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3.5
Integrals 401 to 500
3.5.1
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))} \, dx\) [401]
3.5.2
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [402]
3.5.3
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [403]
3.5.4
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [404]
3.5.5
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [405]
3.5.6
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [406]
3.5.7
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^2} \, dx\) [407]
3.5.8
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx\) [408]
3.5.9
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx\) [409]
3.5.10
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [410]
3.5.11
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [411]
3.5.12
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [412]
3.5.13
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [413]
3.5.14
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^3} \, dx\) [414]
3.5.15
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx\) [415]
3.5.16
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [416]
3.5.17
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [417]
3.5.18
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [418]
3.5.19
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))} \, dx\) [419]
3.5.20
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [420]
3.5.21
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [421]
3.5.22
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [422]
3.5.23
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [423]
3.5.24
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [424]
3.5.25
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^2} \, dx\) [425]
3.5.26
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx\) [426]
3.5.27
\(\int \tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [427]
3.5.28
\(\int \sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [428]
3.5.29
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt {\tan (c+d x)}} \, dx\) [429]
3.5.30
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [430]
3.5.31
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [431]
3.5.32
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [432]
3.5.33
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [433]
3.5.34
\(\int \tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [434]
3.5.35
\(\int \sqrt {\tan (c+d x)} (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [435]
3.5.36
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt {\tan (c+d x)}} \, dx\) [436]
3.5.37
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [437]
3.5.38
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [438]
3.5.39
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [439]
3.5.40
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [440]
3.5.41
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [441]
3.5.42
\(\int \tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [442]
3.5.43
\(\int \sqrt {\tan (c+d x)} (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [443]
3.5.44
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt {\tan (c+d x)}} \, dx\) [444]
3.5.45
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [445]
3.5.46
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [446]
3.5.47
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [447]
3.5.48
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [448]
3.5.49
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [449]
3.5.50
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [450]
3.5.51
\(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^{5/2} (\genfrac {}{}{}{}{3 b B}{2 a}+B \tan (c+d x))}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [451]
3.5.52
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt {a+b \tan (c+d x)}} \, dx\) [452]
3.5.53
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (A+B \tan (c+d x))}{\sqrt {a+b \tan (c+d x)}} \, dx\) [453]
3.5.54
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} \sqrt {a+b \tan (c+d x)}} \, dx\) [454]
3.5.55
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \tan (c+d x)}} \, dx\) [455]
3.5.56
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+b \tan (c+d x)}} \, dx\) [456]
3.5.57
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+b \tan (c+d x)}} \, dx\) [457]
3.5.58
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [458]
3.5.59
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [459]
3.5.60
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx\) [460]
3.5.61
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx\) [461]
3.5.62
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx\) [462]
3.5.63
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [463]
3.5.64
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [464]
3.5.65
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [465]
3.5.66
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^{5/2}} \, dx\) [466]
3.5.67
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx\) [467]
3.5.68
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx\) [468]
3.5.69
\(\int \genfrac {}{}{}{}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [469]
3.5.70
\(\int \genfrac {}{}{}{}{\sqrt {\tan (c+d x)} (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [470]
3.5.71
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\sqrt {\tan (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx\) [471]
3.5.72
\(\int \genfrac {}{}{}{}{a B+b B \tan (c+d x)}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx\) [472]
3.5.73
\(\int (a+b \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx\) [473]
3.5.74
\(\int \sqrt [3]{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [474]
3.5.75
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt [3]{a+b \tan (c+d x)}} \, dx\) [475]
3.5.76
\(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{(a+b \tan (c+d x))^{2/3}} \, dx\) [476]
3.5.77
\(\int \genfrac {}{}{}{}{i-\tan (e+f x)}{\sqrt [3]{c+d \tan (e+f x)}} \, dx\) [477]
3.5.78
\(\int \genfrac {}{}{}{}{d-c \tan (e+f x)}{(c+d \tan (e+f x))^{2/3}} \, dx\) [478]
3.5.79
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx\) [479]
3.5.80
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [480]
3.5.81
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [481]
3.5.82
\(\int \tan ^m(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [482]
3.5.83
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [483]
3.5.84
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [484]
3.5.85
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [485]
3.5.86
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx\) [486]
3.5.87
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [487]
3.5.88
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [488]
3.5.89
\(\int \tan ^m(c+d x) \sqrt {a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [489]
3.5.90
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{\sqrt {a+b \tan (c+d x)}} \, dx\) [490]
3.5.91
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx\) [491]
3.5.92
\(\int \genfrac {}{}{}{}{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx\) [492]
3.5.93
\(\int \tan ^m(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [493]
3.5.94
\(\int \tan ^4(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [494]
3.5.95
\(\int \tan ^3(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [495]
3.5.96
\(\int \tan ^2(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [496]
3.5.97
\(\int \tan (c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [497]
3.5.98
\(\int (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [498]
3.5.99
\(\int \cot (c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [499]
3.5.100
\(\int \cot ^2(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [500]
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