evaluate the integral by using integration by parts
Recall that the IBP formula is $\displaystyle \int u\,dv=uv-\int v\,du$
Let $\displaystyle u=x$ and $\displaystyle \,dv=\cos^2x\,dx$.
I leave the computation work for you to do, but take note that $\displaystyle \cos^2x=\tfrac{1}{2}\left(1+\cos\!\left(2x\right)\ right)$.
Can you try to take it from here?