Homework Help: Calculus

Posted by Scott on Thursday, September 23, 2010 at 11:02am.

Evaluate the integral e^x sin4x dx.

I know the answer is 1/17 e^x sin4x - 4/17 e^x cos4x + C but I don't know how to solve it out.

Calculus - MathMate, Thursday, September 23, 2010 at 4:01pm
Use integration by parts:

I=∫e^xsin(4x)dx
=e^xsin(4x)-4∫e^xcos(4x)dx
=e^xsin(4x)-4e^xcos(4x)-16∫e^xsin(4x)dx
=e^xsin(4x)-4e^xcos(4x)-16I
Solve for I to get the above results.

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