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Question Number 121713 by mnjuly1970 last updated on 11/Nov/20

     ... advanced  calculus...   please  prove:  Φ=∫_0 ^( ∞) arctan(((2x)/(1+x^2 )))(dx/x) =πln(1+(√2) )                   ...m.n...

$$\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$$\:{please}\:\:{prove}: \\ $$$$\Phi=\int_{\mathrm{0}} ^{\:\infty} {arctan}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\frac{{dx}}{{x}}\:=\pi{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}... \\ $$

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