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Evaluating integrals dependent on a parameter:
Differentiate \( I \) with respect to the parameter within the sign of integrals taking variable of the integrand as constant. Now, evaluate the integral so obtained as a function of the parameter and then integrate the result to get \( I \). Constant of integration can be computed by giving some arbitrary values to the parameter and the corresponding value of \( I \).
If \( \int_{0}^{\pi} \frac{d x}{(a-\cos x)}=\frac{\pi}{\sqrt{a^{2}-1}} \), then the value of \( \int_{0}^{\pi} \frac{d x}{(\sqrt{10}-\cos x)^{3}} \) is
(1) \( \frac{\pi}{81} \)
(2) \( \frac{7 \pi}{162} \)
(3) \( \frac{7 \pi}{81} \)
(4) none of these
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