# Integral of x Cos2x

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

The integration is of the form

Here the first function is $x$ and the second function is $\cos 2x$

Using the formula for integration by parts, we have

Using the formula above, equation (i) becomes

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