Find the integral of the function ^2 x 1 + x - Vidyadip

Question

Find the integral of the function $\frac{{{{\sin }^2}x}}{{1 + \cos x}}$

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Answer

$\int {\frac{{{{\sin }^2}x}}{{1 + \cos x}}} dx$

$= \int {\frac{{1 - {{\cos }^2}x}}{{1 + \cos x}}} dx$

$= \int {\frac{{\left( {1 - \cos x} \right)\left( {1 + \cos x} \right)}}{{1 + \cos x}}} dx$

$= \int {\left( {1 - \cos x} \right)} dx$

$= \int {1dx - \int {\cos x} } dx$

= x - sin x + c

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