# Integral with partial fractions

$\int \frac {5+x^2} {4x^2+x^3}$
$\frac{5+x^{2}}{4x^{2}+x^{3}}=\frac{5}{x^{2}(x+4)}+ \frac{1}{x+4},$ and $\frac{1}{x^{2}(x+4)}=\frac{1}{16}\cdot \frac{x^{2}-(x+4)(x-4)}{x^{2}(x+4)}=\frac{1}{16}\left( \frac{1}{x+4}-\frac{1}{x}+\frac{4}{x^{2}} \right),$ so i think you can take it from there.