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
is not any easier to integrate thanbut look what happens when we integrate again, by parts.
Subsituting this into (2) gives
Addingto both sides gives