`intcos^2n x\ dx`

Explanation

`int cos ^{2} nxdx `

`=int[frac{1+cos 2 n x}{2}] d x[therefore cos ^{2} x=frac{1+cos 2 x}{2}] `

`=frac{1}{2} int(1+cos 2 n x) d x `

`=frac{1}{2}[x+frac{sin 2 n x}{2 n}]+C `

`=frac{x}{2}+frac{sin 2 n x}{4 n}+C`