Integrating arctan(u): Where Do I Begin?

[trajan22]

hi I am 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 $$(arctan(u))=u(arctan(u))-\frac{1}{2}ln(1+u^2)+C$$

i am completely lost please help...any input is much appreciated.

 

[arildno]

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

 

[trajan22]

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

 

[arildno]

Yep, that does the trick!

 

[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..

 

[arildno]

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..

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

 

[Gib Z]

Of Course :D