Integrating 59x(cos(x))2: A Step-by-Step Guide

[Mugen Prospec]

Homework Statement

$$\int$$ 59x(cos(x))² dx

Homework Equations

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.

 

[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 don't know how to do it.

 

[LCKurtz]

Use:

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

and integration by parts.

 

[Mugen Prospec]

ok Ill check it out thanks

 

[Mugen Prospec]

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

 

[lanedance]

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

 

[Mugen Prospec]

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

 

[lanedance]

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