3.7.1 \(\int \genfrac {}{}{}{}{x^3 \sec (a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [601]
3.7.2 \(\int \genfrac {}{}{}{}{x^4 \sec ^2(a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [602]
3.7.3 \(\int \sec ^4(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [603]
3.7.4 \(\int \sec ^3(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [604]
3.7.5 \(\int \sec ^2(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [605]
3.7.6 \(\int \sec (2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [606]
3.7.7 \(\int \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [607]
3.7.8 \(\int \cos (2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [608]
3.7.9 \(\int \cos ^2(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [609]
3.7.10 \(\int \cos ^3(2 (a+b x)) \sqrt {c \tan (a+b x) \tan (2 (a+b x))} \, dx\) [610]
3.7.11 \(\int \sec ^4(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [611]
3.7.12 \(\int \sec ^3(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [612]
3.7.13 \(\int \sec ^2(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [613]
3.7.14 \(\int \sec (2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [614]
3.7.15 \(\int (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [615]
3.7.16 \(\int \cos (2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [616]
3.7.17 \(\int \cos ^2(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [617]
3.7.18 \(\int \cos ^3(2 (a+b x)) (c \tan (a+b x) \tan (2 (a+b x)))^{3/2} \, dx\) [618]
3.7.19 \(\int \genfrac {}{}{}{}{\sec ^4(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [619]
3.7.20 \(\int \genfrac {}{}{}{}{\sec ^3(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [620]
3.7.21 \(\int \genfrac {}{}{}{}{\sec ^2(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [621]
3.7.22 \(\int \genfrac {}{}{}{}{\sec (2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [622]
3.7.23 \(\int \genfrac {}{}{}{}{1}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [623]
3.7.24 \(\int \genfrac {}{}{}{}{\cos (2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [624]
3.7.25 \(\int \genfrac {}{}{}{}{\cos ^2(2 (a+b x))}{\sqrt {c \tan (a+b x) \tan (2 (a+b x))}} \, dx\) [625]
3.7.26 \(\int \genfrac {}{}{}{}{\sec ^4(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [626]
3.7.27 \(\int \genfrac {}{}{}{}{\sec ^3(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [627]
3.7.28 \(\int \genfrac {}{}{}{}{\sec ^2(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [628]
3.7.29 \(\int \genfrac {}{}{}{}{\sec (2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [629]
3.7.30 \(\int \genfrac {}{}{}{}{1}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [630]
3.7.31 \(\int \genfrac {}{}{}{}{\cos (2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [631]
3.7.32 \(\int \genfrac {}{}{}{}{\cos ^2(2 (a+b x))}{(c \tan (a+b x) \tan (2 (a+b x)))^{3/2}} \, dx\) [632]
3.7.33 \(\int \genfrac {}{}{}{}{\cot (x) \csc (x)}{\sqrt {\sin (2 x)}} \, dx\) [633]
3.7.34 \(\int \genfrac {}{}{}{}{\csc ^2(x) \sec (x)}{\sqrt {\sin (2 x)} (-2+\tan (x))} \, dx\) [634]
3.7.35 \(\int \genfrac {}{}{}{}{\cos ^2(x) \sin (x)}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [635]
3.7.36 \(\int \genfrac {}{}{}{}{\cos ^3(x) \cos (2 x)}{(\sin ^2(x)-\sin (2 x)) \sin ^{\genfrac {}{}{}{}{5}{2}}(2 x)} \, dx\) [636]
3.7.37 \(\int (b \sec (c+d x)+a \sin (c+d x))^n (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [637]
3.7.38 \(\int (b \sec (c+d x)+a \sin (c+d x))^3 (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [638]
3.7.39 \(\int (b \sec (c+d x)+a \sin (c+d x))^2 (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [639]
3.7.40 \(\int (b \sec (c+d x)+a \sin (c+d x)) (a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)) \, dx\) [640]
3.7.41 \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{b \sec (c+d x)+a \sin (c+d x)} \, dx\) [641]
3.7.42 \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{(b \sec (c+d x)+a \sin (c+d x))^2} \, dx\) [642]
3.7.43 \(\int \genfrac {}{}{}{}{a \cos (c+d x)+b \sec (c+d x) \tan (c+d x)}{(b \sec (c+d x)+a \sin (c+d x))^3} \, dx\) [643]
3.7.44 \(\int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx\) [644]
3.7.45 \(\int \cos (a+b x) F(c,d,\sin (a+b x),r,s) \, dx\) [645]
3.7.46 \(\int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx\) [646]
3.7.47 \(\int \csc ^2(a+b x) F(c,d,\cot (a+b x),r,s) \, dx\) [647]
3.7.48 \(\int \genfrac {}{}{}{}{\sin (x)}{a+b \cos (x)} \, dx\) [648]
3.7.49 \(\int (a+b \cos (x))^n \sin (x) \, dx\) [649]
3.7.50 \(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {1+\cos ^2(x)}} \, dx\) [650]
3.7.51 \(\int \cos (\cos (x)) \sin (x) \, dx\) [651]
3.7.52 \(\int \cos (x) \cos (\cos (x)) \sin (x) \sin (\cos (x)) \, dx\) [652]
3.7.53 \(\int \cos (\cos (x)) \sin (x) \sin ^2(6 \cos (x)) \, dx\) [653]
3.7.54 \(\int \cos ^3(x) (a+b \cos ^2(x))^3 \sin (x) \, dx\) [654]
3.7.55 \(\int \sin (3 x) \sin (\cos (3 x)) \, dx\) [655]
3.7.56 \(\int e^{\cos (1+3 x)} \cos (1+3 x) \sin (1+3 x) \, dx\) [656]
3.7.57 \(\int \genfrac {}{}{}{}{\cos ^2(x) \sin (x)}{\sqrt {1-\cos ^6(x)}} \, dx\) [657]
3.7.58 \(\int \genfrac {}{}{}{}{\sin ^5(x)}{\sqrt {1-5 \cos (x)}} \, dx\) [658]
3.7.59 \(\int e^{n \cos (a+b x)} \sin (a+b x) \, dx\) [659]
3.7.60 \(\int e^{n \cos (a c+b c x)} \sin (c (a+b x)) \, dx\) [660]
3.7.61 \(\int e^{n \cos (c (a+b x))} \sin (a c+b c x) \, dx\) [661]
3.7.62 \(\int e^{n \cos (a+b x)} \tan (a+b x) \, dx\) [662]
3.7.63 \(\int e^{n \cos (a c+b c x)} \tan (c (a+b x)) \, dx\) [663]
3.7.64 \(\int e^{n \cos (c (a+b x))} \tan (a c+b c x) \, dx\) [664]
3.7.65 \(\int \genfrac {}{}{}{}{\cos (x)}{a+b \sin (x)} \, dx\) [665]
3.7.66 \(\int \cos (x) (a+b \sin (x))^n \, dx\) [666]
3.7.67 \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {1+\sin ^2(x)}} \, dx\) [667]
3.7.68 \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {4-\sin ^2(x)}} \, dx\) [668]
3.7.69 \(\int \genfrac {}{}{}{}{\cos (3 x)}{\sqrt {4-\sin ^2(3 x)}} \, dx\) [669]
3.7.70 \(\int \cos (x) \sqrt {1+\csc (x)} \, dx\) [670]
3.7.71 \(\int \cos (x) \sqrt {4-\sin ^2(x)} \, dx\) [671]
3.7.72 \(\int \cos (x) \sin (x) \sqrt {1+\sin ^2(x)} \, dx\) [672]
3.7.73 \(\int \genfrac {}{}{}{}{\cos (x)}{\sqrt {2 \sin (x)+\sin ^2(x)}} \, dx\) [673]
3.7.74 \(\int \cos (x) \cos (\sin (x)) \, dx\) [674]
3.7.75 \(\int \cos (x) \cos (\sin (x)) \cos (\sin (\sin (x))) \, dx\) [675]
3.7.76 \(\int \cos (x) \sec (\sin (x)) \, dx\) [676]
3.7.77 \(\int \cos (x) \sin ^3(x) (a+b \sin ^2(x))^3 \, dx\) [677]
3.7.78 \(\int e^{\sin (x)} \cos (x) \sin (x) \, dx\) [678]
3.7.79 \(\int \genfrac {}{}{}{}{\cos ^3(x)}{\sqrt {\sin ^3(x)}} \, dx\) [679]
3.7.80 \(\int \genfrac {}{}{}{}{e^{\sqrt {\sin (x)}} \cos (x)}{\sqrt {\sin (x)}} \, dx\) [680]
3.7.81 \(\int e^{4+\sin (x)} \cos (x) \, dx\) [681]
3.7.82 \(\int e^{\cos (x) \sin (x)} \cos (2 x) \, dx\) [682]
3.7.83 \(\int e^{\cos (\genfrac {}{}{}{}{x}{2}) \sin (\genfrac {}{}{}{}{x}{2})} \cos (x) \, dx\) [683]
3.7.84 \(\int e^{n \sin (a+b x)} \cos (a+b x) \, dx\) [684]
3.7.85 \(\int e^{n \sin (a c+b c x)} \cos (c (a+b x)) \, dx\) [685]
3.7.86 \(\int e^{n \sin (c (a+b x))} \cos (a c+b c x) \, dx\) [686]
3.7.87 \(\int e^{n \sin (a+b x)} \cot (a+b x) \, dx\) [687]
3.7.88 \(\int e^{n \sin (a c+b c x)} \cot (c (a+b x)) \, dx\) [688]
3.7.89 \(\int e^{n \sin (c (a+b x))} \cot (a c+b c x) \, dx\) [689]
3.7.90 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{a+b \tan (x)} \, dx\) [690]
3.7.91 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{1-\tan ^2(x)} \, dx\) [691]
3.7.92 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{9+\tan ^2(x)} \, dx\) [692]
3.7.93 \(\int \sec ^2(x) (a+b \tan (x))^n \, dx\) [693]
3.7.94 \(\int \sec ^2(x) (1+\genfrac {}{}{}{}{1}{1+\tan ^2(x)}) \, dx\) [694]
3.7.95 \(\int \genfrac {}{}{}{}{\sec ^2(x) (2+\tan ^2(x))}{1+\tan ^2(x)} \, dx\) [695]
3.7.96 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{2+2 \tan (x)+\tan ^2(x)} \, dx\) [696]
3.7.97 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{\tan ^2(x)+\tan ^3(x)} \, dx\) [697]
3.7.98 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{-\tan ^2(x)+\tan ^3(x)} \, dx\) [698]
3.7.99 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{3-4 \tan ^3(x)} \, dx\) [699]
3.7.100 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{11-5 \tan (x)+5 \tan ^2(x)} \, dx\) [700]