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.