Question

What is the derivative of e^(-x)? I have to integrate e^(-x) * cos(2x) dx and I'm using integration by parts. u=e^(-x) dv=cos(2x) dx. Is that wrong and if not, how do you do you take the derivative of that exp. function.

Answer 1

That's a good way to do it. It will take several steps, but you'll get it.
The derivative of e^(u(x)) = u'(x)e^(u(x)).

Answer 2

Thank you very much

Answer 3

You could also use:
\[\int\limits e^{-x}\cos(2x)dx=\Re \left[ \int\limits e^{-x}e^{2ix}dx\right]\]
Which is trivial to evaluate, find the real part, and you have your solution :)