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Question Number 211528 by mnjuly1970 last updated on 12/Sep/24

$$$$$$$$$$$$$$\mathrm{I}={\int }_0^1\frac{{tanh}^{-1}\left(x^2\right)}{x^2}dx=?$$$$$$$$$$$$$$

Commented by Frix last updated on 12/Sep/24

$$\mathrm{Using}{\mathrm{Feynman}}^{\prime }\mathrm{s}\mathrm{Technique}$$$$f\left(\alpha \right)=\underset{0}{\stackrel{1}{\int }}\frac{{\tanh }^{-1}\left(\alpha x^2\right)}{x^2}dx$$$$\mathrm{I}\mathrm{get}I=f\left(1\right)=\frac{\pi }{4}+\frac{\ln 2}{2}$$

Commented by mnjuly1970 last updated on 12/Sep/24

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