Thread: Need fast help on an integration problem.

Hi, I need urgent help on this problem
int((e^(8x))*cos(9x))dx

I've tried integration by parts but you end up with a even more complicated integral. Tabular integration doesn't work since the e^8x never reduces to 0. I'm stumped , please help thanks!

Originally Posted by HclBr

Hi, I need urgent help on this problem
int((e^(8x))*cos(9x))dx

I've tried integration by parts but you end up with a even more complicated integral. Tabular integration doesn't work since the e^8x never reduces to 0. I'm stumped , please help thanks!

Integrate by parts twice. It may look as though it's getting more complicated, but when you do it a second time it gets you back to a multiple of the integral that you started with. That gives you an equation for the integral. The answer should be of the form (plus a constant of integration, of course).

I suggest (for this problems, 'cause they're well-known) take them more generally:



As Opalg said, this requires a twice integration by parts.

Or we can use the following method:



After some simple calculations we have