Chapter 3
Listing of integrals

 3.1 \(\int \frac{\sinh ^{-1}(c x)}{d+e x} \, dx\)
 3.2 \(\int \frac{\sinh ^{-1}(c x)^2}{d+e x} \, dx\)
 3.3 \(\int \frac{\sinh ^{-1}(c x)^3}{d+e x} \, dx\)
 3.4 \(\int (d+e x)^3 (a+b \sinh ^{-1}(c x)) \, dx\)
 3.5 \(\int (d+e x)^2 (a+b \sinh ^{-1}(c x)) \, dx\)
 3.6 \(\int (d+e x) (a+b \sinh ^{-1}(c x)) \, dx\)
 3.7 \(\int (a+b \sinh ^{-1}(c x)) \, dx\)
 3.8 \(\int \frac{a+b \sinh ^{-1}(c x)}{d+e x} \, dx\)
 3.9 \(\int \frac{a+b \sinh ^{-1}(c x)}{(d+e x)^2} \, dx\)
 3.10 \(\int \frac{a+b \sinh ^{-1}(c x)}{(d+e x)^3} \, dx\)
 3.11 \(\int \frac{a+b \sinh ^{-1}(c x)}{(d+e x)^4} \, dx\)
 3.12 \(\int (d+e x)^3 (a+b \sinh ^{-1}(c x))^2 \, dx\)
 3.13 \(\int (d+e x)^2 (a+b \sinh ^{-1}(c x))^2 \, dx\)
 3.14 \(\int (d+e x) (a+b \sinh ^{-1}(c x))^2 \, dx\)
 3.15 \(\int (a+b \sinh ^{-1}(c x))^2 \, dx\)
 3.16 \(\int \frac{(a+b \sinh ^{-1}(c x))^2}{d+e x} \, dx\)
 3.17 \(\int \frac{(a+b \sinh ^{-1}(c x))^2}{(d+e x)^2} \, dx\)
 3.18 \(\int \frac{(a+b \sinh ^{-1}(c x))^2}{(d+e x)^3} \, dx\)
 3.19 \(\int \frac{(d+e x)^3}{a+b \sinh ^{-1}(c x)} \, dx\)
 3.20 \(\int \frac{(d+e x)^2}{a+b \sinh ^{-1}(c x)} \, dx\)
 3.21 \(\int \frac{d+e x}{a+b \sinh ^{-1}(c x)} \, dx\)
 3.22 \(\int \frac{1}{a+b \sinh ^{-1}(c x)} \, dx\)
 3.23 \(\int \frac{1}{(d+e x) (a+b \sinh ^{-1}(c x))} \, dx\)
 3.24 \(\int \frac{1}{(d+e x)^2 (a+b \sinh ^{-1}(c x))} \, dx\)
 3.25 \(\int \frac{(d+e x)^2}{(a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.26 \(\int \frac{d+e x}{(a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.27 \(\int \frac{1}{(a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.28 \(\int \frac{1}{(d+e x) (a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.29 \(\int \frac{1}{(d+e x)^2 (a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.30 \(\int (d+e x)^m (a+b \sinh ^{-1}(c x))^2 \, dx\)
 3.31 \(\int (d+e x)^m (a+b \sinh ^{-1}(c x)) \, dx\)
 3.32 \(\int \frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)} \, dx\)
 3.33 \(\int \frac{(d+e x)^m}{(a+b \sinh ^{-1}(c x))^2} \, dx\)
 3.34 \(\int (f+g x)^3 \sqrt{d+c^2 d x^2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.35 \(\int (f+g x)^2 \sqrt{d+c^2 d x^2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.36 \(\int (f+g x) \sqrt{d+c^2 d x^2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.37 \(\int \frac{\sqrt{d+c^2 d x^2} (a+b \sinh ^{-1}(c x))}{f+g x} \, dx\)
 3.38 \(\int \frac{\sqrt{d+c^2 d x^2} (a+b \sinh ^{-1}(c x))}{(f+g x)^2} \, dx\)
 3.39 \(\int (f+g x)^3 (d+c^2 d x^2)^{3/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.40 \(\int (f+g x)^2 (d+c^2 d x^2)^{3/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.41 \(\int (f+g x) (d+c^2 d x^2)^{3/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.42 \(\int \frac{(d+c^2 d x^2)^{3/2} (a+b \sinh ^{-1}(c x))}{f+g x} \, dx\)
 3.43 \(\int (f+g x)^3 (d+c^2 d x^2)^{5/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.44 \(\int (f+g x)^2 (d+c^2 d x^2)^{5/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.45 \(\int (f+g x) (d+c^2 d x^2)^{5/2} (a+b \sinh ^{-1}(c x)) \, dx\)
 3.46 \(\int \frac{(d+c^2 d x^2)^{5/2} (a+b \sinh ^{-1}(c x))}{f+g x} \, dx\)
 3.47 \(\int \frac{(f+g x)^3 (a+b \sinh ^{-1}(c x))}{\sqrt{d+c^2 d x^2}} \, dx\)
 3.48 \(\int \frac{(f+g x)^2 (a+b \sinh ^{-1}(c x))}{\sqrt{d+c^2 d x^2}} \, dx\)
 3.49 \(\int \frac{(f+g x) (a+b \sinh ^{-1}(c x))}{\sqrt{d+c^2 d x^2}} \, dx\)
 3.50 \(\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+c^2 d x^2}} \, dx\)
 3.51 \(\int \frac{a+b \sinh ^{-1}(c x)}{(f+g x) \sqrt{d+c^2 d x^2}} \, dx\)
 3.52 \(\int \frac{a+b \sinh ^{-1}(c x)}{(f+g x)^2 \sqrt{d+c^2 d x^2}} \, dx\)
 3.53 \(\int \frac{(a+b \sinh ^{-1}(c x))^n \log (h (f+g x)^m)}{\sqrt{1+c^2 x^2}} \, dx\)
 3.54 \(\int \frac{(a+b \sinh ^{-1}(c x))^2 \log (h (f+g x)^m)}{\sqrt{1+c^2 x^2}} \, dx\)
 3.55 \(\int \frac{(a+b \sinh ^{-1}(c x)) \log (h (f+g x)^m)}{\sqrt{1+c^2 x^2}} \, dx\)
 3.56 \(\int \frac{\log (h (f+g x)^m)}{\sqrt{1+c^2 x^2}} \, dx\)
 3.57 \(\int \frac{\log (h (f+g x)^m)}{\sqrt{1+c^2 x^2} (a+b \sinh ^{-1}(c x))} \, dx\)
 3.58 \(\int x^3 \sinh ^{-1}(a+b x) \, dx\)
 3.59 \(\int x^2 \sinh ^{-1}(a+b x) \, dx\)
 3.60 \(\int x \sinh ^{-1}(a+b x) \, dx\)
 3.61 \(\int \sinh ^{-1}(a+b x) \, dx\)
 3.62 \(\int \frac{\sinh ^{-1}(a+b x)}{x} \, dx\)
 3.63 \(\int \frac{\sinh ^{-1}(a+b x)}{x^2} \, dx\)
 3.64 \(\int \frac{\sinh ^{-1}(a+b x)}{x^3} \, dx\)
 3.65 \(\int \frac{\sinh ^{-1}(a+b x)}{x^4} \, dx\)
 3.66 \(\int \frac{\sinh ^{-1}(a+b x)}{x^5} \, dx\)
 3.67 \(\int x^3 \sinh ^{-1}(a+b x)^2 \, dx\)
 3.68 \(\int x^2 \sinh ^{-1}(a+b x)^2 \, dx\)
 3.69 \(\int x \sinh ^{-1}(a+b x)^2 \, dx\)
 3.70 \(\int \sinh ^{-1}(a+b x)^2 \, dx\)
 3.71 \(\int \frac{\sinh ^{-1}(a+b x)^2}{x} \, dx\)
 3.72 \(\int \frac{\sinh ^{-1}(a+b x)^2}{x^2} \, dx\)
 3.73 \(\int \frac{\sinh ^{-1}(a+b x)^2}{x^3} \, dx\)
 3.74 \(\int \frac{\sinh ^{-1}(a+b x)^2}{x^4} \, dx\)
 3.75 \(\int x^2 \sinh ^{-1}(a+b x)^3 \, dx\)
 3.76 \(\int x \sinh ^{-1}(a+b x)^3 \, dx\)
 3.77 \(\int \sinh ^{-1}(a+b x)^3 \, dx\)
 3.78 \(\int \frac{\sinh ^{-1}(a+b x)^3}{x} \, dx\)
 3.79 \(\int \frac{\sinh ^{-1}(a+b x)^3}{x^2} \, dx\)
 3.80 \(\int \frac{\sinh ^{-1}(a+b x)^3}{x^3} \, dx\)
 3.81 \(\int \frac{x^2}{\sinh ^{-1}(a+b x)} \, dx\)
 3.82 \(\int \frac{x}{\sinh ^{-1}(a+b x)} \, dx\)
 3.83 \(\int \frac{1}{\sinh ^{-1}(a+b x)} \, dx\)
 3.84 \(\int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx\)
 3.85 \(\int \frac{x^2}{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.86 \(\int \frac{x}{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.87 \(\int \frac{1}{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.88 \(\int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx\)
 3.89 \(\int \frac{x^2}{\sinh ^{-1}(a+b x)^3} \, dx\)
 3.90 \(\int \frac{x}{\sinh ^{-1}(a+b x)^3} \, dx\)
 3.91 \(\int \frac{1}{\sinh ^{-1}(a+b x)^3} \, dx\)
 3.92 \(\int \frac{1}{x \sinh ^{-1}(a+b x)^3} \, dx\)
 3.93 \(\int x^m (a+b \sinh ^{-1}(c+d x))^n \, dx\)
 3.94 \(\int x^2 (a+b \sinh ^{-1}(c+d x))^n \, dx\)
 3.95 \(\int x (a+b \sinh ^{-1}(c+d x))^n \, dx\)
 3.96 \(\int (a+b \sinh ^{-1}(c+d x))^n \, dx\)
 3.97 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^n}{x} \, dx\)
 3.98 \(\int x^2 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.99 \(\int x \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.100 \(\int \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.101 \(\int x (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.102 \(\int (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.103 \(\int x (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.104 \(\int (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.105 \(\int \frac{x^2}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.106 \(\int \frac{x}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.107 \(\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.108 \(\int \frac{x}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.109 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.110 \(\int \frac{x}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.111 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.112 \(\int \frac{x}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.113 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.114 \(\int (c e+d e x)^m (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.115 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.116 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.117 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.118 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.119 \(\int (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.120 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{c e+d e x} \, dx\)
 3.121 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx\)
 3.122 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx\)
 3.123 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^4} \, dx\)
 3.124 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^5} \, dx\)
 3.125 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^6} \, dx\)
 3.126 \(\int (c e+d e x)^m (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.127 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.128 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.129 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.130 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.131 \(\int (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.132 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{c e+d e x} \, dx\)
 3.133 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^2} \, dx\)
 3.134 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^3} \, dx\)
 3.135 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^4} \, dx\)
 3.136 \(\int (c e+d e x)^m (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.137 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.138 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.139 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.140 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.141 \(\int (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.142 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{c e+d e x} \, dx\)
 3.143 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^2} \, dx\)
 3.144 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^3} \, dx\)
 3.145 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^4} \, dx\)
 3.146 \(\int (c e+d e x)^m (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.147 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.148 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.149 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.150 \(\int (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.151 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{c e+d e x} \, dx\)
 3.152 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^2} \, dx\)
 3.153 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^3} \, dx\)
 3.154 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^4} \, dx\)
 3.155 \(\int \frac{(c e+d e x)^m}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.156 \(\int \frac{(c e+d e x)^4}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.157 \(\int \frac{(c e+d e x)^3}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.158 \(\int \frac{(c e+d e x)^2}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.159 \(\int \frac{c e+d e x}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.160 \(\int \frac{1}{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.161 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))} \, dx\)
 3.162 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.163 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.164 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.165 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.166 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.167 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^2} \, dx\)
 3.168 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.169 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.170 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.171 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.172 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.173 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^3} \, dx\)
 3.174 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.175 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.176 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.177 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.178 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.179 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^4} \, dx\)
 3.180 \(\int (c e+d e x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.181 \(\int (c e+d e x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.182 \(\int (c e+d e x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.183 \(\int (c e+d e x) \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.184 \(\int \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx\)
 3.185 \(\int \frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{c e+d e x} \, dx\)
 3.186 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.187 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.188 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.189 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.190 \(\int (a+b \sinh ^{-1}(c+d x))^{3/2} \, dx\)
 3.191 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^{3/2}}{c e+d e x} \, dx\)
 3.192 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.193 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.194 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.195 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.196 \(\int (a+b \sinh ^{-1}(c+d x))^{5/2} \, dx\)
 3.197 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^{5/2}}{c e+d e x} \, dx\)
 3.198 \(\int (c e+d e x)^4 (a+b \sinh ^{-1}(c+d x))^{7/2} \, dx\)
 3.199 \(\int (c e+d e x)^3 (a+b \sinh ^{-1}(c+d x))^{7/2} \, dx\)
 3.200 \(\int (c e+d e x)^2 (a+b \sinh ^{-1}(c+d x))^{7/2} \, dx\)
 3.201 \(\int (c e+d e x) (a+b \sinh ^{-1}(c+d x))^{7/2} \, dx\)
 3.202 \(\int (a+b \sinh ^{-1}(c+d x))^{7/2} \, dx\)
 3.203 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^{7/2}}{c e+d e x} \, dx\)
 3.204 \(\int \frac{(c e+d e x)^4}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.205 \(\int \frac{(c e+d e x)^3}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.206 \(\int \frac{(c e+d e x)^2}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.207 \(\int \frac{c e+d e x}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.208 \(\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.209 \(\int \frac{1}{(c e+d e x) \sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx\)
 3.210 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.211 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.212 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.213 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.214 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.215 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^{3/2}} \, dx\)
 3.216 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.217 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.218 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.219 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.220 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.221 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^{5/2}} \, dx\)
 3.222 \(\int \frac{(c e+d e x)^4}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.223 \(\int \frac{(c e+d e x)^3}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.224 \(\int \frac{(c e+d e x)^2}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.225 \(\int \frac{c e+d e x}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.226 \(\int \frac{1}{(a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.227 \(\int \frac{1}{(c e+d e x) (a+b \sinh ^{-1}(c+d x))^{7/2}} \, dx\)
 3.228 \(\int (c e+d e x)^{7/2} (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.229 \(\int (c e+d e x)^{5/2} (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.230 \(\int (c e+d e x)^{3/2} (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.231 \(\int \sqrt{c e+d e x} (a+b \sinh ^{-1}(c+d x)) \, dx\)
 3.232 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{\sqrt{c e+d e x}} \, dx\)
 3.233 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{3/2}} \, dx\)
 3.234 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{5/2}} \, dx\)
 3.235 \(\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{7/2}} \, dx\)
 3.236 \(\int (c e+d e x)^{7/2} (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.237 \(\int (c e+d e x)^{5/2} (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.238 \(\int (c e+d e x)^{3/2} (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.239 \(\int \sqrt{c e+d e x} (a+b \sinh ^{-1}(c+d x))^2 \, dx\)
 3.240 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{\sqrt{c e+d e x}} \, dx\)
 3.241 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^{3/2}} \, dx\)
 3.242 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^{5/2}} \, dx\)
 3.243 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^2}{(c e+d e x)^{7/2}} \, dx\)
 3.244 \(\int (c e+d e x)^{7/2} (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.245 \(\int (c e+d e x)^{5/2} (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.246 \(\int (c e+d e x)^{3/2} (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.247 \(\int \sqrt{c e+d e x} (a+b \sinh ^{-1}(c+d x))^3 \, dx\)
 3.248 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{\sqrt{c e+d e x}} \, dx\)
 3.249 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^{3/2}} \, dx\)
 3.250 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^{5/2}} \, dx\)
 3.251 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^3}{(c e+d e x)^{7/2}} \, dx\)
 3.252 \(\int (c e+d e x)^{7/2} (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.253 \(\int (c e+d e x)^{5/2} (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.254 \(\int (c e+d e x)^{3/2} (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.255 \(\int \sqrt{c e+d e x} (a+b \sinh ^{-1}(c+d x))^4 \, dx\)
 3.256 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{\sqrt{c e+d e x}} \, dx\)
 3.257 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^{3/2}} \, dx\)
 3.258 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^{5/2}} \, dx\)
 3.259 \(\int \frac{(a+b \sinh ^{-1}(c+d x))^4}{(c e+d e x)^{7/2}} \, dx\)
 3.260 \(\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^3 \, dx\)
 3.261 \(\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^2 \, dx\)
 3.262 \(\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x) \, dx\)
 3.263 \(\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)} \, dx\)
 3.264 \(\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.265 \(\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)^3} \, dx\)
 3.266 \(\int (1+a^2+2 a b x+b^2 x^2)^{3/2} \sinh ^{-1}(a+b x)^3 \, dx\)
 3.267 \(\int (1+a^2+2 a b x+b^2 x^2)^{3/2} \sinh ^{-1}(a+b x)^2 \, dx\)
 3.268 \(\int (1+a^2+2 a b x+b^2 x^2)^{3/2} \sinh ^{-1}(a+b x) \, dx\)
 3.269 \(\int \frac{(1+a^2+2 a b x+b^2 x^2)^{3/2}}{\sinh ^{-1}(a+b x)} \, dx\)
 3.270 \(\int \frac{(1+a^2+2 a b x+b^2 x^2)^{3/2}}{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.271 \(\int \frac{(1+a^2+2 a b x+b^2 x^2)^{3/2}}{\sinh ^{-1}(a+b x)^3} \, dx\)
 3.272 \(\int \frac{\sinh ^{-1}(a+b x)^3}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx\)
 3.273 \(\int \frac{\sinh ^{-1}(a+b x)^2}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx\)
 3.274 \(\int \frac{\sinh ^{-1}(a+b x)}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx\)
 3.275 \(\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)} \, dx\)
 3.276 \(\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^2} \, dx\)
 3.277 \(\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^3} \, dx\)
 3.278 \(\int \frac{\sinh ^{-1}(a+b x)^3}{(1+a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
 3.279 \(\int \frac{\sinh ^{-1}(a+b x)^2}{(1+a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
 3.280 \(\int \frac{\sinh ^{-1}(a+b x)}{(1+a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
 3.281 \(\int \frac{1}{(1+a^2+2 a b x+b^2 x^2)^{3/2} \sinh ^{-1}(a+b x)} \, dx\)
 3.282 \(\int \frac{1}{(1+a^2+2 a b x+b^2 x^2)^{3/2} \sinh ^{-1}(a+b x)^2} \, dx\)
 3.283 \(\int x^3 \sinh ^{-1}(a x^2) \, dx\)
 3.284 \(\int x^2 \sinh ^{-1}(a x^2) \, dx\)
 3.285 \(\int x \sinh ^{-1}(a x^2) \, dx\)
 3.286 \(\int \sinh ^{-1}(a x^2) \, dx\)
 3.287 \(\int \frac{\sinh ^{-1}(a x^2)}{x} \, dx\)
 3.288 \(\int \frac{\sinh ^{-1}(a x^2)}{x^2} \, dx\)
 3.289 \(\int \frac{\sinh ^{-1}(a x^2)}{x^3} \, dx\)
 3.290 \(\int \frac{\sinh ^{-1}(a x^2)}{x^4} \, dx\)
 3.291 \(\int \frac{\sinh ^{-1}(a x^5)}{x} \, dx\)
 3.292 \(\int x^2 \sinh ^{-1}(\sqrt{x}) \, dx\)
 3.293 \(\int x \sinh ^{-1}(\sqrt{x}) \, dx\)
 3.294 \(\int \sinh ^{-1}(\sqrt{x}) \, dx\)
 3.295 \(\int \frac{\sinh ^{-1}(\sqrt{x})}{x} \, dx\)
 3.296 \(\int \frac{\sinh ^{-1}(\sqrt{x})}{x^2} \, dx\)
 3.297 \(\int \frac{\sinh ^{-1}(\sqrt{x})}{x^3} \, dx\)
 3.298 \(\int \frac{\sinh ^{-1}(\sqrt{x})}{x^4} \, dx\)
 3.299 \(\int \frac{\sinh ^{-1}(\sqrt{x})}{x^5} \, dx\)
 3.300 \(\int x^2 \sinh ^{-1}(\frac{a}{x}) \, dx\)
 3.301 \(\int x \sinh ^{-1}(\frac{a}{x}) \, dx\)
 3.302 \(\int \sinh ^{-1}(\frac{a}{x}) \, dx\)
 3.303 \(\int \frac{\sinh ^{-1}(\frac{a}{x})}{x} \, dx\)
 3.304 \(\int \frac{\sinh ^{-1}(\frac{a}{x})}{x^2} \, dx\)
 3.305 \(\int \frac{\sinh ^{-1}(\frac{a}{x})}{x^3} \, dx\)
 3.306 \(\int \frac{\sinh ^{-1}(\frac{a}{x})}{x^4} \, dx\)
 3.307 \(\int x^m \sinh ^{-1}(a x^n) \, dx\)
 3.308 \(\int x^2 \sinh ^{-1}(a x^n) \, dx\)
 3.309 \(\int x \sinh ^{-1}(a x^n) \, dx\)
 3.310 \(\int \sinh ^{-1}(a x^n) \, dx\)
 3.311 \(\int \frac{\sinh ^{-1}(a x^n)}{x} \, dx\)
 3.312 \(\int \frac{\sinh ^{-1}(a x^n)}{x^2} \, dx\)
 3.313 \(\int \frac{\sinh ^{-1}(a x^n)}{x^3} \, dx\)
 3.314 \(\int (a+i b \sin ^{-1}(1-i d x^2))^4 \, dx\)
 3.315 \(\int (a+i b \sin ^{-1}(1-i d x^2))^3 \, dx\)
 3.316 \(\int (a+i b \sin ^{-1}(1-i d x^2))^2 \, dx\)
 3.317 \(\int (a+i b \sin ^{-1}(1-i d x^2)) \, dx\)
 3.318 \(\int \frac{1}{a+i b \sin ^{-1}(1-i d x^2)} \, dx\)
 3.319 \(\int \frac{1}{(a+i b \sin ^{-1}(1-i d x^2))^2} \, dx\)
 3.320 \(\int \frac{1}{(a+i b \sin ^{-1}(1-i d x^2))^3} \, dx\)
 3.321 \(\int (a-i b \sin ^{-1}(1+i d x^2))^4 \, dx\)
 3.322 \(\int (a-i b \sin ^{-1}(1+i d x^2))^3 \, dx\)
 3.323 \(\int (a-i b \sin ^{-1}(1+i d x^2))^2 \, dx\)
 3.324 \(\int (a-i b \sin ^{-1}(1+i d x^2)) \, dx\)
 3.325 \(\int \frac{1}{a-i b \sin ^{-1}(1+i d x^2)} \, dx\)
 3.326 \(\int \frac{1}{(a-i b \sin ^{-1}(1+i d x^2))^2} \, dx\)
 3.327 \(\int \frac{1}{(a-i b \sin ^{-1}(1+i d x^2))^3} \, dx\)
 3.328 \(\int (a+i b \sin ^{-1}(1-i d x^2))^{5/2} \, dx\)
 3.329 \(\int (a+i b \sin ^{-1}(1-i d x^2))^{3/2} \, dx\)
 3.330 \(\int \sqrt{a+i b \sin ^{-1}(1-i d x^2)} \, dx\)
 3.331 \(\int \frac{1}{\sqrt{a+i b \sin ^{-1}(1-i d x^2)}} \, dx\)
 3.332 \(\int \frac{1}{(a+i b \sin ^{-1}(1-i d x^2))^{3/2}} \, dx\)
 3.333 \(\int \frac{1}{(a+i b \sin ^{-1}(1-i d x^2))^{5/2}} \, dx\)
 3.334 \(\int \frac{1}{(a+i b \sin ^{-1}(1-i d x^2))^{7/2}} \, dx\)
 3.335 \(\int (a-i b \sin ^{-1}(1+i d x^2))^{5/2} \, dx\)
 3.336 \(\int (a-i b \sin ^{-1}(1+i d x^2))^{3/2} \, dx\)
 3.337 \(\int \sqrt{a-i b \sin ^{-1}(1+i d x^2)} \, dx\)
 3.338 \(\int \frac{1}{\sqrt{a-i b \sin ^{-1}(1+i d x^2)}} \, dx\)
 3.339 \(\int \frac{1}{(a-i b \sin ^{-1}(1+i d x^2))^{3/2}} \, dx\)
 3.340 \(\int \frac{1}{(a-i b \sin ^{-1}(1+i d x^2))^{5/2}} \, dx\)
 3.341 \(\int \frac{1}{(a-i b \sin ^{-1}(1+i d x^2))^{7/2}} \, dx\)
 3.342 \(\int \frac{(a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^n}{1-c^2 x^2} \, dx\)
 3.343 \(\int \frac{(a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^3}{1-c^2 x^2} \, dx\)
 3.344 \(\int \frac{(a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2}{1-c^2 x^2} \, dx\)
 3.345 \(\int \frac{a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}})}{1-c^2 x^2} \, dx\)
 3.346 \(\int \frac{1}{(1-c^2 x^2) (a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))} \, dx\)
 3.347 \(\int \frac{1}{(1-c^2 x^2) (a+b \sinh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2} \, dx\)
 3.348 \(\int \sinh ^{-1}(c e^{a+b x}) \, dx\)
 3.349 \(\int e^{\sinh ^{-1}(a+b x)} x^3 \, dx\)
 3.350 \(\int e^{\sinh ^{-1}(a+b x)} x^2 \, dx\)
 3.351 \(\int e^{\sinh ^{-1}(a+b x)} x \, dx\)
 3.352 \(\int e^{\sinh ^{-1}(a+b x)} \, dx\)
 3.353 \(\int \frac{e^{\sinh ^{-1}(a+b x)}}{x} \, dx\)
 3.354 \(\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^2} \, dx\)
 3.355 \(\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^3} \, dx\)
 3.356 \(\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^4} \, dx\)
 3.357 \(\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^5} \, dx\)
 3.358 \(\int e^{\sinh ^{-1}(a+b x)^2} x^3 \, dx\)
 3.359 \(\int e^{\sinh ^{-1}(a+b x)^2} x^2 \, dx\)
 3.360 \(\int e^{\sinh ^{-1}(a+b x)^2} x \, dx\)
 3.361 \(\int e^{\sinh ^{-1}(a+b x)^2} \, dx\)
 3.362 \(\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x} \, dx\)
 3.363 \(\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x^2} \, dx\)
 3.364 \(\int \frac{\sinh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx\)
 3.365 \(\int \frac{x}{\sqrt{1+x^2} \sinh ^{-1}(x)} \, dx\)
 3.366 \(\int x^3 \sinh ^{-1}(a+b x^4) \, dx\)
 3.367 \(\int x^{-1+n} \sinh ^{-1}(a+b x^n) \, dx\)
 3.368 \(\int \sinh ^{-1}(\frac{c}{a+b x}) \, dx\)
 3.369 \(\int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx\)
 3.370 \(\int \frac{\sinh ^{-1}(\sqrt{-1+b x^2})^n}{\sqrt{-1+b x^2}} \, dx\)
 3.371 \(\int \frac{1}{\sqrt{-1+b x^2} \sinh ^{-1}(\sqrt{-1+b x^2})} \, dx\)