Question

Evaluate $\int {\cos }^{2}xdx$.

Answer 1

As we know that,

$\cos 2x=2{\cos }^{2}x-1$

$\Rightarrow {\cos }^{2}x=\frac{1+\cos 2x}{2}$

Therefore,

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

$=\frac{x}{2}+\frac{\sin 2x}{4}+C$