Integration: arctan(x) rule derivation

Hello,

the task is to derive integration rule (2) from rule (1).

(1) $\displaystyle \int \frac{1}{x^2+1} dx = \arctan (x) $

(2) $\displaystyle \int \frac{1}{x^2+c^2} dx = \frac{1}{c} \arctan (\frac{x}{c}) $

$\displaystyle c$ is constant and $\displaystyle >0$

I tried to massage rule (1) with basic operations, but I always ended up with too many x's and c's. Also, I couldn't find any help using forum's search function. So, any help is welcome. Mucho thanks in advance!