\(\int \cos ^2(c+d x) \cot ^3(c+d x) (a+a \sin (c+d x)) \, dx\) [501]
   \(\int \cos (c+d x) \cot ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [502]
   \(\int \cot ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [503]
   \(\int \cot ^5(c+d x) \csc (c+d x) (a+a \sin (c+d x)) \, dx\) [504]
   \(\int \cot ^5(c+d x) \csc ^2(c+d x) (a+a \sin (c+d x)) \, dx\) [505]
   \(\int \cot ^5(c+d x) \csc ^3(c+d x) (a+a \sin (c+d x)) \, dx\) [506]
   \(\int \cot ^5(c+d x) \csc ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [507]
   \(\int \cot ^5(c+d x) \csc ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [508]
   \(\int \cot ^5(c+d x) \csc ^6(c+d x) (a+a \sin (c+d x)) \, dx\) [509]
   \(\int \cot ^5(c+d x) \csc ^7(c+d x) (a+a \sin (c+d x)) \, dx\) [510]
   \(\int \cos ^5(c+d x) \sin ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\) [511]
   \(\int \cos ^5(c+d x) \sin ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [512]
   \(\int \cos ^5(c+d x) \sin (c+d x) (a+a \sin (c+d x))^2 \, dx\) [513]
   \(\int \cos ^4(c+d x) \cot (c+d x) (a+a \sin (c+d x))^2 \, dx\) [514]
   \(\int \cos ^3(c+d x) \cot ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [515]
   \(\int \cos ^2(c+d x) \cot ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\) [516]
   \(\int \cos (c+d x) \cot ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [517]
   \(\int \cot ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [518]
   \(\int \cot ^5(c+d x) \csc (c+d x) (a+a \sin (c+d x))^2 \, dx\) [519]
   \(\int \cot ^5(c+d x) \csc ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [520]
   \(\int \cos ^5(c+d x) \sin ^2(c+d x) (a+a \sin (c+d x))^3 \, dx\) [521]
   \(\int \cos ^5(c+d x) \sin (c+d x) (a+a \sin (c+d x))^3 \, dx\) [522]
   \(\int \cos ^4(c+d x) \cot (c+d x) (a+a \sin (c+d x))^3 \, dx\) [523]
   \(\int \cos ^3(c+d x) \cot ^2(c+d x) (a+a \sin (c+d x))^3 \, dx\) [524]
   \(\int \cos ^2(c+d x) \cot ^3(c+d x) (a+a \sin (c+d x))^3 \, dx\) [525]
   \(\int \cos (c+d x) \cot ^4(c+d x) (a+a \sin (c+d x))^3 \, dx\) [526]
   \(\int \cot ^5(c+d x) (a+a \sin (c+d x))^3 \, dx\) [527]
   \(\int \cot ^5(c+d x) \csc (c+d x) (a+a \sin (c+d x))^3 \, dx\) [528]
   \(\int \cot ^5(c+d x) \csc ^2(c+d x) (a+a \sin (c+d x))^3 \, dx\) [529]
   \(\int \cos (c+d x) \cot ^4(c+d x) (a+a \sin (c+d x))^4 \, dx\) [530]
   \(\int \cot ^5(c+d x) (a+a \sin (c+d x))^4 \, dx\) [531]
   \(\int \cot ^5(c+d x) \csc (c+d x) (a+a \sin (c+d x))^4 \, dx\) [532]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^3(c+d x)}{a+a \sin (c+d x)} \, dx\) [533]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx\) [534]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin (c+d x)}{a+a \sin (c+d x)} \, dx\) [535]
   \(\int \genfrac {}{}{}{}{\cos ^4(c+d x) \cot (c+d x)}{a+a \sin (c+d x)} \, dx\) [536]
   \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) \cot ^2(c+d x)}{a+a \sin (c+d x)} \, dx\) [537]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) \cot ^3(c+d x)}{a+a \sin (c+d x)} \, dx\) [538]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) \cot ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [539]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{a+a \sin (c+d x)} \, dx\) [540]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc (c+d x)}{a+a \sin (c+d x)} \, dx\) [541]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx\) [542]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc ^3(c+d x)}{a+a \sin (c+d x)} \, dx\) [543]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [544]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^2(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [545]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin (c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [546]
   \(\int \genfrac {}{}{}{}{\cos ^4(c+d x) \cot (c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [547]
   \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) \cot ^2(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [548]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) \cot ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [549]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) \cot ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [550]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [551]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc (c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [552]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc ^2(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [553]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^3(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [554]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^2(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [555]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin (c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [556]
   \(\int \genfrac {}{}{}{}{\cos ^4(c+d x) \cot (c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [557]
   \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) \cot ^2(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [558]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) \cot ^3(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [559]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) \cot ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [560]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [561]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc (c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [562]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [563]
   \(\int \genfrac {}{}{}{}{\cot ^5(c+d x) \csc (c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [564]
   \(\int \cos ^5(c+d x) \sin ^n(c+d x) (a+a \sin (c+d x))^3 \, dx\) [565]
   \(\int \cos ^5(c+d x) \sin ^n(c+d x) (a+a \sin (c+d x))^2 \, dx\) [566]
   \(\int \cos ^5(c+d x) \sin ^n(c+d x) (a+a \sin (c+d x)) \, dx\) [567]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^n(c+d x)}{a+a \sin (c+d x)} \, dx\) [568]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^n(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [569]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^n(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [570]
   \(\int \genfrac {}{}{}{}{\cos ^5(c+d x) \sin ^n(c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [571]
   \(\int \cos ^6(c+d x) \sin ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [572]
   \(\int \cos ^6(c+d x) \sin ^3(c+d x) (a+a \sin (c+d x)) \, dx\) [573]
   \(\int \cos ^6(c+d x) \sin ^2(c+d x) (a+a \sin (c+d x)) \, dx\) [574]
   \(\int \cos ^6(c+d x) \sin (c+d x) (a+a \sin (c+d x)) \, dx\) [575]
   \(\int \cos ^5(c+d x) \cot (c+d x) (a+a \sin (c+d x)) \, dx\) [576]
   \(\int \cos ^4(c+d x) \cot ^2(c+d x) (a+a \sin (c+d x)) \, dx\) [577]
   \(\int \cos ^3(c+d x) \cot ^3(c+d x) (a+a \sin (c+d x)) \, dx\) [578]
   \(\int \cos ^2(c+d x) \cot ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [579]
   \(\int \cos (c+d x) \cot ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [580]
   \(\int \cot ^6(c+d x) (a+a \sin (c+d x)) \, dx\) [581]
   \(\int \cot ^6(c+d x) \csc (c+d x) (a+a \sin (c+d x)) \, dx\) [582]
   \(\int \cot ^6(c+d x) \csc ^2(c+d x) (a+a \sin (c+d x)) \, dx\) [583]
   \(\int \cot ^6(c+d x) \csc ^3(c+d x) (a+a \sin (c+d x)) \, dx\) [584]
   \(\int \cot ^6(c+d x) \csc ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [585]
   \(\int \cot ^6(c+d x) \csc ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [586]
   \(\int \cot ^6(c+d x) \csc ^6(c+d x) (a+a \sin (c+d x)) \, dx\) [587]
   \(\int \cos ^6(c+d x) \sin ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [588]
   \(\int \cos ^6(c+d x) \sin ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\) [589]
   \(\int \cos ^6(c+d x) \sin ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [590]
   \(\int \cos ^6(c+d x) \sin (c+d x) (a+a \sin (c+d x))^2 \, dx\) [591]
   \(\int \cos ^5(c+d x) \cot (c+d x) (a+a \sin (c+d x))^2 \, dx\) [592]
   \(\int \cos ^4(c+d x) \cot ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [593]
   \(\int \cos ^3(c+d x) \cot ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\) [594]
   \(\int \cos ^2(c+d x) \cot ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [595]
   \(\int \cos (c+d x) \cot ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [596]
   \(\int \cot ^6(c+d x) (a+a \sin (c+d x))^2 \, dx\) [597]
   \(\int \cot ^6(c+d x) \csc (c+d x) (a+a \sin (c+d x))^2 \, dx\) [598]
   \(\int \cot ^6(c+d x) \csc ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\) [599]
   \(\int \cot ^6(c+d x) \csc ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\) [600]