\(\int \cot ^3(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [501]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [502]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [503]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [504]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [505]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [506]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [507]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [508]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [509]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [510]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [511]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [512]
   \(\int \cot ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [513]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [514]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [515]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [516]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [517]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [518]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx\) [519]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx\) [520]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx\) [521]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))} \, dx\) [522]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx\) [523]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx\) [524]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx\) [525]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx\) [526]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^2} \, dx\) [527]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx\) [528]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx\) [529]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx\) [530]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx\) [531]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^3} \, dx\) [532]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [533]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [534]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx\) [535]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [536]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [537]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [538]
   \(\int \sqrt {\cot (c+d x)} \sqrt {a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx\) [539]
   \(\int \genfrac {}{}{}{}{\sqrt {a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [540]
   \(\int \cot ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [541]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [542]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [543]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [544]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx\) [545]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [546]
   \(\int \cot ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [547]
   \(\int \cot ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [548]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [549]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [550]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [551]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx\) [552]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [553]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [554]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [555]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{\sqrt {a+i a \tan (c+d x)}} \, dx\) [556]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} \sqrt {a+i a \tan (c+d x)}} \, dx\) [557]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx\) [558]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx\) [559]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx\) [560]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx\) [561]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx\) [562]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx\) [563]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx\) [564]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx\) [565]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx\) [566]
   \(\int \cot ^m(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [567]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [568]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [569]
   \(\int \sqrt {\cot (c+d x)} (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx\) [570]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [571]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [572]
   \(\int \genfrac {}{}{}{}{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [573]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [574]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [575]
   \(\int \sqrt {\cot (c+d x)} (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx\) [576]
   \(\int \genfrac {}{}{}{}{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [577]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [578]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [579]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [580]
   \(\int \sqrt {\cot (c+d x)} (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx\) [581]
   \(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [582]
   \(\int \cot ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [583]
   \(\int \cot ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [584]
   \(\int \cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [585]
   \(\int \cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [586]
   \(\int \sqrt {\cot (c+d x)} (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx\) [587]
   \(\int \genfrac {}{}{}{}{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt {\cot (c+d x)}} \, dx\) [588]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [589]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [590]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx\) [591]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+b \tan (c+d x))} \, dx\) [592]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [593]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx\) [594]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [595]
   \(\int \genfrac {}{}{}{}{\sqrt {\cot (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx\) [596]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\sqrt {\cot (c+d x)} (a+b \tan (c+d x))^2} \, dx\) [597]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx\) [598]
   \(\int \genfrac {}{}{}{}{A+B \tan (c+d x)}{\cot ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx\) [599]
   \(\int \genfrac {}{}{}{}{\cot ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx\) [600]