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3.2
Integrals 101 to 171
3.2.1
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{a+b \tan (e+f x)} \, dx\) [101]
3.2.2
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^2} \, dx\) [102]
3.2.3
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^3} \, dx\) [103]
3.2.4
\(\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [104]
3.2.5
\(\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [105]
3.2.6
\(\int (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [106]
3.2.7
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{a+b \tan (e+f x)} \, dx\) [107]
3.2.8
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^2} \, dx\) [108]
3.2.9
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^3} \, dx\) [109]
3.2.10
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [110]
3.2.11
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [111]
3.2.12
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [112]
3.2.13
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx\) [113]
3.2.14
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) \sqrt {c+d \tan (e+f x)}} \, dx\) [114]
3.2.15
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 \sqrt {c+d \tan (e+f x)}} \, dx\) [115]
3.2.16
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [116]
3.2.17
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [117]
3.2.18
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [118]
3.2.19
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{3/2}} \, dx\) [119]
3.2.20
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}} \, dx\) [120]
3.2.21
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}} \, dx\) [121]
3.2.22
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [122]
3.2.23
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [123]
3.2.24
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [124]
3.2.25
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{5/2}} \, dx\) [125]
3.2.26
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}} \, dx\) [126]
3.2.27
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}} \, dx\) [127]
3.2.28
\(\int (a+b \tan (e+f x))^{5/2} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [128]
3.2.29
\(\int (a+b \tan (e+f x))^{3/2} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [129]
3.2.30
\(\int \sqrt {a+b \tan (e+f x)} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [130]
3.2.31
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [131]
3.2.32
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [132]
3.2.33
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [133]
3.2.34
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [134]
3.2.35
\(\int (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [135]
3.2.36
\(\int \sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [136]
3.2.37
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [137]
3.2.38
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [138]
3.2.39
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [139]
3.2.40
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [140]
3.2.41
\(\int \sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [141]
3.2.42
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [142]
3.2.43
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [143]
3.2.44
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [144]
3.2.45
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [145]
3.2.46
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{9/2}} \, dx\) [146]
3.2.47
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [147]
3.2.48
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [148]
3.2.49
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [149]
3.2.50
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} \sqrt {c+d \tan (e+f x)}} \, dx\) [150]
3.2.51
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} \sqrt {c+d \tan (e+f x)}} \, dx\) [151]
3.2.52
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} \sqrt {c+d \tan (e+f x)}} \, dx\) [152]
3.2.53
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [153]
3.2.54
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [154]
3.2.55
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [155]
3.2.56
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}} \, dx\) [156]
3.2.57
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}} \, dx\) [157]
3.2.58
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}} \, dx\) [158]
3.2.59
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [159]
3.2.60
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [160]
3.2.61
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [161]
3.2.62
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}} \, dx\) [162]
3.2.63
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}} \, dx\) [163]
3.2.64
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^n (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [164]
3.2.65
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [165]
3.2.66
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [166]
3.2.67
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [167]
3.2.68
\(\int (a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [168]
3.2.69
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{c+d \tan (e+f x)} \, dx\) [169]
3.2.70
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^2} \, dx\) [170]
3.2.71
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^3} \, dx\) [171]
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