# Integration of arctan(u)

1. Dec 28, 2006

### trajan22

hi im having trouble integrating arctan(u).

i have no idea where to even start. i know the derivative of arctan is
$$\frac{1}{x^2+1}$$ so i would assume that the integral would be the opposite?
but i am supposed to prove that $$(arctan(u))=u(arctan(u))-\frac{1}{2}ln(1+u^2)+C$$

2. Dec 28, 2006

### arildno

Remember:
$$arctan(u)=1*arctan(u)$$

3. Dec 28, 2006

### trajan22

so then you are saying that by using integration by parts i should be able to prove this?

4. Dec 28, 2006

### arildno

Yep, that does the trick!

5. Dec 31, 2006

### Gib Z

hehe I was thinking that to, love that trick. I need to learn where to use it though, sometimes it leads me off to nowhere..

6. Dec 31, 2006

### arildno

But blundering about is a far better thing to do than not dare to commit anything to paper..

7. Dec 31, 2006

Of Course :D