$\displaystyle \int \frac{x^2}{1+x^2}dx$
Tried both u substitution letting u = 1+x^2, and u = atan(x), neither worked. Tried using integration by parts as well. Any suggestions in the right direction?
$\displaystyle \dfrac{x^2}{1+x^2} = \dfrac{x^2+1-1}{1+x^2} = \dfrac{x^2+1}{1+x^2} - \dfrac{1}{1+x^2} = 1 - \dfrac{1}{1+x^2}$
$\displaystyle \int \dfrac{x^2}{1+x^2}dx = \int 1dx - \int \dfrac{1}{1+x^2}dx$
The second integral is a standard integral according to Wolfram (are you "allowed" to know this result or do you have to show/derive it?)