3.2 Integrals 101 to 171

\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{a+b \tan (e+f x)} \, dx\) [101]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^2} \, dx\) [102]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^3} \, dx\) [103]
\(\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [104]
\(\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [105]
\(\int (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [106]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{a+b \tan (e+f x)} \, dx\) [107]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^2} \, dx\) [108]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^3} \, dx\) [109]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [110]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [111]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [112]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {c+d \tan (e+f x)}} \, dx\) [113]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) \sqrt {c+d \tan (e+f x)}} \, dx\) [114]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 \sqrt {c+d \tan (e+f x)}} \, dx\) [115]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [116]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [117]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [118]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{3/2}} \, dx\) [119]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}} \, dx\) [120]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}} \, dx\) [121]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [122]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [123]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [124]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{5/2}} \, dx\) [125]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}} \, dx\) [126]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}} \, dx\) [127]
\(\int (a+b \tan (e+f x))^{5/2} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [128]
\(\int (a+b \tan (e+f x))^{3/2} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [129]
\(\int \sqrt {a+b \tan (e+f x)} \sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [130]
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [131]
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [132]
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [133]
\(\int \genfrac {}{}{}{}{\sqrt {c+d \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [134]
\(\int (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [135]
\(\int \sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [136]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [137]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [138]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [139]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [140]
\(\int \sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [141]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {a+b \tan (e+f x)}} \, dx\) [142]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{3/2}} \, dx\) [143]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{5/2}} \, dx\) [144]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{7/2}} \, dx\) [145]
\(\int \genfrac {}{}{}{}{(c+d \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(a+b \tan (e+f x))^{9/2}} \, dx\) [146]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [147]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [148]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{\sqrt {c+d \tan (e+f x)}} \, dx\) [149]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} \sqrt {c+d \tan (e+f x)}} \, dx\) [150]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} \sqrt {c+d \tan (e+f x)}} \, dx\) [151]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} \sqrt {c+d \tan (e+f x)}} \, dx\) [152]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [153]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [154]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{3/2}} \, dx\) [155]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}} \, dx\) [156]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}} \, dx\) [157]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}} \, dx\) [158]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{5/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [159]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^{3/2} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [160]
\(\int \genfrac {}{}{}{}{\sqrt {a+b \tan (e+f x)} (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^{5/2}} \, dx\) [161]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt {a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}} \, dx\) [162]
\(\int \genfrac {}{}{}{}{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}} \, dx\) [163]
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^n (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [164]
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^3 (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [165]
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^2 (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [166]
\(\int (a+b \tan (e+f x))^m (c+d \tan (e+f x)) (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [167]
\(\int (a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x)) \, dx\) [168]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{c+d \tan (e+f x)} \, dx\) [169]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^2} \, dx\) [170]
\(\int \genfrac {}{}{}{}{(a+b \tan (e+f x))^m (A+B \tan (e+f x)+C \tan ^2(e+f x))}{(c+d \tan (e+f x))^3} \, dx\) [171]