# Thread: 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?

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

James

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

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

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
$\displaystyle du = \frac {dx}{1+x^2}$

Therefore

$\displaystyle \int udu$

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

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