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 \(\int \frac{(a+b x+c x^2) \log (1-d x) \text{PolyLog}(2,d x)}{x^5} \, dx\)