So I have never done this before.. no idea what to do. Any help?

Question

luigi0210 · Answer

Integration by parts:
$$\LARGE \int\limits 2x~\sin2x~dx$$

anonymous · Answer

Integration by parts is my favorite thing ever.

anonymous · Answer

And by that I mean I hate it.
But I've been studying it recently so I can help you.

What looks good for a u and v? Any ideas?

luigi0210 · Answer

Isn't there like a formula for this?

anonymous · Answer

Yes. http://imgs.xkcd.com/comics/integration_by_parts.png Just kidding, it's: $$\int u dv = uv - \int v du$$

anonymous · Answer

What that means is you generally want a u that is going to look nicer when you differentiate it and a v that is going to look nicer when you integrate it. Otherwise your problem will spiral out of control and you will be sad.

luigi0210 · Answer

You make it sound fun  xD

anonymous · Answer

lol

anonymous · Answer

it is fun ^_^

anonymous · Answer

So, any ideas what to put in "u" and what to put in "dv"?

luigi0210 · Answer

Uhm, u=x and dv= sin(2x)*2x?

luigi0210 · Answer

*2dx

anonymous · Answer

We want to stick as much in u as possible, because, quite honestly, u is easier to deal with. We just don't want something that explodes into a gigantic mess when you take its derivative.
A good choice is:
$$u = 2x \ du = 2 dx$$

anonymous · Answer

That means
$$dv = \sin 2x dx$$$$v = -\frac{\cos 2x}{2} $$
You have to integrate dv twice. Which is why it is annoying.

luigi0210 · Answer

I haven't had calc in a year so.. I'm very rusty on my derivatives .-.

anonymous · Answer

It's ok! 
Take what we have and plug it into $uv - \int v du$

luigi0210 · Answer

So:
$$\LARGE 2x*\frac{\cos~2x}{2}-\int\limits \frac{\cos~2x}{2}$$

anonymous · Answer

Yes. The left side can simplify of course. And you can rewrite that /2 as a $\frac{1}{2}$ and move it outside of the integral as a constant. Then the integral is actually not too awful.

anonymous · Answer

Oh, and remember to make it +, because v is negative.

anonymous · Answer

You also forgot to write the du part. Which you can't leave off here because it also introduces a constant.

luigi0210 · Answer

Still learning :P
but if I did it right.. it would be:
$$\LARGE \frac{1}{2}\sin(2x)-xcos(2x)+C$$?

anonymous · Answer

I think so!

luigi0210 · Answer

Well thank you :)

anonymous · Answer

I did a problem very similar to this one the other day. http://openstudy.com/study#/updates/527b26c5e4b0de4fd476791e I'm not sure if studying it is any use to you, but there it is.

anonymous · Answer

Glad to help. :D