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Chapter 3
Listing of integrals
3.1
\(\int x^7 S(b x) \, dx\)
3.2
\(\int x^6 S(b x) \, dx\)
3.3
\(\int x^5 S(b x) \, dx\)
3.4
\(\int x^4 S(b x) \, dx\)
3.5
\(\int x^3 S(b x) \, dx\)
3.6
\(\int x^2 S(b x) \, dx\)
3.7
\(\int x S(b x) \, dx\)
3.8
\(\int S(b x) \, dx\)
3.9
\(\int \frac{S(b x)}{x} \, dx\)
3.10
\(\int \frac{S(b x)}{x^2} \, dx\)
3.11
\(\int \frac{S(b x)}{x^3} \, dx\)
3.12
\(\int \frac{S(b x)}{x^4} \, dx\)
3.13
\(\int \frac{S(b x)}{x^5} \, dx\)
3.14
\(\int \frac{S(b x)}{x^6} \, dx\)
3.15
\(\int \frac{S(b x)}{x^7} \, dx\)
3.16
\(\int \frac{S(b x)}{x^8} \, dx\)
3.17
\(\int \frac{S(b x)}{x^9} \, dx\)
3.18
\(\int \frac{S(b x)}{x^{10}} \, dx\)
3.19
\(\int (c+d x)^3 S(a+b x) \, dx\)
3.20
\(\int (c+d x)^2 S(a+b x) \, dx\)
3.21
\(\int (c+d x) S(a+b x) \, dx\)
3.22
\(\int S(a+b x) \, dx\)
3.23
\(\int \frac{S(a+b x)}{c+d x} \, dx\)
3.24
\(\int \frac{S(a+b x)}{(c+d x)^2} \, dx\)
3.25
\(\int x^3 S(a+b x) \, dx\)
3.26
\(\int x^2 S(a+b x) \, dx\)
3.27
\(\int x S(a+b x) \, dx\)
3.28
\(\int S(a+b x) \, dx\)
3.29
\(\int \frac{S(a+b x)}{x} \, dx\)
3.30
\(\int \frac{S(a+b x)}{x^2} \, dx\)
3.31
\(\int x^7 S(b x)^2 \, dx\)
3.32
\(\int x^6 S(b x)^2 \, dx\)
3.33
\(\int x^5 S(b x)^2 \, dx\)
3.34
\(\int x^4 S(b x)^2 \, dx\)
3.35
\(\int x^3 S(b x)^2 \, dx\)
3.36
\(\int x^2 S(b x)^2 \, dx\)
3.37
\(\int x S(b x)^2 \, dx\)
3.38
\(\int S(b x)^2 \, dx\)
3.39
\(\int \frac{S(b x)^2}{x} \, dx\)
3.40
\(\int \frac{S(b x)^2}{x^2} \, dx\)
3.41
\(\int \frac{S(b x)^2}{x^3} \, dx\)
3.42
\(\int \frac{S(b x)^2}{x^4} \, dx\)
3.43
\(\int \frac{S(b x)^2}{x^5} \, dx\)
3.44
\(\int \frac{S(b x)^2}{x^6} \, dx\)
3.45
\(\int \frac{S(b x)^2}{x^7} \, dx\)
3.46
\(\int \frac{S(b x)^2}{x^8} \, dx\)
3.47
\(\int \frac{S(b x)^2}{x^9} \, dx\)
3.48
\(\int \frac{S(b x)^2}{x^{10}} \, dx\)
3.49
\(\int (c+d x)^2 S(a+b x)^2 \, dx\)
3.50
\(\int (c+d x) S(a+b x)^2 \, dx\)
3.51
\(\int S(a+b x)^2 \, dx\)
3.52
\(\int \frac{S(a+b x)^2}{c+d x} \, dx\)
3.53
\(\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx\)
3.54
\(\int x^2 S(d (a+b \log (c x^n))) \, dx\)
3.55
\(\int x S(d (a+b \log (c x^n))) \, dx\)
3.56
\(\int S(d (a+b \log (c x^n))) \, dx\)
3.57
\(\int \frac{S(d (a+b \log (c x^n)))}{x} \, dx\)
3.58
\(\int \frac{S(d (a+b \log (c x^n)))}{x^2} \, dx\)
3.59
\(\int \frac{S(d (a+b \log (c x^n)))}{x^3} \, dx\)
3.60
\(\int (e x)^m S(d (a+b \log (c x^n))) \, dx\)
3.61
\(\int e^{c+\frac{1}{2} i b^2 \pi x^2} S(b x) \, dx\)
3.62
\(\int e^{c-\frac{1}{2} i b^2 \pi x^2} S(b x) \, dx\)
3.63
\(\int S(b x) \sin (c+\frac{1}{2} b^2 \pi x^2) \, dx\)
3.64
\(\int \cos (c+\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.65
\(\int S(b x)^2 \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.66
\(\int S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.67
\(\int \frac{\sin (\frac{1}{2} b^2 \pi x^2)}{S(b x)} \, dx\)
3.68
\(\int \frac{\sin (\frac{1}{2} b^2 \pi x^2)}{S(b x)^2} \, dx\)
3.69
\(\int \frac{\sin (\frac{1}{2} b^2 \pi x^2)}{S(b x)^3} \, dx\)
3.70
\(\int S(b x)^n \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.71
\(\int x^8 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.72
\(\int x^7 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.73
\(\int x^6 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.74
\(\int x^5 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.75
\(\int x^4 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.76
\(\int x^3 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.77
\(\int x^2 S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.78
\(\int x S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.79
\(\int S(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.80
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x} \, dx\)
3.81
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^2} \, dx\)
3.82
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^3} \, dx\)
3.83
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^4} \, dx\)
3.84
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^5} \, dx\)
3.85
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^6} \, dx\)
3.86
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^7} \, dx\)
3.87
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^8} \, dx\)
3.88
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^9} \, dx\)
3.89
\(\int \frac{S(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^{10}} \, dx\)
3.90
\(\int \cos (\frac{1}{2} b^2 \pi x^2) S(b x)^n \, dx\)
3.91
\(\int x^8 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.92
\(\int x^7 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.93
\(\int x^6 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.94
\(\int x^5 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.95
\(\int x^4 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.96
\(\int x^3 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.97
\(\int x^2 \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.98
\(\int x \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.99
\(\int \cos (\frac{1}{2} b^2 \pi x^2) S(b x) \, dx\)
3.100
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x} \, dx\)
3.101
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^2} \, dx\)
3.102
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^3} \, dx\)
3.103
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^4} \, dx\)
3.104
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^5} \, dx\)
3.105
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^6} \, dx\)
3.106
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^7} \, dx\)
3.107
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^8} \, dx\)
3.108
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^9} \, dx\)
3.109
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) S(b x)}{x^{10}} \, dx\)
3.110
\(\int x^7 \text{FresnelC}(b x) \, dx\)
3.111
\(\int x^6 \text{FresnelC}(b x) \, dx\)
3.112
\(\int x^5 \text{FresnelC}(b x) \, dx\)
3.113
\(\int x^4 \text{FresnelC}(b x) \, dx\)
3.114
\(\int x^3 \text{FresnelC}(b x) \, dx\)
3.115
\(\int x^2 \text{FresnelC}(b x) \, dx\)
3.116
\(\int x \text{FresnelC}(b x) \, dx\)
3.117
\(\int \text{FresnelC}(b x) \, dx\)
3.118
\(\int \frac{\text{FresnelC}(b x)}{x} \, dx\)
3.119
\(\int \frac{\text{FresnelC}(b x)}{x^2} \, dx\)
3.120
\(\int \frac{\text{FresnelC}(b x)}{x^3} \, dx\)
3.121
\(\int \frac{\text{FresnelC}(b x)}{x^4} \, dx\)
3.122
\(\int \frac{\text{FresnelC}(b x)}{x^5} \, dx\)
3.123
\(\int \frac{\text{FresnelC}(b x)}{x^6} \, dx\)
3.124
\(\int \frac{\text{FresnelC}(b x)}{x^7} \, dx\)
3.125
\(\int \frac{\text{FresnelC}(b x)}{x^8} \, dx\)
3.126
\(\int \frac{\text{FresnelC}(b x)}{x^9} \, dx\)
3.127
\(\int \frac{\text{FresnelC}(b x)}{x^{10}} \, dx\)
3.128
\(\int (c+d x)^3 \text{FresnelC}(a+b x) \, dx\)
3.129
\(\int (c+d x)^2 \text{FresnelC}(a+b x) \, dx\)
3.130
\(\int (c+d x) \text{FresnelC}(a+b x) \, dx\)
3.131
\(\int \text{FresnelC}(a+b x) \, dx\)
3.132
\(\int \frac{\text{FresnelC}(a+b x)}{c+d x} \, dx\)
3.133
\(\int \frac{\text{FresnelC}(a+b x)}{(c+d x)^2} \, dx\)
3.134
\(\int x^3 \text{FresnelC}(a+b x) \, dx\)
3.135
\(\int x^2 \text{FresnelC}(a+b x) \, dx\)
3.136
\(\int x \text{FresnelC}(a+b x) \, dx\)
3.137
\(\int \text{FresnelC}(a+b x) \, dx\)
3.138
\(\int \frac{\text{FresnelC}(a+b x)}{x} \, dx\)
3.139
\(\int \frac{\text{FresnelC}(a+b x)}{x^2} \, dx\)
3.140
\(\int x^7 \text{FresnelC}(b x)^2 \, dx\)
3.141
\(\int x^6 \text{FresnelC}(b x)^2 \, dx\)
3.142
\(\int x^5 \text{FresnelC}(b x)^2 \, dx\)
3.143
\(\int x^4 \text{FresnelC}(b x)^2 \, dx\)
3.144
\(\int x^3 \text{FresnelC}(b x)^2 \, dx\)
3.145
\(\int x^2 \text{FresnelC}(b x)^2 \, dx\)
3.146
\(\int x \text{FresnelC}(b x)^2 \, dx\)
3.147
\(\int \text{FresnelC}(b x)^2 \, dx\)
3.148
\(\int \frac{\text{FresnelC}(b x)^2}{x} \, dx\)
3.149
\(\int \frac{\text{FresnelC}(b x)^2}{x^2} \, dx\)
3.150
\(\int \frac{\text{FresnelC}(b x)^2}{x^3} \, dx\)
3.151
\(\int \frac{\text{FresnelC}(b x)^2}{x^4} \, dx\)
3.152
\(\int \frac{\text{FresnelC}(b x)^2}{x^5} \, dx\)
3.153
\(\int \frac{\text{FresnelC}(b x)^2}{x^6} \, dx\)
3.154
\(\int \frac{\text{FresnelC}(b x)^2}{x^7} \, dx\)
3.155
\(\int \frac{\text{FresnelC}(b x)^2}{x^8} \, dx\)
3.156
\(\int \frac{\text{FresnelC}(b x)^2}{x^9} \, dx\)
3.157
\(\int \frac{\text{FresnelC}(b x)^2}{x^{10}} \, dx\)
3.158
\(\int (c+d x)^2 \text{FresnelC}(a+b x)^2 \, dx\)
3.159
\(\int (c+d x) \text{FresnelC}(a+b x)^2 \, dx\)
3.160
\(\int \text{FresnelC}(a+b x)^2 \, dx\)
3.161
\(\int \frac{\text{FresnelC}(a+b x)^2}{c+d x} \, dx\)
3.162
\(\int \frac{\text{FresnelC}(a+b x)^2}{(c+d x)^2} \, dx\)
3.163
\(\int x^2 \text{FresnelC}(d (a+b \log (c x^n))) \, dx\)
3.164
\(\int x \text{FresnelC}(d (a+b \log (c x^n))) \, dx\)
3.165
\(\int \text{FresnelC}(d (a+b \log (c x^n))) \, dx\)
3.166
\(\int \frac{\text{FresnelC}(d (a+b \log (c x^n)))}{x} \, dx\)
3.167
\(\int \frac{\text{FresnelC}(d (a+b \log (c x^n)))}{x^2} \, dx\)
3.168
\(\int \frac{\text{FresnelC}(d (a+b \log (c x^n)))}{x^3} \, dx\)
3.169
\(\int (e x)^m \text{FresnelC}(d (a+b \log (c x^n))) \, dx\)
3.170
\(\int e^{c+\frac{1}{2} i b^2 \pi x^2} \text{FresnelC}(b x) \, dx\)
3.171
\(\int e^{c-\frac{1}{2} i b^2 \pi x^2} \text{FresnelC}(b x) \, dx\)
3.172
\(\int \text{FresnelC}(b x) \sin (c+\frac{1}{2} b^2 \pi x^2) \, dx\)
3.173
\(\int \cos (c+\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.174
\(\int \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)^2 \, dx\)
3.175
\(\int \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.176
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2)}{\text{FresnelC}(b x)} \, dx\)
3.177
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2)}{\text{FresnelC}(b x)^2} \, dx\)
3.178
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2)}{\text{FresnelC}(b x)^3} \, dx\)
3.179
\(\int \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)^n \, dx\)
3.180
\(\int x^8 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.181
\(\int x^7 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.182
\(\int x^6 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.183
\(\int x^5 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.184
\(\int x^4 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.185
\(\int x^3 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.186
\(\int x^2 \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.187
\(\int x \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.188
\(\int \cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x) \, dx\)
3.189
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x} \, dx\)
3.190
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^2} \, dx\)
3.191
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^3} \, dx\)
3.192
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^4} \, dx\)
3.193
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^5} \, dx\)
3.194
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^6} \, dx\)
3.195
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^7} \, dx\)
3.196
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^8} \, dx\)
3.197
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^9} \, dx\)
3.198
\(\int \frac{\cos (\frac{1}{2} b^2 \pi x^2) \text{FresnelC}(b x)}{x^{10}} \, dx\)
3.199
\(\int \text{FresnelC}(b x)^n \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.200
\(\int x^8 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.201
\(\int x^7 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.202
\(\int x^6 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.203
\(\int x^5 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.204
\(\int x^4 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.205
\(\int x^3 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.206
\(\int x^2 \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.207
\(\int x \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.208
\(\int \text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2) \, dx\)
3.209
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x} \, dx\)
3.210
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^2} \, dx\)
3.211
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^3} \, dx\)
3.212
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^4} \, dx\)
3.213
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^5} \, dx\)
3.214
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^6} \, dx\)
3.215
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^7} \, dx\)
3.216
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^8} \, dx\)
3.217
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^9} \, dx\)
3.218
\(\int \frac{\text{FresnelC}(b x) \sin (\frac{1}{2} b^2 \pi x^2)}{x^{10}} \, dx\)
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