\(\int \csc (c+d x) \sec ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [801]
   \(\int \csc ^2(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [802]
   \(\int \csc ^3(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x)) \, dx\) [803]
   \(\int (a+a \sin (c+d x))^2 \tan ^4(c+d x) \, dx\) [804]
   \(\int \sec (c+d x) (a+a \sin (c+d x))^2 \tan ^3(c+d x) \, dx\) [805]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x))^2 \tan ^2(c+d x) \, dx\) [806]
   \(\int \sec ^3(c+d x) (a+a \sin (c+d x))^2 \tan (c+d x) \, dx\) [807]
   \(\int \csc (c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [808]
   \(\int \csc ^2(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [809]
   \(\int \csc ^3(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\) [810]
   \(\int (a+a \sin (c+d x))^3 \tan ^4(c+d x) \, dx\) [811]
   \(\int \sec (c+d x) (a+a \sin (c+d x))^3 \tan ^3(c+d x) \, dx\) [812]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x))^3 \tan ^2(c+d x) \, dx\) [813]
   \(\int \sec ^3(c+d x) (a+a \sin (c+d x))^3 \tan (c+d x) \, dx\) [814]
   \(\int \csc (c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^3 \, dx\) [815]
   \(\int \csc ^2(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^3 \, dx\) [816]
   \(\int \csc ^3(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^3 \, dx\) [817]
   \(\int \csc ^4(c+d x) \sec ^4(c+d x) (a+a \sin (c+d x))^3 \, dx\) [818]
   \(\int (a+a \sin (c+d x))^4 \tan ^4(c+d x) \, dx\) [819]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x))^4 \tan ^2(c+d x) \, dx\) [820]
   \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [821]
   \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [822]
   \(\int \genfrac {}{}{}{}{\tan ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [823]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^3(c+d x)}{a+a \sin (c+d x)} \, dx\) [824]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^2(c+d x)}{a+a \sin (c+d x)} \, dx\) [825]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) \tan (c+d x)}{a+a \sin (c+d x)} \, dx\) [826]
   \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [827]
   \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [828]
   \(\int \genfrac {}{}{}{}{\sin ^3(c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [829]
   \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [830]
   \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [831]
   \(\int \genfrac {}{}{}{}{\tan ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [832]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [833]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^2(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [834]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) \tan (c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [835]
   \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [836]
   \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [837]
   \(\int \genfrac {}{}{}{}{\csc ^3(c+d x) \sec ^4(c+d x)}{(a+a \sin (c+d x))^2} \, dx\) [838]
   \(\int \genfrac {}{}{}{}{\sin ^3(c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [839]
   \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [840]
   \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [841]
   \(\int \genfrac {}{}{}{}{\tan ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [842]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^3(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [843]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^2(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [844]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) \tan (c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [845]
   \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [846]
   \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^4(c+d x)}{(a+a \sin (c+d x))^3} \, dx\) [847]
   \(\int \genfrac {}{}{}{}{\tan ^4(c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [848]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^3(c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [849]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^2(c+d x)}{(a+a \sin (c+d x))^4} \, dx\) [850]
   \(\int \sin (c+d x) (a+a \sin (c+d x)) \tan ^5(c+d x) \, dx\) [851]
   \(\int (a+a \sin (c+d x)) \tan ^5(c+d x) \, dx\) [852]
   \(\int \sec (c+d x) (a+a \sin (c+d x)) \tan ^4(c+d x) \, dx\) [853]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x)) \tan ^3(c+d x) \, dx\) [854]
   \(\int \sec ^3(c+d x) (a+a \sin (c+d x)) \tan ^2(c+d x) \, dx\) [855]
   \(\int \sec ^4(c+d x) (a+a \sin (c+d x)) \tan (c+d x) \, dx\) [856]
   \(\int \csc (c+d x) \sec ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [857]
   \(\int \csc ^2(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [858]
   \(\int \csc ^3(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [859]
   \(\int \csc ^4(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x)) \, dx\) [860]
   \(\int (a+a \sin (c+d x))^2 \tan ^5(c+d x) \, dx\) [861]
   \(\int \sec (c+d x) (a+a \sin (c+d x))^2 \tan ^4(c+d x) \, dx\) [862]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x))^2 \tan ^3(c+d x) \, dx\) [863]
   \(\int \sec ^3(c+d x) (a+a \sin (c+d x))^2 \tan ^2(c+d x) \, dx\) [864]
   \(\int \sec ^4(c+d x) (a+a \sin (c+d x))^2 \tan (c+d x) \, dx\) [865]
   \(\int \csc (c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [866]
   \(\int \csc ^2(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [867]
   \(\int \csc ^3(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [868]
   \(\int \csc ^4(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^2 \, dx\) [869]
   \(\int (a+a \sin (c+d x))^3 \tan ^5(c+d x) \, dx\) [870]
   \(\int \sec (c+d x) (a+a \sin (c+d x))^3 \tan ^4(c+d x) \, dx\) [871]
   \(\int \sec ^2(c+d x) (a+a \sin (c+d x))^3 \tan ^3(c+d x) \, dx\) [872]
   \(\int \sec ^3(c+d x) (a+a \sin (c+d x))^3 \tan ^2(c+d x) \, dx\) [873]
   \(\int \sec ^4(c+d x) (a+a \sin (c+d x))^3 \tan (c+d x) \, dx\) [874]
   \(\int \csc (c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^3 \, dx\) [875]
   \(\int \csc ^2(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^3 \, dx\) [876]
   \(\int \csc ^3(c+d x) \sec ^5(c+d x) (a+a \sin (c+d x))^3 \, dx\) [877]
   \(\int \genfrac {}{}{}{}{\sin ^4(c+d x) \tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [878]
   \(\int \genfrac {}{}{}{}{\sin ^3(c+d x) \tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [879]
   \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [880]
   \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [881]
   \(\int \genfrac {}{}{}{}{\tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [882]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^6(c+d x)}{a+a \sin (c+d x)} \, dx\) [883]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^5(c+d x)}{a+a \sin (c+d x)} \, dx\) [884]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) \tan ^4(c+d x)}{a+a \sin (c+d x)} \, dx\) [885]
   \(\int \genfrac {}{}{}{}{\sec ^4(c+d x) \tan ^3(c+d x)}{a+a \sin (c+d x)} \, dx\) [886]
   \(\int \genfrac {}{}{}{}{\sec ^5(c+d x) \tan ^2(c+d x)}{a+a \sin (c+d x)} \, dx\) [887]
   \(\int \genfrac {}{}{}{}{\sec ^6(c+d x) \tan (c+d x)}{a+a \sin (c+d x)} \, dx\) [888]
   \(\int \genfrac {}{}{}{}{\sec ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [889]
   \(\int \genfrac {}{}{}{}{\csc (c+d x) \sec ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [890]
   \(\int \genfrac {}{}{}{}{\csc ^2(c+d x) \sec ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [891]
   \(\int \genfrac {}{}{}{}{\csc ^3(c+d x) \sec ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [892]
   \(\int \genfrac {}{}{}{}{\csc ^4(c+d x) \sec ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [893]
   \(\int \sec ^5(c+d x) (a+a \sin (c+d x))^2 \tan ^3(c+d x) \, dx\) [894]
   \(\int \genfrac {}{}{}{}{\sin ^3(c+d x) \tan ^9(c+d x)}{a+a \sin (c+d x)} \, dx\) [895]
   \(\int \genfrac {}{}{}{}{\sin ^2(c+d x) \tan ^9(c+d x)}{a+a \sin (c+d x)} \, dx\) [896]
   \(\int \genfrac {}{}{}{}{\sin (c+d x) \tan ^9(c+d x)}{a+a \sin (c+d x)} \, dx\) [897]
   \(\int \genfrac {}{}{}{}{\tan ^9(c+d x)}{a+a \sin (c+d x)} \, dx\) [898]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) \tan ^8(c+d x)}{a+a \sin (c+d x)} \, dx\) [899]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) \tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\) [900]