`int (4x^2+2x-1)/(x^3+x^2)dx`

To solve using partial fraction method, the denominator of the integrand should be factored.

`(4x^2+2x-1)/(x^3+x^2)=(4x^2+2x-1)/(x^2(x+1))`

Take note that if the factor in the denominator is linear and non-repeating, each factor in the denominator has a partial fraction form of `A/(ax+b)` .

And if the factor is linear and repeating, its partial fraction decomposition has a form `A_1/(ax+b) + A_2/(ax+b)^2+... +A_n/(ax+b)^n` .

So, expressing the integrand as sum of fractions, it becomes:

`(4x^2+2x-1)/(x^2(x+1))=A/x+B/x^2+C/(x+1)`

To determine the...

(The entire section contains 339 words.)

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