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3.15
Integrals 1401 to 1500
3.15.1
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sqrt {\sec (c+d x)}} \, dx\) [1401]
3.15.2
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1402]
3.15.3
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1403]
3.15.4
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^3} \, dx\) [1404]
3.15.5
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^3} \, dx\) [1405]
3.15.6
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^3} \, dx\) [1406]
3.15.7
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sqrt {\sec (c+d x)}} \, dx\) [1407]
3.15.8
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1408]
3.15.9
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1409]
3.15.10
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1410]
3.15.11
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1411]
3.15.12
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1412]
3.15.13
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1413]
3.15.14
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1414]
3.15.15
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1415]
3.15.16
\(\int \sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1416]
3.15.17
\(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1417]
3.15.18
\(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1418]
3.15.19
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1419]
3.15.20
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1420]
3.15.21
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1421]
3.15.22
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1422]
3.15.23
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1423]
3.15.24
\(\int (a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1424]
3.15.25
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1425]
3.15.26
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x) \, dx\) [1426]
3.15.27
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1427]
3.15.28
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1428]
3.15.29
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1429]
3.15.30
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1430]
3.15.31
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1431]
3.15.32
\(\int (a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1432]
3.15.33
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1433]
3.15.34
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1434]
3.15.35
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1435]
3.15.36
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1436]
3.15.37
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1437]
3.15.38
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1438]
3.15.39
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{\sqrt {a+b \cos (c+d x)} \sqrt {\sec (c+d x)}} \, dx\) [1439]
3.15.40
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1440]
3.15.41
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1441]
3.15.42
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1442]
3.15.43
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1443]
3.15.44
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{3/2} \sqrt {\sec (c+d x)}} \, dx\) [1444]
3.15.45
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{3/2} \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1445]
3.15.46
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1446]
3.15.47
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1447]
3.15.48
\(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1448]
3.15.49
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{5/2} \sqrt {\sec (c+d x)}} \, dx\) [1449]
3.15.50
\(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{5/2} \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1450]
3.15.51
\(\int (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1451]
3.15.52
\(\int (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1452]
3.15.53
\(\int (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1453]
3.15.54
\(\int (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1454]
3.15.55
\(\int (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1455]
3.15.56
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1456]
3.15.57
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1457]
3.15.58
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1458]
3.15.59
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1459]
3.15.60
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1460]
3.15.61
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1461]
3.15.62
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1462]
3.15.63
\(\int (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1463]
3.15.64
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1464]
3.15.65
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1465]
3.15.66
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1466]
3.15.67
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1467]
3.15.68
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1468]
3.15.69
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1469]
3.15.70
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1470]
3.15.71
\(\int (a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1471]
3.15.72
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1472]
3.15.73
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^3 (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1473]
3.15.74
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x) \, dx\) [1474]
3.15.75
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1475]
3.15.76
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1476]
3.15.77
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1477]
3.15.78
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1478]
3.15.79
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1479]
3.15.80
\(\int (a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1480]
3.15.81
\(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^4 (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1481]
3.15.82
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{a+b \cos (c+d x)} \, dx\) [1482]
3.15.83
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{a+b \cos (c+d x)} \, dx\) [1483]
3.15.84
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{a+b \cos (c+d x)} \, dx\) [1484]
3.15.85
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{a+b \cos (c+d x)} \, dx\) [1485]
3.15.86
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x)) \sqrt {\sec (c+d x)}} \, dx\) [1486]
3.15.87
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1487]
3.15.88
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1488]
3.15.89
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^2} \, dx\) [1489]
3.15.90
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^2} \, dx\) [1490]
3.15.91
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^2} \, dx\) [1491]
3.15.92
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sqrt {\sec (c+d x)}} \, dx\) [1492]
3.15.93
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1493]
3.15.94
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1494]
3.15.95
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^3} \, dx\) [1495]
3.15.96
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^3} \, dx\) [1496]
3.15.97
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^3} \, dx\) [1497]
3.15.98
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sqrt {\sec (c+d x)}} \, dx\) [1498]
3.15.99
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1499]
3.15.100
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1500]
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