Integration of e^x Cos x

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

The integration of the form

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

By using integration by parts formula

Equation (i) will becomes

Again using integration by parts formula, we have

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