Evaluate the following integral: `int_0^pix/(1+cos alpha sin x)dx`

Explanation

Consider `I=int_{0}^{pi} frac{x}{1+cos alpha sin x} d x ldots (i)`

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Rightarrow I=int_{0}^{pi} frac{(pi-x)}{1+cos alpha sin (pi-x)} d x `

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Rightarrow quad I=int_{0}^{pi} frac{(pi-x)}{1+cos alpha sin x} d x ldots (ii) `



add Eqs. (I) and (II), we obtain

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2 I=pi int_{0}^{pi} frac{d x}{1+cos alpha sin x} `

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