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 \(\int \tan ^{-1}(x \sqrt{1-x^2}) \, dx\)