^2 x 2 dx - Vidyadip

Question

$\int\cos^2\frac{\text{x}}{2}\text{dx}$

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Answer

$\int\cos^2\frac{\text{x}}{2}\text{dx}$
$=\int\Big(\frac{1+\cos\text{x}}{2}\Big)\text{dx}$ $\Big[\therefore\cos^2\frac{\text{x}}{2}=\frac{1+\cos\text{x}}{2}\Big]$
$=\frac{1}{2}\int(1+\cos\text{x})\text{dx}$
$=\frac{1}{2}[\text{x}+\sin\text{x}]+\text{C}$

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