# How do I find the integral int(5x^2+3x-2)/(x^3+2x^2)dx ?

Sep 28, 2014

$\int \frac{5 {x}^{2} + 3 x - 2}{{x}^{3} + 2 {x}^{2}} \mathrm{dx} = 2 \ln | x | + \frac{1}{x} + 3 \ln | x + 2 | + C$

Let us look at some details.

$\int \frac{5 {x}^{2} + 3 x - 2}{{x}^{3} + 2 {x}^{2}} \mathrm{dx}$

by Partial Fraction Decomposition (details not included),

$= \int \left(\frac{2}{x} - \frac{1}{x} ^ 2 + \frac{3}{x + 2}\right) \mathrm{dx}$

by Log Rule and Power Rule,

$= 2 \ln | x | + \frac{1}{x} + 3 \ln | x + 2 | + C$

I hope that this was helpful.