# Integration of e^x Cos x

In this tutorial we shall derive the integral of e^x into the cosine function, and this integral can be evaluated by using the integration by parts method.

The integration is of the form

Here the first function is $f\left( x \right) = {e^x}$ and the second function is $g\left( x \right) = \cos x$

By using the integration by parts formula

Equation (i) will become

Again using the integration by parts formula, we have

But using $I = \int {{e^x}\cos xdx}$, we have