3.8.1 \(\int \genfrac {}{}{}{}{(d \tan (e+f x))^n}{(a+b \tan (e+f x))^2} \, dx\) [701]
  3.8.2 \(\int \tan ^m(c+d x) (a+b \tan (c+d x))^{3/2} \, dx\) [702]
  3.8.3 \(\int \tan ^m(c+d x) \sqrt {a+b \tan (c+d x)} \, dx\) [703]
  3.8.4 \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{\sqrt {a+b \tan (c+d x)}} \, dx\) [704]
  3.8.5 \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx\) [705]
  3.8.6 \(\int (d \tan (e+f x))^n (a+b \tan (e+f x))^m \, dx\) [706]
  3.8.7 \(\int \tan ^4(c+d x) (a+b \tan (c+d x))^n \, dx\) [707]
  3.8.8 \(\int \tan ^3(c+d x) (a+b \tan (c+d x))^n \, dx\) [708]
  3.8.9 \(\int \tan ^2(c+d x) (a+b \tan (c+d x))^n \, dx\) [709]
  3.8.10 \(\int \tan (c+d x) (a+b \tan (c+d x))^n \, dx\) [710]
  3.8.11 \(\int (a+b \tan (c+d x))^n \, dx\) [711]
  3.8.12 \(\int \cot (c+d x) (a+b \tan (c+d x))^n \, dx\) [712]
  3.8.13 \(\int \cot ^2(c+d x) (a+b \tan (c+d x))^n \, dx\) [713]
  3.8.14 \(\int \cot ^3(c+d x) (a+b \tan (c+d x))^n \, dx\) [714]
  3.8.15 \(\int \tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^n \, dx\) [715]
  3.8.16 \(\int \sqrt {\tan (c+d x)} (a+b \tan (c+d x))^n \, dx\) [716]
  3.8.17 \(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^n}{\sqrt {\tan (c+d x)}} \, dx\) [717]
  3.8.18 \(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^n}{\tan ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [718]
  3.8.19 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x)) \, dx\) [719]
  3.8.20 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x)) \, dx\) [720]
  3.8.21 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x)) \, dx\) [721]
  3.8.22 \(\int \genfrac {}{}{}{}{a+i a \tan (c+d x)}{\sqrt {\cot (c+d x)}} \, dx\) [722]
  3.8.23 \(\int \genfrac {}{}{}{}{a+i a \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [723]
  3.8.24 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx\) [724]
  3.8.25 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx\) [725]
  3.8.26 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx\) [726]
  3.8.27 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^2 \, dx\) [727]
  3.8.28 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^2}{\sqrt {\cot (c+d x)}} \, dx\) [728]
  3.8.29 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^2}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [729]
  3.8.30 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx\) [730]
  3.8.31 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx\) [731]
  3.8.32 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx\) [732]
  3.8.33 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^3 \, dx\) [733]
  3.8.34 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^3}{\sqrt {\cot (c+d x)}} \, dx\) [734]
  3.8.35 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{a+i a \tan (c+d x)} \, dx\) [735]
  3.8.36 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{a+i a \tan (c+d x)} \, dx\) [736]
  3.8.37 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))} \, dx\) [737]
  3.8.38 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx\) [738]
  3.8.39 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx\) [739]
  3.8.40 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx\) [740]
  3.8.41 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{(a+i a \tan (c+d x))^2} \, dx\) [741]
  3.8.42 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^2} \, dx\) [742]
  3.8.43 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx\) [743]
  3.8.44 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx\) [744]
  3.8.45 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx\) [745]
  3.8.46 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{(a+i a \tan (c+d x))^3} \, dx\) [746]
  3.8.47 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^3} \, dx\) [747]
  3.8.48 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [748]
  3.8.49 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [749]
  3.8.50 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [750]
  3.8.51 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} \, dx\) [751]
  3.8.52 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} \, dx\) [752]
  3.8.53 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} \, dx\) [753]
  3.8.54 \(\int \sqrt {\cot (c+d x)} \sqrt {a+i a \tan (c+d x)} \, dx\) [754]
  3.8.55 \(\int \genfrac {}{}{}{}{\sqrt {a+i a \tan (c+d x)}}{\sqrt {\cot (c+d x)}} \, dx\) [755]
  3.8.56 \(\int \genfrac {}{}{}{}{\sqrt {a+i a \tan (c+d x)}}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [756]
  3.8.57 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx\) [757]
  3.8.58 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx\) [758]
  3.8.59 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx\) [759]
  3.8.60 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{3/2} \, dx\) [760]
  3.8.61 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^{3/2}}{\sqrt {\cot (c+d x)}} \, dx\) [761]
  3.8.62 \(\int \cot ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx\) [762]
  3.8.63 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx\) [763]
  3.8.64 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx\) [764]
  3.8.65 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx\) [765]
  3.8.66 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{5/2} \, dx\) [766]
  3.8.67 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^{5/2}}{\sqrt {\cot (c+d x)}} \, dx\) [767]
  3.8.68 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [768]
  3.8.69 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [769]
  3.8.70 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [770]
  3.8.71 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} \sqrt {a+i a \tan (c+d x)}} \, dx\) [771]
  3.8.72 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)}} \, dx\) [772]
  3.8.73 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)}} \, dx\) [773]
  3.8.74 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx\) [774]
  3.8.75 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx\) [775]
  3.8.76 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{(a+i a \tan (c+d x))^{3/2}} \, dx\) [776]
  3.8.77 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx\) [777]
  3.8.78 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx\) [778]
  3.8.79 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx\) [779]
  3.8.80 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx\) [780]
  3.8.81 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx\) [781]
  3.8.82 \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx\) [782]
  3.8.83 \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)}}{(a+i a \tan (c+d x))^{5/2}} \, dx\) [783]
  3.8.84 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx\) [784]
  3.8.85 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx\) [785]
  3.8.86 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx\) [786]
  3.8.87 \(\int \genfrac {}{}{}{}{1}{\cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx\) [787]
  3.8.88 \(\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^3 \, dx\) [788]
  3.8.89 \(\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^2 \, dx\) [789]
  3.8.90 \(\int (d \cot (e+f x))^n (a+i a \tan (e+f x)) \, dx\) [790]
  3.8.91 \(\int \genfrac {}{}{}{}{(d \cot (e+f x))^n}{a+i a \tan (e+f x)} \, dx\) [791]
  3.8.92 \(\int \genfrac {}{}{}{}{(d \cot (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx\) [792]
  3.8.93 \(\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^m \, dx\) [793]
  3.8.94 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^n \, dx\) [794]
  3.8.95 \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^n \, dx\) [795]
  3.8.96 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^n}{\sqrt {\cot (c+d x)}} \, dx\) [796]
  3.8.97 \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^n}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [797]
  3.8.98 \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \tan (c+d x)) \, dx\) [798]
  3.8.99 \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x)) \, dx\) [799]
  3.8.100 \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x)) \, dx\) [800]