\(\int (a+b \sin ^2(e+f x))^{3/2} \tan (e+f x) \, dx\) [501]
   \(\int \cot (e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [502]
   \(\int \cot ^3(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [503]
   \(\int \cot ^5(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [504]
   \(\int (a+b \sin ^2(e+f x))^{3/2} \tan ^4(e+f x) \, dx\) [505]
   \(\int (a+b \sin ^2(e+f x))^{3/2} \tan ^2(e+f x) \, dx\) [506]
   \(\int (a+b \sin ^2(e+f x))^{3/2} \, dx\) [507]
   \(\int \cot ^2(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [508]
   \(\int \cot ^4(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [509]
   \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [510]
   \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [511]
   \(\int \genfrac {}{}{}{}{\tan (e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [512]
   \(\int \genfrac {}{}{}{}{\cot (e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [513]
   \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [514]
   \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [515]
   \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [516]
   \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [517]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [518]
   \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [519]
   \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [520]
   \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [521]
   \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [522]
   \(\int \genfrac {}{}{}{}{\tan (e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [523]
   \(\int \genfrac {}{}{}{}{\cot (e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [524]
   \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [525]
   \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [526]
   \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [527]
   \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [528]
   \(\int \genfrac {}{}{}{}{1}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [529]
   \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [530]
   \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [531]
   \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [532]
   \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [533]
   \(\int \genfrac {}{}{}{}{\tan (e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [534]
   \(\int \genfrac {}{}{}{}{\cot (e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [535]
   \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [536]
   \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [537]
   \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [538]
   \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [539]
   \(\int \genfrac {}{}{}{}{1}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [540]
   \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [541]
   \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [542]
   \(\int (a+b \sin ^2(e+f x))^p (d \tan (e+f x))^m \, dx\) [543]
   \(\int (a+b \sin ^2(c+d x))^p \tan ^3(c+d x) \, dx\) [544]
   \(\int (a+b \sin ^2(c+d x))^p \tan (c+d x) \, dx\) [545]
   \(\int \cot (c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [546]
   \(\int \cot ^3(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [547]
   \(\int (a+b \sin ^2(c+d x))^p \tan ^4(c+d x) \, dx\) [548]
   \(\int (a+b \sin ^2(c+d x))^p \tan ^2(c+d x) \, dx\) [549]
   \(\int \cot ^2(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [550]
   \(\int \cot ^4(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [551]
   \(\int \genfrac {}{}{}{}{\cot ^3(x)}{a+b \sin ^3(x)} \, dx\) [552]
   \(\int \cot (x) \sqrt {a+b \sin ^3(x)} \, dx\) [553]
   \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt {a+b \sin ^3(x)}} \, dx\) [554]
   \(\int \cot (c+d x) \sqrt {a+b \sin ^4(c+d x)} \, dx\) [555]
   \(\int \genfrac {}{}{}{}{\tan ^3(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [556]
   \(\int \genfrac {}{}{}{}{\tan (c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [557]
   \(\int \genfrac {}{}{}{}{\cot (c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [558]
   \(\int \genfrac {}{}{}{}{\cot ^3(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [559]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [560]
   \(\int \genfrac {}{}{}{}{\tan ^2(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [561]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [562]
   \(\int \genfrac {}{}{}{}{\cot ^2(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [563]
   \(\int (a+b \sin ^4(c+d x))^p \tan ^m(c+d x) \, dx\) [564]
   \(\int (a+b \sin ^4(c+d x))^p \tan ^3(c+d x) \, dx\) [565]
   \(\int (a+b \sin ^4(c+d x))^p \tan (c+d x) \, dx\) [566]
   \(\int \cot (c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [567]
   \(\int \cot ^3(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [568]
   \(\int (a+b \sin ^4(c+d x))^p \tan ^4(c+d x) \, dx\) [569]
   \(\int (a+b \sin ^4(c+d x))^p \tan ^2(c+d x) \, dx\) [570]
   \(\int (a+b \sin ^4(c+d x))^p \, dx\) [571]
   \(\int \cot ^2(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [572]
   \(\int \cot ^4(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [573]
   \(\int (a+b \sin ^n(c+d x))^3 \tan ^m(c+d x) \, dx\) [574]
   \(\int (a+b \sin ^n(c+d x))^2 \tan ^m(c+d x) \, dx\) [575]
   \(\int (a+b \sin ^n(c+d x)) \tan ^m(c+d x) \, dx\) [576]
   \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx\) [577]
   \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{(a+b \sin ^n(c+d x))^2} \, dx\) [578]
   \(\int \cot (x) \sqrt {a+b \sin ^n(x)} \, dx\) [579]
   \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt {a+b \sin ^n(x)}} \, dx\) [580]
   \(\int (a+b \sin ^n(c+d x))^p \tan ^m(c+d x) \, dx\) [581]
   \(\int (a+b \sin ^n(c+d x))^p \tan ^3(c+d x) \, dx\) [582]
   \(\int (a+b \sin ^n(c+d x))^p \tan (c+d x) \, dx\) [583]
   \(\int \cot (c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [584]
   \(\int \cot ^3(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [585]
   \(\int (a+b \sin ^n(c+d x))^p \tan ^4(c+d x) \, dx\) [586]
   \(\int (a+b \sin ^n(c+d x))^p \tan ^2(c+d x) \, dx\) [587]
   \(\int (a+b \sin ^n(c+d x))^p \, dx\) [588]
   \(\int \cot ^2(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [589]
   \(\int \cot ^4(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [590]
   \(\int \genfrac {}{}{}{}{a+b \sin ^2(e+f x)}{(g \cos (e+f x))^{5/2} \sqrt {d \sin (e+f x)}} \, dx\) [591]
   \(\int (c \cos (e+f x))^m (d \sin (e+f x))^n (a+b \sin ^2(e+f x))^p \, dx\) [592]
   \(\int \sqrt {a+(c \cos (e+f x)+b \sin (e+f x))^2} \, dx\) [593]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {a+(c \cos (e+f x)+b \sin (e+f x))^2}} \, dx\) [594]