## Integrating a Product of Exponential and Trigonometric Functions

Products of functions can often be integrated by parts or using a suitable substitution to obtain a sipler function which can be integrated. Sometimes it happens that the integration by parts method does not result in a simpler integral, but the integral can still be evaluated. A very good example of this is the integral

This function can be integrated by parts:

TakeandthenandSubstituting into (1) gives

(2)

is not any easier to integrate thanbut look what happens when we integrate again, by parts.

To integratetakeandthenand

Subsituting this into (2) gives