Evaluate ∫ 6 x 3 − 5 x 2 2 x 2 − 3 x − 2 d x

Question

Evaluate   ∫            6              x        3            −      5              x        2                    2              x        2            −      3      x      −      2        d  x

veirenca77 · Accepted Answer

Integrating with partial fractions with non-supcated linear factors

\int \frac{6 x^{3} - 5 x^{2}}{2 x^{2} - 3 x - 2} d x

For partial fraction function should be in

\frac{f (x)}{q (x)} where q (x) \neq 0

and degree of p(x) < degree of q(x)

\frac{f (x)}{q (x)} = \frac{6 x^{3} - 5 x^{2}}{2 x^{2} - 3 x - 2}

Here degree of p(x)=3
degree of q(x)=2
To make degree of q(x)> degree of p(x) we need to divide p(x) by q(x)
on on division we get

= (\frac{12 x + 4}{2 x^{2} - 3 x - 2} + 3 x + 2)

Evaluate int (6x^3-5x^2)/(2x^2-3x-2)dx

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Answer & Explanation

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