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Chapter 3
Listing of integrals
3.1
\(\int \frac{1}{\sqrt{2}+\cos (z)+\sin (z)} \, dz\)
3.2
\(\int \frac{1}{(\sqrt{1-x}+\sqrt{1+x})^2} \, dx\)
3.3
\(\int \frac{1}{(1+\cos (x))^2} \, dx\)
3.4
\(\int \frac{\sin (x)}{\sqrt{1+x}} \, dx\)
3.5
\(\int \frac{1}{(\cos (x)+\sin (x))^6} \, dx\)
3.6
\(\int \log (\frac{1}{x^4}+x^4) \, dx\)
3.7
\(\int \frac{\log (1+x)}{x \sqrt{1+\sqrt{1+x}}} \, dx\)
3.8
\(\int \frac{\sqrt{1+\sqrt{1+x}} \log (1+x)}{x} \, dx\)
3.9
\(\int \frac{1}{1+\sqrt{x+\sqrt{1+x^2}}} \, dx\)
3.10
\(\int \frac{\sqrt{1+x}}{x+\sqrt{1+\sqrt{1+x}}} \, dx\)
3.11
\(\int \frac{1}{x-\sqrt{1+\sqrt{1+x}}} \, dx\)
3.12
\(\int \frac{x}{x+\sqrt{1-\sqrt{1+x}}} \, dx\)
3.13
\(\int \frac{\sqrt{x+\sqrt{1+x}}}{\sqrt{1+x} (1+x^2)} \, dx\)
3.14
\(\int \frac{\sqrt{x+\sqrt{1+x}}}{1+x^2} \, dx\)
3.15
\(\int \sqrt{1+\sqrt{x}+\sqrt{1+2 \sqrt{x}+2 x}} \, dx\)
3.16
\(\int \sqrt{\sqrt{2}+\sqrt{x}+\sqrt{2+2 \sqrt{2} \sqrt{x}+2 x}} \, dx\)
3.17
\(\int \frac{\sqrt{x+\sqrt{1+x}}}{x^2} \, dx\)
3.18
\(\int \sqrt{\sqrt{1+\frac{1}{x}}+\frac{1}{x}} \, dx\)
3.19
\(\int \frac{\sqrt{1+e^{-x}}}{-e^{-x}+e^x} \, dx\)
3.20
\(\int \sqrt{1+e^{-x}} \text{csch}(x) \, dx\)
3.21
\(\int \frac{1}{(\cos (x)+\cos (3 x))^5} \, dx\)
3.22
\(\int \frac{1}{(1+\cos (x)+\sin (x))^2} \, dx\)
3.23
\(\int \sqrt{1+\tanh (4 x)} \, dx\)
3.24
\(\int \frac{\tanh (x)}{\sqrt{e^x+e^{2 x}}} \, dx\)
3.25
\(\int \sqrt{\text{sech}(x) \sinh (2 x)} \, dx\)
3.26
\(\int \log (x^2+\sqrt{1-x^2}) \, dx\)
3.27
\(\int \frac{\log (1+e^x)}{1+e^{2 x}} \, dx\)
3.28
\(\int \cosh (x) \log ^2(1+\cosh ^2(x)) \, dx\)
3.29
\(\int \cosh (x) \log ^2(\cosh ^2(x)+\sinh (x)) \, dx\)
3.30
\(\int \frac{\log (x+\sqrt{1+x})}{1+x^2} \, dx\)
3.31
\(\int \frac{\log ^2(x+\sqrt{1+x})}{(1+x)^2} \, dx\)
3.32
\(\int \frac{\log (x+\sqrt{1+x})}{x} \, dx\)
3.33
\(\int \tan ^{-1}(2 \tan (x)) \, dx\)
3.34
\(\int \frac{\tan ^{-1}(x) \log (x)}{x} \, dx\)
3.35
\(\int \sqrt{1+x^2} \tan ^{-1}(x)^2 \, dx\)
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