# How do I find the antiderivative of f(x)=(5x^2) / (x^2 + 1)?

$f \left(x\right) = \frac{5 {x}^{2}}{{x}^{2} + 1} = = 5 - \frac{5}{{x}^{2} + 1}$
$\int f \left(x\right) \mathrm{dx} = \int \left(5 - \frac{5}{{x}^{2} + 1}\right) \mathrm{dx} =$
$= \int 5 \mathrm{dx} - \int \frac{5}{{x}^{2} + 1} \mathrm{dx} =$
$= 5 x - 5 \arctan \left(x\right) + c$