How Do You Solve Integral of e^(2y)sin(2y) dy Using Integration by Parts?

[Nick_273]

Homework Statement

Evaluate integral of e^2ysin(2y)dy using integration by parts.

Homework Equations

integral udv = uv - integral vdu

The Attempt at a Solution

I tried applying the above equation several times, but the integral and derivative of both e^2y and sin(2y) will always have a y in them.

Let me know if you have any ideas,

Thanks.

 

[hgfalling]

Integrate by parts twice. Then you'll get back to your original integral and will be able to write it in terms of the uv terms you've accumulated.

 

[_Bd_]

once you integrate once you're going to get another integral (the integral vdu) which is going to be another integration by parts. . .do that again and the third integral will also be an integration by parts. . .but luckily enough it will be e^(2y) sin(2y)dy so then you have your equation

int{e^(2y) sin(2y)dy} = BLAH BLAH BLAH - int{e^(2y) sin(2y)dy}
so since you have the same thing on both sides of the equation you can just solve for it. . .