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Chapter 3
Listing of integrals
3.1
\(\int F^{c (a+b x)} \sin ^n(d+e x) \, dx\)
3.2
\(\int F^{c (a+b x)} \sin ^3(d+e x) \, dx\)
3.3
\(\int F^{c (a+b x)} \sin ^2(d+e x) \, dx\)
3.4
\(\int F^{c (a+b x)} \sin (d+e x) \, dx\)
3.5
\(\int F^{c (a+b x)} \csc (d+e x) \, dx\)
3.6
\(\int F^{c (a+b x)} \csc ^2(d+e x) \, dx\)
3.7
\(\int F^{c (a+b x)} \csc ^3(d+e x) \, dx\)
3.8
\(\int F^{c (a+b x)} \csc ^4(d+e x) \, dx\)
3.9
\(\int e^x \sin ^4(x) \, dx\)
3.10
\(\int F^{c (a+b x)} \cos ^n(d+e x) \, dx\)
3.11
\(\int F^{c (a+b x)} \cos ^3(d+e x) \, dx\)
3.12
\(\int F^{c (a+b x)} \cos ^2(d+e x) \, dx\)
3.13
\(\int F^{c (a+b x)} \cos (d+e x) \, dx\)
3.14
\(\int F^{c (a+b x)} \sec (d+e x) \, dx\)
3.15
\(\int F^{c (a+b x)} \sec ^2(d+e x) \, dx\)
3.16
\(\int F^{c (a+b x)} \sec ^3(d+e x) \, dx\)
3.17
\(\int F^{c (a+b x)} \sec ^4(d+e x) \, dx\)
3.18
\(\int e^x \cos ^4(x) \, dx\)
3.19
\(\int e^{c (a+b x)} \tan ^3(d+e x) \, dx\)
3.20
\(\int e^{c (a+b x)} \tan ^2(d+e x) \, dx\)
3.21
\(\int e^{c (a+b x)} \tan (d+e x) \, dx\)
3.22
\(\int e^{c (a+b x)} \cot (d+e x) \, dx\)
3.23
\(\int e^{c (a+b x)} \cot ^2(d+e x) \, dx\)
3.24
\(\int e^{c (a+b x)} \cot ^3(d+e x) \, dx\)
3.25
\(\int F^{a+b x} \tan (\frac{\pi }{4}+\frac{1}{2} (-c-d x)) \, dx\)
3.26
\(\int F^{c (a+b x)} \sec ^n(d+e x) \, dx\)
3.27
\(\int F^{c (a+b x)} \csc ^n(d+e x) \, dx\)
3.28
\(\int F^{c (a+b x)} (f x)^m \sin (d+e x) \, dx\)
3.29
\(\int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx\)
3.30
\(\int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx\)
3.31
\(\int f F^{c (a+b x)} (f x)^{-2+m} (e x \cos (d+e x)+(-1+m+b c x \log (F)) \sin (d+e x)) \, dx\)
3.32
\(\int f F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx\)
3.33
\(\int \frac{F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(m+b c x \log (F)) \sin (d+e x))}{x} \, dx\)
3.34
\(\int F^{c (a+b x)} (e x \cos (d+e x)+(1+b c x \log (F)) \sin (d+e x)) \, dx\)
3.35
\(\int F^{c (a+b x)} (e \cos (d+e x)+b c \log (F) \sin (d+e x)) \, dx\)
3.36
\(\int \frac{F^{c (a+b x)} (e x \cos (d+e x)+(-1+b c x \log (F)) \sin (d+e x))}{x^2} \, dx\)
3.37
\(\int \frac{F^{c (a+b x)} (e x \cos (d+e x)+(-2+b c x \log (F)) \sin (d+e x))}{x^3} \, dx\)
3.38
\(\int e^{a+b x} \cos (c+d x) \sin (c+d x) \, dx\)
3.39
\(\int e^{a+b x} \cos (c+d x) \sin ^2(c+d x) \, dx\)
3.40
\(\int e^{a+b x} \cos (c+d x) \sin ^3(c+d x) \, dx\)
3.41
\(\int e^{a+b x} \cos ^2(c+d x) \sin (c+d x) \, dx\)
3.42
\(\int e^{a+b x} \cos ^2(c+d x) \sin ^2(c+d x) \, dx\)
3.43
\(\int e^{a+b x} \cos ^2(c+d x) \sin ^3(c+d x) \, dx\)
3.44
\(\int e^{a+b x} \cos ^3(c+d x) \sin (c+d x) \, dx\)
3.45
\(\int e^{a+b x} \cos ^3(c+d x) \sin ^2(c+d x) \, dx\)
3.46
\(\int e^{a+b x} \cos ^3(c+d x) \sin ^3(c+d x) \, dx\)
3.47
\(\int e^x x \sin (x) \, dx\)
3.48
\(\int e^x x^2 \sin (x) \, dx\)
3.49
\(\int e^x x \cos (x) \, dx\)
3.50
\(\int e^x x^2 \cos (x) \, dx\)
3.51
\(\int e^{3 x} (-5 \cos (4 x)+2 \sin (4 x)) \, dx\)
3.52
\(\int (e^{-x} \sin (x)+e^x \sin (x)) \, dx\)
3.53
\(\int \frac{F^{a+b x} \cos (c+d x)}{e+e \sin (c+d x)} \, dx\)
3.54
\(\int \frac{F^{a+b x} \cos (c+d x)}{e-e \sin (c+d x)} \, dx\)
3.55
\(\int \frac{F^{a+b x} \sin (c+d x)}{e+e \cos (c+d x)} \, dx\)
3.56
\(\int \frac{F^{a+b x} \sin (c+d x)}{e-e \cos (c+d x)} \, dx\)
3.57
\(\int e^{x^2} \sin (b x) \, dx\)
3.58
\(\int e^{x^2} \cos (b x) \, dx\)
3.59
\(\int e^{x^2} \sin (a+b x) \, dx\)
3.60
\(\int e^{x^2} \cos (a+b x) \, dx\)
3.61
\(\int e^{2 x^2} x \cos (2 x^2) \, dx\)
3.62
\(\int e^x \sin (e^x) \, dx\)
3.63
\(\int e^x \csc (e^x) \sec (e^x) \, dx\)
3.64
\(\int e^x \cos (e^x) \, dx\)
3.65
\(\int e^{2 x} \cos (e^{2 x}) \, dx\)
3.66
\(\int e^{-2 x} \cos (e^{-2 x}) \, dx\)
3.67
\(\int e^{2 x} \cos (e^x) \, dx\)
3.68
\(\int e^{-1+3 x} \cos (e^{-1+3 x}) \sin (1+e^{-1+3 x}) \, dx\)
3.69
\(\int e^x \tan (e^x) \, dx\)
3.70
\(\int e^x \sec (e^x) \, dx\)
3.71
\(\int e^x \sec (e^x) \tan (e^x) \, dx\)
3.72
\(\int e^x \csc ^2(e^x) \, dx\)
3.73
\(\int e^x \sin (a+b x) \, dx\)
3.74
\(\int e^x \sin (a+c x^2) \, dx\)
3.75
\(\int e^x \sin (a+b x+c x^2) \, dx\)
3.76
\(\int e^{x^2} \sin (a+b x) \, dx\)
3.77
\(\int e^{x^2} \sin (a+c x^2) \, dx\)
3.78
\(\int e^{x^2} \sin (a+b x+c x^2) \, dx\)
3.79
\(\int f^{a+b x} \sin (d+f x^2) \, dx\)
3.80
\(\int f^{a+b x} \sin ^2(d+f x^2) \, dx\)
3.81
\(\int f^{a+b x} \sin ^3(d+f x^2) \, dx\)
3.82
\(\int f^{a+b x} \sin (d+e x+f x^2) \, dx\)
3.83
\(\int f^{a+b x} \sin ^2(d+e x+f x^2) \, dx\)
3.84
\(\int f^{a+b x} \sin ^3(d+e x+f x^2) \, dx\)
3.85
\(\int f^{a+c x^2} \sin (d+e x) \, dx\)
3.86
\(\int f^{a+c x^2} \sin ^2(d+e x) \, dx\)
3.87
\(\int f^{a+c x^2} \sin ^3(d+e x) \, dx\)
3.88
\(\int f^{a+c x^2} \sin (d+f x^2) \, dx\)
3.89
\(\int f^{a+c x^2} \sin ^2(d+f x^2) \, dx\)
3.90
\(\int f^{a+c x^2} \sin ^3(d+f x^2) \, dx\)
3.91
\(\int f^{a+c x^2} \sin (d+e x+f x^2) \, dx\)
3.92
\(\int f^{a+c x^2} \sin ^2(d+e x+f x^2) \, dx\)
3.93
\(\int f^{a+c x^2} \sin ^3(d+e x+f x^2) \, dx\)
3.94
\(\int f^{a+b x+c x^2} \sin (d+e x) \, dx\)
3.95
\(\int f^{a+b x+c x^2} \sin ^2(d+e x) \, dx\)
3.96
\(\int f^{a+b x+c x^2} \sin ^3(d+e x) \, dx\)
3.97
\(\int f^{a+b x+c x^2} \sin (d+f x^2) \, dx\)
3.98
\(\int f^{a+b x+c x^2} \sin ^2(d+f x^2) \, dx\)
3.99
\(\int f^{a+b x+c x^2} \sin ^3(d+f x^2) \, dx\)
3.100
\(\int f^{a+b x+c x^2} \sin (d+e x+f x^2) \, dx\)
3.101
\(\int f^{a+b x+c x^2} \sin ^2(d+e x+f x^2) \, dx\)
3.102
\(\int f^{a+b x+c x^2} \sin ^3(d+e x+f x^2) \, dx\)
3.103
\(\int f^{a+b x+c x^2} \sin (a+b x+e x^2) \, dx\)
3.104
\(\int e^x \cos (a+b x) \, dx\)
3.105
\(\int e^x \cos (a+c x^2) \, dx\)
3.106
\(\int e^x \cos (a+b x+c x^2) \, dx\)
3.107
\(\int e^{x^2} \cos (a+b x) \, dx\)
3.108
\(\int e^{x^2} \cos (a+c x^2) \, dx\)
3.109
\(\int e^{x^2} \cos (a+b x+c x^2) \, dx\)
3.110
\(\int f^{a+b x} \cos (d+f x^2) \, dx\)
3.111
\(\int f^{a+b x} \cos ^2(d+f x^2) \, dx\)
3.112
\(\int f^{a+b x} \cos ^3(d+f x^2) \, dx\)
3.113
\(\int f^{a+b x} \cos (d+e x+f x^2) \, dx\)
3.114
\(\int f^{a+b x} \cos ^2(d+e x+f x^2) \, dx\)
3.115
\(\int f^{a+b x} \cos ^3(d+e x+f x^2) \, dx\)
3.116
\(\int f^{a+c x^2} \cos (d+e x) \, dx\)
3.117
\(\int f^{a+c x^2} \cos ^2(d+e x) \, dx\)
3.118
\(\int f^{a+c x^2} \cos ^3(d+e x) \, dx\)
3.119
\(\int f^{a+c x^2} \cos (d+f x^2) \, dx\)
3.120
\(\int f^{a+c x^2} \cos ^2(d+f x^2) \, dx\)
3.121
\(\int f^{a+c x^2} \cos ^3(d+f x^2) \, dx\)
3.122
\(\int f^{a+c x^2} \cos (d+e x+f x^2) \, dx\)
3.123
\(\int f^{a+c x^2} \cos ^2(d+e x+f x^2) \, dx\)
3.124
\(\int f^{a+c x^2} \cos ^3(d+e x+f x^2) \, dx\)
3.125
\(\int f^{a+b x+c x^2} \cos (d+e x) \, dx\)
3.126
\(\int f^{a+b x+c x^2} \cos ^2(d+e x) \, dx\)
3.127
\(\int f^{a+b x+c x^2} \cos ^3(d+e x) \, dx\)
3.128
\(\int f^{a+b x+c x^2} \cos (d+f x^2) \, dx\)
3.129
\(\int f^{a+b x+c x^2} \cos ^2(d+f x^2) \, dx\)
3.130
\(\int f^{a+b x+c x^2} \cos ^3(d+f x^2) \, dx\)
3.131
\(\int f^{a+b x+c x^2} \cos (d+e x+f x^2) \, dx\)
3.132
\(\int f^{a+b x+c x^2} \cos ^2(d+e x+f x^2) \, dx\)
3.133
\(\int f^{a+b x+c x^2} \cos ^3(d+e x+f x^2) \, dx\)
3.134
\(\int f^{a+b x+c x^2} \cos (a+b x+e x^2) \, dx\)
3.135
\(\int F^{c (a+b x)} (f+f \sin (d+e x))^2 \, dx\)
3.136
\(\int F^{c (a+b x)} (f+f \sin (d+e x)) \, dx\)
3.137
\(\int \frac{F^{c (a+b x)}}{f+f \sin (d+e x)} \, dx\)
3.138
\(\int \frac{F^{c (a+b x)}}{(f+f \sin (d+e x))^2} \, dx\)
3.139
\(\int F^{c (a+b x)} (f+f \cos (d+e x))^2 \, dx\)
3.140
\(\int F^{c (a+b x)} (f+f \cos (d+e x)) \, dx\)
3.141
\(\int \frac{F^{c (a+b x)}}{f+f \cos (d+e x)} \, dx\)
3.142
\(\int \frac{F^{c (a+b x)}}{(f+f \cos (d+e x))^2} \, dx\)
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