1. More Calculus

I've gotten as far as the line before the last, but I'm not sure whether the last line has integrated by parts (yet again - third time) the integral, or what it has assumed?

2. The last line simply recognises that $\int e^{x} cos(mx)$ is I, the thing you tried to integrate in the first place.

Then it factorises.

3. Originally Posted by maggiec

I've gotten as far as the line before the last, but I'm not sure whether the last line has integrated by parts (yet again - third time) the integral, or what it has assumed?

The last line simply recognises that $\int e^{x} cos(mx)$ is I, the thing you tried to integrate in the first place.