# FInd this integral

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## Homework Statement

Evaluate $\displaystyle \int_0^{\pi} \log (1+a\cos x) dx$

## The Attempt at a Solution

Using Leibnitz's Rule,
F'(a)=$\displaystyle \int_0^{\pi} \dfrac{\cos x}{1+a \cos x} dx$

Now, If I assume sinx=t, then the above integral changes to
$\displaystyle \int_0^{0} \dfrac{dt}{1+a \sqrt{1-t^2}}$

Since both the limits are zero now, shouldn't the value of integral be 0!

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haruspex
$\displaystyle \int_0^{0} \dfrac{dt}{1+a \sqrt{1-t^2}}$