Question Number 208421 by lepuissantcedricjunior last updated on 15/Jun/24
Commented by Frix last updated on 15/Jun/24
$$\Psi=\mathrm{2}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{tan}\:\mathrm{2}{x}}}\:\overset{{t}=\sqrt{\mathrm{tan}\:\mathrm{2}{x}}} {=}\:\mathrm{2}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{1}}=\frac{\sqrt{\mathrm{2}}\pi}{\mathrm{2}} \\ $$