How Do I Solve ∫e^-x cos(2x)dx Using Integration by Parts?

[mickellowery]

Homework Statement

∫e^-x cos(2x)dx

Homework Equations

I'm trying integration by parts and I set u=e^-x and dv=cos(2x)

The Attempt at a Solution

I got to where ∫udv= (e^-x)(1/2 sin(2x))+1/2∫sin(2x)e^-x
I am trying to run through a second time and I'm a little stuck

 

[rock.freak667]

Take ∫sin(2x)e^-x dx separately.

u= e^-x du=?

dv= sin(2x)dx v =?

 

[Mark44]

Continuing as you are, you should get an equation with ∫e^-x cos(2x)dx on one side and the same on the other side, plus some other terms. Move both integral terms to one side of the equation and solve algebraically for the integral.