Integration by Parts: Solving \int t sin(2t) dt

[maff is tuff]

Homework Statement

$$\int$$ t sin(2t) dt

Homework Equations

Integration by parts formula:

$$\int$$udv = uv - $$\int$$vdu

The Attempt at a Solution

I chose t to be u so,

u=t
du=dt
dv=sin(2t)dt
v=(sin)^2 (hope that's right. I used double angle formula to change sin(2t) into 2sint cost)

So now by the integration by parts formula I get:


$$\int$$t sin(2t)dt = t(sint)^2 - $$\int$$(sint)^2 dt

Now I have no idea how to integrate sin²t

I don't know if I messed up somewhere way up there or if it's right and I'm just stuck on this part. Any help would be greatly appreciated. Thanks in advance!

 

[Dick]

You integrate sin(t)^2 by using the double angle approach again. But the whole thing is a lot easier if you integrate sin(2t) just using the substitution u=2t.

 

[maff is tuff]

Wow thanks Dick I can't believe I overlooked that. Also, thanks a lot for the prompt reply!