Evaluate each of the following integral: `int_(-pi//2)^(pi//2)log((a-sin theta)/(a+sin theta))d theta`

Explanation

Let


`I=int_{-pi / 2}^{pi / 2} log (frac{a-sin theta}{a+sin theta}) d theta`


Let `f(theta)=log frac{(a-sin theta)}{(a+sin theta)}`


Then `f(-theta)=log frac{(a-sin (-theta))}{(a+sin (-theta))} `

`=log frac{(a+sin theta)}{(a-sin theta)} `

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