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