Evaluate: `int_0^pix/(1+sinx)dx`

Explanation

`int_0^pix/(1+sinx)dx ---(1)`

`int_0^pi frac{pi-x}{1+sin(pi-x)}dx `

`=int_0^pi frac{pi-x}{1+sinx}dx ---(2)`

Adding eq. 1 and 2 `=>`

`2I=int_0^pi frac{pi}{1+sinx}dx`

`=pi int_0^pi frac{1-sinx}{(1+sinx)(1-sinx)}dx`

`=pi int_0^pi(sec^2x-secx tanx)dx`

`=pi[tan x-secx]_0^pi`
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