3.15.1 \(\int \genfrac {}{}{}{}{\csc ^2(e+f x)}{(g \cos (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1401]
3.15.2 \(\int \genfrac {}{}{}{}{\sin ^4(e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1402]
3.15.3 \(\int \genfrac {}{}{}{}{\sin ^3(e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1403]
3.15.4 \(\int \genfrac {}{}{}{}{\sin ^2(e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1404]
3.15.5 \(\int \genfrac {}{}{}{}{\sin (e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1405]
3.15.6 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1406]
3.15.7 \(\int \genfrac {}{}{}{}{\csc ^2(e+f x)}{(g \cos (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1407]
3.15.8 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)} (d \sin (e+f x))^{5/2}}{a+b \sin (e+f x)} \, dx\) [1408]
3.15.9 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)} (d \sin (e+f x))^{3/2}}{a+b \sin (e+f x)} \, dx\) [1409]
3.15.10 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)} \sqrt {d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\) [1410]
3.15.11 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)}}{\sqrt {d \sin (e+f x)} (a+b \sin (e+f x))} \, dx\) [1411]
3.15.12 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)}}{(d \sin (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1412]
3.15.13 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)}}{(d \sin (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1413]
3.15.14 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)}}{(d \sin (e+f x))^{7/2} (a+b \sin (e+f x))} \, dx\) [1414]
3.15.15 \(\int \genfrac {}{}{}{}{\sqrt {g \cos (e+f x)}}{(d \sin (e+f x))^{9/2} (a+b \sin (e+f x))} \, dx\) [1415]
3.15.16 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2} (d \sin (e+f x))^{3/2}}{a+b \sin (e+f x)} \, dx\) [1416]
3.15.17 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2} \sqrt {d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\) [1417]
3.15.18 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{\sqrt {d \sin (e+f x)} (a+b \sin (e+f x))} \, dx\) [1418]
3.15.19 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{(d \sin (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1419]
3.15.20 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{(d \sin (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1420]
3.15.21 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{(d \sin (e+f x))^{7/2} (a+b \sin (e+f x))} \, dx\) [1421]
3.15.22 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{(d \sin (e+f x))^{9/2} (a+b \sin (e+f x))} \, dx\) [1422]
3.15.23 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2} \sqrt {d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\) [1423]
3.15.24 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{\sqrt {d \sin (e+f x)} (a+b \sin (e+f x))} \, dx\) [1424]
3.15.25 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{(d \sin (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1425]
3.15.26 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{(d \sin (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1426]
3.15.27 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{(d \sin (e+f x))^{7/2} (a+b \sin (e+f x))} \, dx\) [1427]
3.15.28 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{(d \sin (e+f x))^{9/2} (a+b \sin (e+f x))} \, dx\) [1428]
3.15.29 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{5/2}}{(d \sin (e+f x))^{11/2} (a+b \sin (e+f x))} \, dx\) [1429]
3.15.30 \(\int \genfrac {}{}{}{}{(d \sin (e+f x))^{5/2}}{\sqrt {g \cos (e+f x)} (a+b \sin (e+f x))} \, dx\) [1430]
3.15.31 \(\int \genfrac {}{}{}{}{(d \sin (e+f x))^{3/2}}{\sqrt {g \cos (e+f x)} (a+b \sin (e+f x))} \, dx\) [1431]
3.15.32 \(\int \genfrac {}{}{}{}{\sqrt {d \sin (e+f x)}}{\sqrt {g \cos (e+f x)} (a+b \sin (e+f x))} \, dx\) [1432]
3.15.33 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \cos (e+f x)} \sqrt {d \sin (e+f x)} (a+b \sin (e+f x))} \, dx\) [1433]
3.15.34 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \cos (e+f x)} (d \sin (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1434]
3.15.35 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \cos (e+f x)} (d \sin (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1435]
3.15.36 \(\int \genfrac {}{}{}{}{(d \sin (e+f x))^{5/2}}{(g \cos (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1436]
3.15.37 \(\int \genfrac {}{}{}{}{(d \sin (e+f x))^{3/2}}{(g \cos (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1437]
3.15.38 \(\int \genfrac {}{}{}{}{\sqrt {d \sin (e+f x)}}{(g \cos (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1438]
3.15.39 \(\int \genfrac {}{}{}{}{1}{(g \cos (e+f x))^{3/2} \sqrt {d \sin (e+f x)} (a+b \sin (e+f x))} \, dx\) [1439]
3.15.40 \(\int \genfrac {}{}{}{}{1}{(g \cos (e+f x))^{3/2} (d \sin (e+f x))^{3/2} (a+b \sin (e+f x))} \, dx\) [1440]
3.15.41 \(\int \genfrac {}{}{}{}{1}{(g \cos (e+f x))^{3/2} (d \sin (e+f x))^{5/2} (a+b \sin (e+f x))} \, dx\) [1441]
3.15.42 \(\int \genfrac {}{}{}{}{(g \cos (e+f x))^{3/2}}{\sqrt {d \sin (e+f x)} (a+b \sin (e+f x))^2} \, dx\) [1442]
3.15.43 \(\int \sin ^2(c+d x) (a+b \sin (c+d x)) \tan ^2(c+d x) \, dx\) [1443]
3.15.44 \(\int \sin (c+d x) (a+b \sin (c+d x)) \tan ^2(c+d x) \, dx\) [1444]
3.15.45 \(\int (a+b \sin (c+d x)) \tan ^2(c+d x) \, dx\) [1445]
3.15.46 \(\int \sec (c+d x) (a+b \sin (c+d x)) \tan (c+d x) \, dx\) [1446]
3.15.47 \(\int \csc (c+d x) \sec ^2(c+d x) (a+b \sin (c+d x)) \, dx\) [1447]
3.15.48 \(\int \csc ^2(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x)) \, dx\) [1448]
3.15.49 \(\int \csc ^3(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x)) \, dx\) [1449]
3.15.50 \(\int \sin (c+d x) (a+b \sin (c+d x))^2 \tan ^2(c+d x) \, dx\) [1450]
3.15.51 \(\int (a+b \sin (c+d x))^2 \tan ^2(c+d x) \, dx\) [1451]
3.15.52 \(\int \sec (c+d x) (a+b \sin (c+d x))^2 \tan (c+d x) \, dx\) [1452]
3.15.53 \(\int \csc (c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1453]
3.15.54 \(\int \csc ^2(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1454]
3.15.55 \(\int \csc ^3(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1455]
3.15.56 \(\int \csc ^4(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1456]
3.15.57 \(\int \sin (c+d x) (a+b \sin (c+d x))^3 \tan ^2(c+d x) \, dx\) [1457]
3.15.58 \(\int (a+b \sin (c+d x))^3 \tan ^2(c+d x) \, dx\) [1458]
3.15.59 \(\int \sec (c+d x) (a+b \sin (c+d x))^3 \tan (c+d x) \, dx\) [1459]
3.15.60 \(\int \csc (c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^3 \, dx\) [1460]
3.15.61 \(\int \csc ^2(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^3 \, dx\) [1461]
3.15.62 \(\int \csc ^3(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^3 \, dx\) [1462]
3.15.63 \(\int \csc ^4(c+d x) \sec ^2(c+d x) (a+b \sin (c+d x))^3 \, dx\) [1463]
3.15.64 \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1464]
3.15.65 \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1465]
3.15.66 \(\int \genfrac {}{}{}{}{\tan ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1466]
3.15.67 \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan (c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1467]
3.15.68 \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1468]
3.15.69 \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1469]
3.15.70 \(\int \genfrac {}{}{}{}{\csc ^3(c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\) [1470]
3.15.71 \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1471]
3.15.72 \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1472]
3.15.73 \(\int \genfrac {}{}{}{}{\tan ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1473]
3.15.74 \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan (c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1474]
3.15.75 \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1475]
3.15.76 \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1476]
3.15.77 \(\int \genfrac {}{}{}{}{\csc ^3(c+d x) \sec ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\) [1477]
3.15.78 \(\int \genfrac {}{}{}{}{\sec ^2(e+f x) \sqrt {a+b \sin (e+f x)}}{\sqrt {d \sin (e+f x)}} \, dx\) [1478]
3.15.79 \(\int \genfrac {}{}{}{}{\sec ^2(e+f x) (a+b \sin (e+f x))^{3/2}}{\sqrt {d \sin (e+f x)}} \, dx\) [1479]
3.15.80 \(\int \genfrac {}{}{}{}{\sec ^4(e+f x) (a+b \sin (e+f x))^{5/2}}{\sqrt {d \sin (e+f x)}} \, dx\) [1480]
3.15.81 \(\int \sin ^2(c+d x) (a+b \sin (c+d x)) \tan ^5(c+d x) \, dx\) [1481]
3.15.82 \(\int \sin (c+d x) (a+b \sin (c+d x)) \tan ^5(c+d x) \, dx\) [1482]
3.15.83 \(\int (a+b \sin (c+d x)) \tan ^5(c+d x) \, dx\) [1483]
3.15.84 \(\int \sec (c+d x) (a+b \sin (c+d x)) \tan ^4(c+d x) \, dx\) [1484]
3.15.85 \(\int \sec ^2(c+d x) (a+b \sin (c+d x)) \tan ^3(c+d x) \, dx\) [1485]
3.15.86 \(\int \sec ^3(c+d x) (a+b \sin (c+d x)) \tan ^2(c+d x) \, dx\) [1486]
3.15.87 \(\int \sec ^4(c+d x) (a+b \sin (c+d x)) \tan (c+d x) \, dx\) [1487]
3.15.88 \(\int \csc (c+d x) \sec ^5(c+d x) (a+b \sin (c+d x)) \, dx\) [1488]
3.15.89 \(\int \csc ^2(c+d x) \sec ^5(c+d x) (a+b \sin (c+d x)) \, dx\) [1489]
3.15.90 \(\int \csc ^3(c+d x) \sec ^5(c+d x) (a+b \sin (c+d x)) \, dx\) [1490]
3.15.91 \(\int \csc ^4(c+d x) \sec ^5(c+d x) (a+b \sin (c+d x)) \, dx\) [1491]
3.15.92 \(\int \sin (c+d x) (a+b \sin (c+d x))^2 \tan ^5(c+d x) \, dx\) [1492]
3.15.93 \(\int (a+b \sin (c+d x))^2 \tan ^5(c+d x) \, dx\) [1493]
3.15.94 \(\int \sec (c+d x) (a+b \sin (c+d x))^2 \tan ^4(c+d x) \, dx\) [1494]
3.15.95 \(\int \sec ^2(c+d x) (a+b \sin (c+d x))^2 \tan ^3(c+d x) \, dx\) [1495]
3.15.96 \(\int \sec ^3(c+d x) (a+b \sin (c+d x))^2 \tan ^2(c+d x) \, dx\) [1496]
3.15.97 \(\int \sec ^4(c+d x) (a+b \sin (c+d x))^2 \tan (c+d x) \, dx\) [1497]
3.15.98 \(\int \csc (c+d x) \sec ^5(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1498]
3.15.99 \(\int \csc ^2(c+d x) \sec ^5(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1499]
3.15.100 \(\int \csc ^3(c+d x) \sec ^5(c+d x) (a+b \sin (c+d x))^2 \, dx\) [1500]