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Question Number 108583 by mathmax by abdo last updated on 17/Aug/20

$$\mathrm{find}{\int }_0^1\frac{\ln (1+{\mathrm{x}}^2)}{1+{\mathrm{x}}^2}\mathrm{dx}$$

Answered by mnjuly1970 last updated on 18/Aug/20

$$\mathrm{subs}:\mathrm{x}=\tan \left(\mathrm{t}\right)$$$$\Rightarrow \mathrm{\Omega }=-2{\int }_0^{\frac{\pi }{4}}\ln \left(\cos \left(\mathrm{t}\right)\right)\mathrm{dt}=-2(\frac{\mathrm{G}}{2}-\frac{\pi }{4}\ln \left(2\right))$$$$\mathrm{\Omega }=\frac{\pi }{2}\ln \left(2\right)-\mathrm{G}....\mathrm{G}\mathrm{is}\mathrm{catalan}$$$$\mathrm{constant}....$$

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