You may use the formula
∫udvdx dx=uv−∫vdudx dx\displaystyle\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx∫udxdvdx=uv−∫vdxdudx
Use integration by parts to find
∫xcosx dx\displaystyle\int x\cos x\,dx∫xcosxdx