Prove-that-0-pi-2-ln-a-sin-2-x-dx-piln-a-1-a-1-pi-2-ln-a-4-a-gt-0-Im-a-0-

Question Number 170384 by amin96 last updated on 22/May/22

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