If , show that _ 0 ^ (1+a x) x dx = ^ -1…

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

If ∣a∣<1|a| < 1 , show that ∫0πlog⁡(1+acos⁡x)cos⁡xdx=πsin⁡−1a.\int_{0}^{\pi} \frac{\log(1+a \cos x)}{\cos x} dx = \pi \sin^{-1} a.

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