Question

Integrate the following w.r.t. $x$
${\cos }^{2}x$.

Answer 1

$y={\cos }^{2}x$
Integrating both sides w.r.t. $x$, we get
$I=\int ydx$
$=\int {\cos }^{2}xdx$
$=\int (1+\frac{\cos 2x}{2})dx$
$=\int \frac{1}{2}dx+\int \frac{\cos 2x}{2}dx$
$=\frac{x}{2}+\frac{\sin 2x}{2\times 2}+c=\frac{1}{2}(x+\frac{\sin 2x}{2})+c$.