# Integration of arctan(u)

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

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

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#### arildno

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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

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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

Science Advisor
Homework Helper
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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..

Homework Helper
Of Course :D