Evaluate each of the following integral: `int_0^(pi//2)log((3+5cosx)/(3+5sinx))dx`

Explanation

Let `I=\int_{0}^{\frac{\pi}{2}} \log (\frac{3+5 \cos x}{3+5 \sin x}) d x . `


`=\int_{0}^{\frac{\pi}{2}} \log [\frac{3+5 \cos (\frac{\pi}{2}-x)}{3+5 \sin (\frac{\pi}{2}-x)}] d x`



`=\int_{0}^{\frac{\pi}{2}} \log (\frac{3+5 \sin x}{3+5 \cos x}) d x \ldots \ldots`



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