Evaluate the following integrals: ^2x 1+ dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{\sin^2\text{x}}{1+\cos\text{x}}\text{dx}$

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Answer

$\int\frac{\sin^2\text{x}}{1+\cos\text{x}}\text{dx}$
$=\int\frac{(1-\cos^2\text{x})}{(1+\cos\text{x})}\text{dx}$
$=\int\frac{(1-\cos\text{x})(1+\cos\text{x})}{(1+\cos\text{x})}\text{dx}$
$=\int(1-\cos\text{x})\text{dx}$
$=\text{x}-\sin\text{x}+\text{C}$

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