Evaluate : `int_0^pi1/(1+sinx)dx`

Explanation

`I=\int_{0}^{\pi} \frac{1}{1+\sin x} d x `


`=\int_{0}^{\frac{\pi}{2}} \frac{1}{(\cos \frac{x}{2}+\sin \frac{x}{2})^{2}} d x `



`=\int_{0}^{\frac{\pi}{2}} \frac{\sec ^{2} \frac{x}{2}}{(1+\tan \frac{x}{2})^{2}} d x `



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