# Finding integrals of the product of trig functions

1. Jun 21, 2011

### DrWillVKN

1. The problem statement, all variables and given/known data
I've come across integrals of exponential and trig functions and I have no idea how to do them. Integration by parts doesn't really work because they just derive into either e or another trig function.

One of them is $\int$sin(a)*sin(b - a)da
Another is $\int$e(a)*sin(a)da

2. Relevant equations
sin(x + y) =sinx(cosy) + siny(cosx)
cos(x + y) = cosx(cosy) - sinx(siny)
sin^2(x) = (1 - cos2x)/2

3. The attempt at a solution
I've tried to use the trig identity for sin(b-a), but that just gives an extremely long sin and cos statement that doesn't help. the one with e is even more confusing. How am I supposed to manually solve them?

Last edited: Jun 21, 2011
2. Jun 21, 2011

### Char. Limit

For the second problem, let

$$I = \int e^{a} sin(a) da$$

Then integrate the right side by parts twice, and note that you get, as your integral, I. From there, just solve for I.

3. Jun 21, 2011

### LCKurtz

Another trick for integrating integrals like ∫exsin(x)dx is to instead do the integral ∫exeixdx =∫e(1+i)xdx as a simple exponential. Rationalize the result and note your original integral is the imaginary part. This avoids two integrations by parts and gives you the ∫excos(x)dx from the real part as a free bonus.

4. Jun 21, 2011

### DrWillVKN

thanks for the replies, found the answers. i just didn't go far enough with the identities and integration by parts.