# Math Help - Integration by substitution?

1. ## Integration by substitution?

Hi

I have this function which I am asked to integrate, I think Integration by substitution is the way to go but I'm not sure where to begin?

$\displaystyle\int\dfrac{\arctan x}{1 + x^2}dx$

James

2. let $arctan x=u$
$du=\frac{dx}{1+x^2}$

3. Thanks, its obvious now.

4. Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

Thanks

5. Originally Posted by bobred
Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

Thanks
$\displaystyle\int\dfrac{\arctan x}{1 + x^2}dx$
$=\displaystyle\int u du$
$=\frac{u^2}{2}+C$
$=\frac{(arctanx)^2}{2}+C$

6. Originally Posted by bobred
Sorry, I might have been a bit hasty, I going round in circles again. Any chance you cound ellaborate on that a little?

Thanks
Let u = arctanx
$du = \frac {dx}{1+x^2}$

Therefore

$\int udu$

$\frac {1}{2} u^2+c$

$\frac {\arctan^2 x}{2} +c$