Question

integral 0 to infinity of e^-xcosxdx

Answer 1

By parts?

Answer 2

that was more of a hint rather than a offer to do it for you :)

Answer 3

You only need to double by part it.
Here is the link http://www.wolframalpha.com/input/?i=integrate+e%5E-xcosxdx+ , If you want to see how it's done click 'show steps'. And if you still have doubt, ask it here. I am too lazy to type it all out.

Answer 4

Oo ... I was scared
http://www.wolframalpha.com/input/?i=Integrate+from+0+to+infinity+e%5E%28-+x+cos+x%29