Calculus
posted by Scott on .
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.

Use integration by parts:
I=∫e^{x}sin(4x)dx
=e^{x}sin(4x)4∫e^{x}cos(4x)dx
=e^{x}sin(4x)4e^{x}cos(4x)16∫e^{x}sin(4x)dx
=e^{x}sin(4x)4e^{x}cos(4x)16I
Solve for I to get the above results.