\(\int \genfrac {}{}{}{}{x^3 \sec (a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [601]
   \(\int \genfrac {}{}{}{}{x^4 \sec ^2(a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [602]
   \(\int \sec ^4(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [603]
   \(\int \sec ^3(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [604]
   \(\int \sec ^2(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [605]
   \(\int \sec (2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [606]
   \(\int \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [607]
   \(\int \cos (2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [608]
   \(\int \cos ^2(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [609]
   \(\int \cos ^3(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [610]
   \(\int \sec ^4(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [611]
   \(\int \sec ^3(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [612]
   \(\int \sec ^2(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [613]
   \(\int \sec (2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [614]
   \(\int (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [615]
   \(\int \cos (2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [616]
   \(\int \cos ^2(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [617]
   \(\int \cos ^3(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [618]
   \(\int \genfrac {}{}{}{}{\sec ^4(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [619]
   \(\int \genfrac {}{}{}{}{\sec ^3(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [620]
   \(\int \genfrac {}{}{}{}{\sec ^2(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [621]
   \(\int \genfrac {}{}{}{}{\sec (2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [622]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [623]
   \(\int \genfrac {}{}{}{}{\cos (2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [624]
   \(\int \genfrac {}{}{}{}{\cos ^2(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [625]
   \(\int \genfrac {}{}{}{}{\sec ^4(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [626]
   \(\int \genfrac {}{}{}{}{\sec ^3(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [627]
   \(\int \genfrac {}{}{}{}{\sec ^2(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [628]
   \(\int \genfrac {}{}{}{}{\sec (2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [629]
   \(\int \genfrac {}{}{}{}{1}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [630]
   \(\int \genfrac {}{}{}{}{\cos (2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [631]
   \(\int \genfrac {}{}{}{}{\cos ^2(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [632]
   \(\int \genfrac {}{}{}{}{\cot (x) \csc (x)}{\sqrt {\sin (2 x)}} \, dx\) [633]
   \(\int \genfrac {}{}{}{}{\csc ^2(x) \sec (x)}{\sqrt {\sin (2 x)} (-2+\tan (x))} \, dx\) [634]
   \(\int \genfrac {}{}{}{}{\cos ^2(x) \sin (x)}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [635]
   \(\int \genfrac {}{}{}{}{\cos ^3(x) \cos (2 x)}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [636]
   \(\int (b \sec (c+d x)+a \sin (c+d x))^n (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [637]
   \(\int (b \sec (c+d x)+a \sin (c+d x))^3 (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [638]
   \(\int (b \sec (c+d x)+a \sin (c+d x))^2 (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [639]
   \(\int (b \sec (c+d x)+a \sin (c+d x)) (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [640]
   \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{b \sec (c+d x)+a \sin (c+d x)} \, dx\) [641]
   \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{(b \sec (c+d x)+a \sin (c+d x))^2} \, dx\) [642]
   \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{(b \sec (c+d x)+a \sin (c+d x))^3} \, dx\) [643]
   \(\int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx\) [644]
   \(\int \cos (a+b x) F(c,d,\sin (a+b x),r,s) \, dx\) [645]
   \(\int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx\) [646]
   \(\int \csc ^2(a+b x) F(c,d,\cot (a+b x),r,s) \, dx\) [647]
   \(\int \genfrac {}{}{}{}{\sin (x)}{a+b \cos (x)} \, dx\) [648]
   \(\int (a+b \cos (x))^n \sin (x) \, dx\) [649]
   \(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {1+\cos ^2(x)}} \, dx\) [650]
   \(\int \cos (\cos (x)) \sin (x) \, dx\) [651]
   \(\int \cos (x) \cos (\cos (x)) \sin (x) \sin (\cos (x)) \, dx\) [652]
   \(\int \cos (\cos (x)) \sin (x) \sin ^2(6 \cos (x)) \, dx\) [653]
   \(\int \cos ^3(x) (a+b \cos ^2(x))^3 \sin (x) \, dx\) [654]
   \(\int \sin (3 x) \sin (\cos (3 x)) \, dx\) [655]
   \(\int e^{\cos (1+3 x)} \cos (1+3 x) \sin (1+3 x) \, dx\) [656]
   \(\int \genfrac {}{}{}{}{\cos ^2(x) \sin (x)}{\sqrt {1-\cos ^6(x)}} \, dx\) [657]
   \(\int \genfrac {}{}{}{}{\sin ^5(x)}{\sqrt {1-5 \cos (x)}} \, dx\) [658]
   \(\int e^{n \cos (a+b x)} \sin (a+b x) \, dx\) [659]
   \(\int e^{n \cos (a c+b c x)} \sin (c (a+b x)) \, dx\) [660]
   \(\int e^{n \cos (c (a+b x))} \sin (a c+b c x) \, dx\) [661]
   \(\int e^{n \cos (a+b x)} \tan (a+b x) \, dx\) [662]
   \(\int e^{n \cos (a c+b c x)} \tan (c (a+b x)) \, dx\) [663]
   \(\int e^{n \cos (c (a+b x))} \tan (a c+b c x) \, dx\) [664]
   \(\int \genfrac {}{}{}{}{\cos (x)}{a+b \sin (x)} \, dx\) [665]
   \(\int \cos (x) (a+b \sin (x))^n \, dx\) [666]
   \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {1+\sin ^2(x)}} \, dx\) [667]
   \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {4-\sin ^2(x)}} \, dx\) [668]
   \(\int \genfrac {}{}{}{}{\cos (3 x)}{\sqrt {4-\sin ^2(3 x)}} \, dx\) [669]
   \(\int \cos (x) \sqrt {1+\csc (x)} \, dx\) [670]
   \(\int \cos (x) \sqrt {4-\sin ^2(x)} \, dx\) [671]
   \(\int \cos (x) \sin (x) \sqrt {1+\sin ^2(x)} \, dx\) [672]
   \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {2 \sin (x)+\sin ^2(x)}} \, dx\) [673]
   \(\int \cos (x) \cos (\sin (x)) \, dx\) [674]
   \(\int \cos (x) \cos (\sin (x)) \cos (\sin (\sin (x))) \, dx\) [675]
   \(\int \cos (x) \sec (\sin (x)) \, dx\) [676]
   \(\int \cos (x) \sin ^3(x) (a+b \sin ^2(x))^3 \, dx\) [677]
   \(\int e^{\sin (x)} \cos (x) \sin (x) \, dx\) [678]
   \(\int \genfrac {}{}{}{}{\cos ^3(x)}{\sqrt {\sin ^3(x)}} \, dx\) [679]
   \(\int \genfrac {}{}{}{}{e^{\sqrt {\sin (x)}} \cos (x)}{\sqrt {\sin (x)}} \, dx\) [680]
   \(\int e^{4+\sin (x)} \cos (x) \, dx\) [681]
   \(\int e^{\cos (x) \sin (x)} \cos (2 x) \, dx\) [682]
   \(\int e^{\cos (\genfrac {}{}{}{}{x}{2}) \sin (\genfrac {}{}{}{}{x}{2})} \cos (x) \, dx\) [683]
   \(\int e^{n \sin (a+b x)} \cos (a+b x) \, dx\) [684]
   \(\int e^{n \sin (a c+b c x)} \cos (c (a+b x)) \, dx\) [685]
   \(\int e^{n \sin (c (a+b x))} \cos (a c+b c x) \, dx\) [686]
   \(\int e^{n \sin (a+b x)} \cot (a+b x) \, dx\) [687]
   \(\int e^{n \sin (a c+b c x)} \cot (c (a+b x)) \, dx\) [688]
   \(\int e^{n \sin (c (a+b x))} \cot (a c+b c x) \, dx\) [689]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{a+b \tan (x)} \, dx\) [690]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{1-\tan ^2(x)} \, dx\) [691]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{9+\tan ^2(x)} \, dx\) [692]
   \(\int \sec ^2(x) (a+b \tan (x))^n \, dx\) [693]
   \(\int \sec ^2(x) (1+\genfrac {}{}{}{}{1}{1+\tan ^2(x)}) \, dx\) [694]
   \(\int \genfrac {}{}{}{}{\sec ^2(x) (2+\tan ^2(x))}{1+\tan ^2(x)} \, dx\) [695]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{2+2 \tan (x)+\tan ^2(x)} \, dx\) [696]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{\tan ^2(x)+\tan ^3(x)} \, dx\) [697]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{-\tan ^2(x)+\tan ^3(x)} \, dx\) [698]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{3-4 \tan ^3(x)} \, dx\) [699]
   \(\int \genfrac {}{}{}{}{\sec ^2(x)}{11-5 \tan (x)+5 \tan ^2(x)} \, dx\) [700]