# Integral of x Cos2x

In this tutorial we shall find integral of x Cos2x function. To evaluate this integral we shall use the integration by parts method.

The integration of the form

Here we have First function is $x$ and second function will be $\cos 2x$

Using formula for integration by parts, we have

Equation (i) becomes using above formula, we have

Using the integral rule $\int {\cos kx} dx = \frac{{\sin kx}}{k} + c$, we have

Using the integral rule $\int {\sin kx} dx = - \frac{{\cos kx}}{k} + c$, we have