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Question Number 208421 by lepuissantcedricjunior last updated on 15/Jun/24

Commented by Frix last updated on 15/Jun/24

$$\mathrm{\Psi }=2\underset{0}{\stackrel{\frac{\pi }{4}}{\int }}\frac{dx}{\sqrt{\tan 2x}}\stackrel{t=\sqrt{\tan 2x}}{=}2\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{dt}{t^4+1}=\frac{\sqrt{2}\pi }{2}$$

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