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

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Answer 1 · 2014-09-28T17:02:15

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

Let us look at some details.

$int{5x^2+3x-2}/{x^3+2x^2} dx$

by Partial Fraction Decomposition (details not included),

$=int (2/x-1/x^2+3/{x+2}) dx$

by Log Rule and Power Rule,

$=2ln|x|+1/x+3ln|x+2|+C$

I hope that this was helpful.

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