Chapter 3
Listing of integrals

 3.1 \(\int \sin ^{-1}(x) \log (x) \, dx\)
 3.2 \(\int \frac {x \sin ^{-1}(x)}{\sqrt {1-x^2}} \, dx\)
 3.3 \(\int -\sin ^{-1}(\sqrt {x}-\sqrt {1+x}) \, dx\)
 3.4 \(\int \log (1+x \sqrt {1+x^2}) \, dx\)
 3.5 \(\int \frac {\cos ^2(x)}{\sqrt {1+\cos ^2(x)+\cos ^4(x)}} \, dx\)
 3.6 \(\int \tan (x) \sqrt {1+\tan ^4(x)} \, dx\)
 3.7 \(\int \frac {\tan (x)}{\sqrt {1+\sec ^3(x)}} \, dx\)
 3.8 \(\int \sqrt {2+2 \tan (x)+\tan ^2(x)} \, dx\)
 3.9 \(\int \tan ^{-1}(\sqrt {-1+\sec (x)}) \sin (x) \, dx\)
 3.10 \(\int \frac {e^{\sin ^{-1}(x)} x^3}{\sqrt {1-x^2}} \, dx\)
 3.11 \(\int \frac {x \log (1+x^2) \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\)
 3.12 \(\int \tan ^{-1}(x+\sqrt {1-x^2}) \, dx\)
 3.13 \(\int \frac {x \tan ^{-1}(x+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\)
 3.14 \(\int \frac {\sin ^{-1}(x)}{1+\sqrt {1-x^2}} \, dx\)
 3.15 \(\int \frac {\log (x+\sqrt {1+x^2})}{(1-x^2)^{3/2}} \, dx\)
 3.16 \(\int \frac {\sin ^{-1}(x)}{(1+x^2)^{3/2}} \, dx\)
 3.17 \(\int \frac {\log (x+\sqrt {-1+x^2})}{(1+x^2)^{3/2}} \, dx\)
 3.18 \(\int \frac {\log (x)}{x^2 \sqrt {-1+x^2}} \, dx\)
 3.19 \(\int \frac {\sqrt {1+x^3}}{x} \, dx\)
 3.20 \(\int \frac {x \log (x+\sqrt {-1+x^2})}{\sqrt {-1+x^2}} \, dx\)
 3.21 \(\int \frac {x^3 \sin ^{-1}(x)}{\sqrt {1-x^4}} \, dx\)
 3.22 \(\int \frac {x^3 \sec ^{-1}(x)}{\sqrt {-1+x^4}} \, dx\)
 3.23 \(\int \frac {x \tan ^{-1}(x) \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\)
 3.24 \(\int \frac {x \log (1+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\)
 3.25 \(\int \frac {x \log (x+\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\)
 3.26 \(\int \frac {x \log (x+\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\)
 3.27 \(\int \frac {\log (x)}{x^2 \sqrt {1-x^2}} \, dx\)
 3.28 \(\int \frac {x \tan ^{-1}(x)}{\sqrt {1+x^2}} \, dx\)
 3.29 \(\int \frac {\tan ^{-1}(x)}{x^2 \sqrt {1-x^2}} \, dx\)
 3.30 \(\int \frac {x \tan ^{-1}(x)}{\sqrt {1-x^2}} \, dx\)
 3.31 \(\int \frac {\tan ^{-1}(x)}{x^2 \sqrt {1+x^2}} \, dx\)
 3.32 \(\int \frac {\sin ^{-1}(x)}{x^2 \sqrt {1-x^2}} \, dx\)
 3.33 \(\int \frac {x \log (x)}{\sqrt {-1+x^2}} \, dx\)
 3.34 \(\int \frac {\log (x)}{x^2 \sqrt {1+x^2}} \, dx\)
 3.35 \(\int \frac {x \sec ^{-1}(x)}{\sqrt {-1+x^2}} \, dx\)
 3.36 \(\int \frac {x \log (x)}{\sqrt {1+x^2}} \, dx\)
 3.37 \(\int \frac {\sin (x)}{1+\sin ^2(x)} \, dx\)
 3.38 \(\int \frac {1+x^2}{(1-x^2) \sqrt {1+x^4}} \, dx\)
 3.39 \(\int \frac {1-x^2}{(1+x^2) \sqrt {1+x^4}} \, dx\)
 3.40 \(\int \frac {\log (\sin (x))}{1+\sin (x)} \, dx\)
 3.41 \(\int \log (\sin (x)) \sqrt {1+\sin (x)} \, dx\)
 3.42 \(\int \frac {\sec (x)}{\sqrt {-1+\sec ^4(x)}} \, dx\)
 3.43 \(\int \frac {\tan (x)}{\sqrt {1+\tan ^4(x)}} \, dx\)
 3.44 \(\int \frac {\sin (x)}{\sqrt {1-\sin ^6(x)}} \, dx\)
 3.45 \(\int \sqrt {-\sqrt {-1+\sec (x)}+\sqrt {1+\sec (x)}} \, dx\)
 3.46 \(\int x \tan ^{-1}(x)^2 \log (1+x^2) \, dx\)
 3.47 \(\int \tan ^{-1}(x \sqrt {1+x^2}) \, dx\)
 3.48 \(\int -\tan ^{-1}(\sqrt {x}-\sqrt {1+x}) \, dx\)
 3.49 \(\int \sin ^{-1}(\frac {x}{\sqrt {1-x^2}}) \, dx\)
 3.50 \(\int \tan ^{-1}(x \sqrt {1-x^2}) \, dx\)