Evaluate the following integral

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Evaluate the following integral, showing every step clearly: (i) Obtain the indefinite integral ∫cos⁡x1+sin⁡x dx\displaystyle\int \dfrac{\cos x}{1+\sin x}\,dx. (ii) Hence, calculate ∫0π/4cos⁡x1+sin⁡x dx\displaystyle\int_{0}^{\pi/4} \dfrac{\cos x}{1+\sin x}\,dx.

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