The value of \( f(x)=\int_{0}^{\pi / 2} \frac{\log \left(1+x \sin ^...

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The value of \( f(x)=\int_{0}^{\pi / 2} \frac{\log \left(1+x \sin ^{2} \theta\right)}{\sin ^{2} \theta} d \theta, x \geq 0 \) is equal to
\( \mathrm{P} \)
(a) \( \frac{1}{\pi}(\sqrt{1+x}-1) \)
(b) \( \sqrt{\pi}(\sqrt{1+x}-1) \)
(c) \( \pi(\sqrt{1+x}-1) \)
(d) None of these
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