# Integration by parts

1. Jan 20, 2008

### polorob3

1. The problem statement, all variables and given/known data

$$\int$$(x-3x^2)cos(2x)dx

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 20, 2008

### rocomath

What did you try?

3. Jan 20, 2008

### ColdFusion85

I think you should get $$\frac{3}{4}sin(2x)+C$$, but I could be wrong...show your work.

4. Jan 20, 2008

### rocomath

I haven't done it, but that's wrong. The answer will need to have more than 2 terms.

Last edited: Jan 21, 2008
5. Jan 21, 2008

### dynamicsolo

Quite so! A rule of thumb (probably isn't hard to prove) for integration of an nth-degree polynomial times sin kx, cos kx, or e^kx is that you will have (n+1) terms, running from x^n times the sinusoidal or exponential function down to a constant times that function. (OK, I'm not counting the arbitrary constant...)