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