# Integration of arctan(u)

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

arildno
Homework Helper
Gold Member
Dearly Missed
Remember:
$$arctan(u)=1*arctan(u)$$

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

arildno
Homework Helper
Gold Member
Dearly Missed
Yep, that does the trick!

Gib Z
Homework Helper
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
Homework Helper
Gold Member
Dearly Missed
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
Homework Helper
Of Course :D