1. ## Challenging Integral

$\int e^x cosx dx$

Can someone walk me through this integral?

2. Do you know integration by parts?

If so do this twice.

3. After integrating twice I get:

$e^x sinx + e^x cosx - \int cosx e^x$

Then what do I do?

4. Originally Posted by penguinpwn
After integrating twice I get:

$e^x sinx + e^x cosx - \int cosx e^x$

Then what do I do?
$\int e^x \cos{x} \, dx = e^x \sin{x} + e^x \cos{x} - \int \cos{x} \cdot e^x \, dx$

$2\int e^x \cos{x} \, dx = e^x \sin{x} + e^x \cos{x} + C$

finish up

5. Woah, did not know that trick.

Thanks a ton!