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Question Number 163510 by mnjuly1970 last updated on 07/Jan/22

        If  𝛗=∫_0 ^( (π/2)) (( 1)/( (√(sin^( 5) (x).cos(x))) +(√(cos^( 5) (x).sin(x)))))dx =     find the value of  : Γ^( 2) ((3/4) ). 𝛗

$$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f} \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\mathrm{1}}{\:\sqrt{{sin}^{\:\mathrm{5}} \left({x}\right).{cos}\left({x}\right)}\:+\sqrt{{cos}^{\:\mathrm{5}} \left({x}\right).{sin}\left({x}\right)}}{dx}\:= \\ $$$$\:\:\:{find}\:{the}\:{value}\:{of}\:\::\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\:\right).\:\boldsymbol{\phi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Commented by Ar Brandon last updated on 07/Jan/22

Looks like Q163414, Sir.

$$\mathrm{Looks}\:\mathrm{like}\:\mathrm{Q163414},\:\mathrm{Sir}. \\ $$

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