[577,4405,4406],{"xmlns":579},[581,4407,4408,4421],{},[584,4409,4410,4413,4415,4417,4419],{},[587,4411,4412],{},"arctan",[591,4414,593],{},[587,4416,607],{},[591,4418,1167],{},[587,4420,1170],{},[614,4422,4423],{"encoding":616},"\\arctan x + C",[568,4425,4427,4452],{"className":4426,"ariaHidden":622},[621],[568,4428,4430,4434,4437,4440,4443,4446,4449],{"className":4429},[626],[568,4431],{"className":4432,"style":4433},[630],"height:0.6984em;vertical-align:-0.0833em;",[568,4435,4412],{"className":4436},[635],[568,4438],{"className":4439,"style":640},[639],[568,4441,607],{"className":4442},[644,648],[568,4444],{"className":4445,"style":825},[639],[568,4447,1167],{"className":4448},[829],[568,4450],{"className":4451,"style":825},[639],[568,4453,4455,4458],{"className":4454},[626],[568,4456],{"className":4457,"style":1455},[630],[568,4459,1170],{"className":4460,"style":1459},[644,648],", also ",[568,4463,4465,4520],{"className":4464},[571],[568,4466,4468],{"className":4467},[575],[577,4469,4470],{"xmlns":579},[581,4471,4472,4517],{},[584,4473,4474,4482,4498,4500,4502,4504,4506,4512,4514],{},[1694,4475,4476,4478,4480],{},[591,4477,1104],{},[681,4479,1700],{},[681,4481,683],{},[678,4483,4484,4486],{},[681,4485,683],{},[584,4487,4488,4494,4496],{},[698,4489,4490,4492],{},[587,4491,607],{},[681,4493,1575],{},[591,4495,1167],{},[681,4497,683],{},[993,4499,995],{},[587,4501,975],{},[587,4503,607],{},[591,4505,906],{},[678,4507,4508,4510],{},[587,4509,2813],{},[681,4511,2816],{},[591,4513,1773],{},[681,4515,4516],{},"0,7854",[614,4518,4519],{"encoding":616},"\\int_0^1 \\frac{1}{x^2 + 1}\\,dx = \\frac{\\pi}{4} \\approx 0{,}7854",[568,4521,4523,4706,4791],{"className":4522,"ariaHidden":622},[621],[568,4524,4526,4530,4585,4588,4688,4691,4694,4697,4700,4703],{"className":4525},[626],[568,4527],{"className":4528,"style":4529},[630],"height:1.4123em;vertical-align:-0.4033em;",[568,4531,4533,4536],{"className":4532},[635],[568,4534,1104],{"className":4535,"style":2600},[635,1187,2599],[568,4537,4539],{"className":4538},[849],[568,4540,4542,4576],{"className":4541},[738,739],[568,4543,4545,4573],{"className":4544},[743],[568,4546,4549,4561],{"className":4547,"style":4548},[747],"height:1.009em;",[568,4550,4552,4555],{"style":4551},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[568,4553],{"className":4554,"style":866},[755],[568,4556,4558],{"className":4557},[760,761,762,763],[568,4559,1700],{"className":4560},[644,763],[568,4562,4564,4567],{"style":4563},"top:-3.2579em;margin-right:0.05em;",[568,4565],{"className":4566,"style":866},[755],[568,4568,4570],{"className":4569},[760,761,762,763],[568,4571,683],{"className":4572},[644,763],[568,4574,809],{"className":4575},[808],[568,4577,4579],{"className":4578},[743],[568,4580,4583],{"className":4581,"style":4582},[747],"height:0.3558em;",[568,4584],{},[568,4586],{"className":4587,"style":640},[639],[568,4589,4591,4594,4685],{"className":4590},[644],[568,4592],{"className":4593},[653,731],[568,4595,4597],{"className":4596},[678],[568,4598,4600,4677],{"className":4599},[738,739],[568,4601,4603,4674],{"className":4602},[743],[568,4604,4606,4652,4660],{"className":4605,"style":748},[747],[568,4607,4608,4611],{"style":751},[568,4609],{"className":4610,"style":756},[755],[568,4612,4614],{"className":4613},[760,761,762,763],[568,4615,4617,4646,4649],{"className":4616},[644,763],[568,4618,4620,4623],{"className":4619},[644,763],[568,4621,607],{"className":4622},[644,648,763],[568,4624,4626],{"className":4625},[849],[568,4627,4629],{"className":4628},[738],[568,4630,4632],{"className":4631},[743],[568,4633,4635],{"className":4634,"style":4209},[747],[568,4636,4637,4640],{"style":4212},[568,4638],{"className":4639,"style":2509},[755],[568,4641,4643],{"className":4642},[760,2513,1995,763],[568,4644,1575],{"className":4645},[644,763],[568,4647,1167],{"className":4648},[829,763],[568,4650,683],{"className":4651},[644,763],[568,4653,4654,4657],{"style":781},[568,4655],{"className":4656,"style":756},[755],[568,4658],{"className":4659,"style":789},[788],[568,4661,4662,4665],{"style":792},[568,4663],{"className":4664,"style":756},[755],[568,4666,4668],{"className":4667},[760,761,762,763],[568,4669,4671],{"className":4670},[644,763],[568,4672,683],{"className":4673},[644,763],[568,4675,809],{"className":4676},[808],[568,4678,4680],{"className":4679},[743],[568,4681,4683],{"className":4682,"style":4259},[747],[568,4684],{},[568,4686],{"className":4687},[660,731],[568,4689],{"className":4690,"style":640},[639],[568,4692,975],{"className":4693},[644,648],[568,4695,607],{"className":4696},[644,648],[568,4698],{"className":4699,"style":934},[639],[568,4701,906],{"className":4702},[938],[568,4704],{"className":4705,"style":934},[639],[568,4707,4709,4713,4782,4785,4788],{"className":4708},[626],[568,4710],{"className":4711,"style":4712},[630],"height:1.0404em;vertical-align:-0.345em;",[568,4714,4716,4719,4779],{"className":4715},[644],[568,4717],{"className":4718},[653,731],[568,4720,4722],{"className":4721},[678],[568,4723,4725,4771],{"className":4724},[738,739],[568,4726,4728,4768],{"className":4727},[743],[568,4729,4732,4746,4754],{"className":4730,"style":4731},[747],"height:0.6954em;",[568,4733,4734,4737],{"style":751},[568,4735],{"className":4736,"style":756},[755],[568,4738,4740],{"className":4739},[760,761,762,763],[568,4741,4743],{"className":4742},[644,763],[568,4744,2816],{"className":4745},[644,763],[568,4747,4748,4751],{"style":781},[568,4749],{"className":4750,"style":756},[755],[568,4752],{"className":4753,"style":789},[788],[568,4755,4756,4759],{"style":792},[568,4757],{"className":4758,"style":756},[755],[568,4760,4762],{"className":4761},[760,761,762,763],[568,4763,4765],{"className":4764},[644,763],[568,4766,2813],{"className":4767,"style":3021},[644,648,763],[568,4769,809],{"className":4770},[808],[568,4772,4774],{"className":4773},[743],[568,4775,4777],{"className":4776,"style":2370},[747],[568,4778],{},[568,4780],{"className":4781},[660,731],[568,4783],{"className":4784,"style":934},[639],[568,4786,1773],{"className":4787},[938],[568,4789],{"className":4790,"style":934},[639],[568,4792,4794,4797,4800,4806],{"className":4793},[626],[568,4795],{"className":4796,"style":2142},[630],[568,4798,1700],{"className":4799},[644],[568,4801,4803],{"className":4802},[644],[568,4804,2153],{"className":4805},[2152],[568,4807,4809],{"className":4808},[644],"7854",[4080,4811,4812],{},"Den Betrag weglassen, obwohl der Nenner negativ werden kann.",[4080,4814,4815],{},"Über eine Nullstelle des Nenners hinweg integrieren.",{"title":4817,"searchDepth":4818,"depth":4818,"links":4819},"",2,[4820,4821,4822],{"id":561,"depth":4818,"text":562},{"id":1552,"depth":4818,"text":1553},{"id":4074,"depth":4818,"text":4075},[4824,4827,4830,4832,4835,4838,4840,4843,4846],{"lhs":4825,"rhs":4826},"log(1^2 + 1) - log(0^2 + 1)","log(2)",{"lhs":4828,"rhs":4829},"round(log(2), 4)","0.6931",{"lhs":4831,"rhs":4829},"round(sum(map(0:999, f(k) = 2 * (k + 0.5) \u002F 1000 \u002F (((k + 0.5) \u002F 1000)^2 + 1))) \u002F 1000, 4)",{"lhs":4833,"rhs":4834},"-log(abs(cos(pi\u002F4))) + log(abs(cos(0)))","log(2) \u002F 2",{"lhs":4836,"rhs":4837},"round(log(2) \u002F 2, 4)","0.3466",{"lhs":4839,"rhs":4837},"round(sum(map(0:999, f(k) = tan((k + 0.5) * pi \u002F 4000))) * pi \u002F 4000, 4)",{"lhs":4841,"rhs":4842},"1\u002F2 * (2*x) \u002F (x^2 + 4)","x \u002F (x^2 + 4)",{"lhs":4844,"rhs":4845},"round(sum(map(0:999, f(k) = 1 \u002F (((k + 0.5) \u002F 1000)^2 + 1))) \u002F 1000, 4)","round(pi \u002F 4, 4)",{"lhs":4845,"rhs":4847},"0.7854","f \\text{ stetig differenzierbar},\\ f(x) \\neq 0 \\text{ im Integrationsbereich}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\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>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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> \u003Cspan class=\"katex\">im Integrationsbereich\u003C\u002Fspan>",null,"md","logarithmic-integration","\\int \\frac{f'(x)}{f(x)}\\,dx = \\ln\\left|f(x)\\right| + 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>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>ln\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int \\frac{f'(x)}{f(x)}\\,dx = \\ln\\left|f(x)\\right| + 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:2.3649em;vertical-align:-0.936em;\">\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=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4289em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.936em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">ln\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">∣\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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