# FInd this integral

1. Sep 23, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
Evaluate $\displaystyle \int_0^{\pi} \log (1+a\cos x) dx$

2. Relevant equations

3. 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!

2. Sep 23, 2014

### haruspex

No. For one thing, the use of the square root function hides the fact that cos(t) will change sign over the range. Split it into two integrals to be safe.