Prove that ∫_0 ^( (π/2)) ln(a−sin^2 (x))dx=πln((√((a−1)/a))+1)+(π/2)ln((a/4)) a>0 Im{a}≠0


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Question Number 170384 by amin96 last updated on 22/May/22
$Prove that ∫_0 ^( (π/2)) ln(a−sin^2 (x))dx=πln((√((a−1)/a))+1)+(π/2)ln((a/4)) a>0 Im{a}≠0$
$Prove that$ $\int_{0}^{\frac{π}{2}} \ln (a - \sin^{2} (x)) dx = π \ln (\sqrt{\frac{a - 1}{a}} + 1) + \frac{π}{2} \ln (\frac{a}{4})$ $a > 0 I m {a} \neq 0$
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