# Homework Help: Trig Integral

1. Oct 20, 2009

### Mugen Prospec

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

$$\int$$ 59x(cos(x))2 dx

2. Relevant equations

3. The attempt at a solution

I tried doing integration by parts with u= (cos(x))2 and dv= xdx
v= $$\frac{x^2}{2}$$
However this didnt get me very far can some one tell me what the first step or two are.

2. Oct 20, 2009

### Mugen Prospec

I got the the answer to be 59($$\frac{1}{4}$$x sin(2x) + $$\frac{1}{8}$$cos(2x) + $$\frac{x^2}{4}$$)
But this was from my calculator I still dont know how to do it.

3. Oct 20, 2009

### LCKurtz

Use:

$$\cos^2(x) = \frac {1 + \cos{(2x)}}{2}$$

and integration by parts.

4. Oct 20, 2009

### Mugen Prospec

ok Ill check it out thanks

5. Oct 20, 2009

### Mugen Prospec

OK I tried it and it just got more complicated. Whats the next step?

6. Oct 20, 2009

### lanedance

what LCKurtz suggested shoudl lead to a pretty simple integral, maybe show what you did

7. Oct 20, 2009

### Mugen Prospec

just did x(1+co(2x)/(2))
Do i distribute or use by parts now?

8. Oct 20, 2009

### lanedance

yep multiply out and use parts on the (x.cos(2x)) part