Question

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

Answer 1

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

$=\frac{1}{2}\int 2{\cos }^{2}xdx$ using $\cos 2x=2{\cos }^{2}x-1\Rightarrow 2{\cos }^{2}x=\cos 2x+1$

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

$=\frac{1}{2}[\frac{\sin 2x}{2}+x]+c$

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