3.9.1 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx\) [801]
3.9.2 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx\) [802]
3.9.3 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx\) [803]
3.9.4 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx\) [804]
3.9.5 \(\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx\) [805]
3.9.6 \(\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx\) [806]
3.9.7 \(\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx\) [807]
3.9.8 \(\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) \sqrt {c-i c \tan (e+f x)} \, dx\) [808]
3.9.9 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{\sqrt {c-i c \tan (e+f x)}} \, dx\) [809]
3.9.10 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx\) [810]
3.9.11 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx\) [811]
3.9.12 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx\) [812]
3.9.13 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx\) [813]
3.9.14 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx\) [814]
3.9.15 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{13/2}} \, dx\) [815]
3.9.16 \(\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2} \, dx\) [816]
3.9.17 \(\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx\) [817]
3.9.18 \(\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx\) [818]
3.9.19 \(\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx\) [819]
3.9.20 \(\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) \sqrt {c-i c \tan (e+f x)} \, dx\) [820]
3.9.21 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{\sqrt {c-i c \tan (e+f x)}} \, dx\) [821]
3.9.22 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx\) [822]
3.9.23 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx\) [823]
3.9.24 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx\) [824]
3.9.25 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx\) [825]
3.9.26 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx\) [826]
3.9.27 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{13/2}} \, dx\) [827]
3.9.28 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{15/2}} \, dx\) [828]
3.9.29 \(\int \genfrac {}{}{}{}{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{17/2}} \, dx\) [829]
3.9.30 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{\sqrt {a+i a \tan (e+f x)}} \, dx\) [830]
3.9.31 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{\sqrt {a+i a \tan (e+f x)}} \, dx\) [831]
3.9.32 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) \sqrt {c-i c \tan (e+f x)}}{\sqrt {a+i a \tan (e+f x)}} \, dx\) [832]
3.9.33 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{\sqrt {a+i a \tan (e+f x)} \sqrt {c-i c \tan (e+f x)}} \, dx\) [833]
3.9.34 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{\sqrt {a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}} \, dx\) [834]
3.9.35 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{\sqrt {a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}} \, dx\) [835]
3.9.36 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx\) [836]
3.9.37 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx\) [837]
3.9.38 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx\) [838]
3.9.39 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) \sqrt {c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{3/2}} \, dx\) [839]
3.9.40 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} \sqrt {c-i c \tan (e+f x)}} \, dx\) [840]
3.9.41 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}} \, dx\) [841]
3.9.42 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}} \, dx\) [842]
3.9.43 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx\) [843]
3.9.44 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx\) [844]
3.9.45 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx\) [845]
3.9.46 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx\) [846]
3.9.47 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) \sqrt {c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{5/2}} \, dx\) [847]
3.9.48 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} \sqrt {c-i c \tan (e+f x)}} \, dx\) [848]
3.9.49 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}} \, dx\) [849]
3.9.50 \(\int \genfrac {}{}{}{}{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}} \, dx\) [850]
3.9.51 \(\int (a+i a \tan (e+f x))^m (A+B \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx\) [851]
3.9.52 \(\int (a+i a \tan (e+f x))^{1+m} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{-1-m} \, dx\) [852]
3.9.53 \(\int \genfrac {}{}{}{}{(c-i c \tan (e+f x))^n (-i (2+n)+(-2+n) \tan (e+f x))}{(-i+\tan (e+f x))^2} \, dx\) [853]
3.9.54 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c+d \tan (e+f x))}{(a+i a \tan (e+f x))^2} \, dx\) [854]
3.9.55 \(\int \genfrac {}{}{}{}{(A+B \tan (e+f x)) (c+d \tan (e+f x))}{(a+i a \tan (e+f x))^{3/2}} \, dx\) [855]