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3.7
Integrals 601 to 700
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]
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