# Integral with partial fractions

• February 19th 2010, 03:47 AM
coobe
Integral with partial fractions
Hello, couild someone explain me how to integrate this ? i tried but i never get the result from wolfram alpha

$\int \frac {5+x^2} {4x^2+x^3}$
• February 19th 2010, 04:02 AM
Krizalid
$\frac{5+x^{2}}{4x^{2}+x^{3}}=\frac{5}{x^{2}(x+4)}+ \frac{1}{x+4},$ 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.