What is the integral of ((2x^3-3)/x) ?

The integral of ((2x^3-3)/x) is (2x^3)/3-3ln|x|+C

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integral of ((2x^3-3)/x)

\int (\frac{2 x ^{3} - 3}{x}) d x

\frac{2 x ^{3}}{3} - 3 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{2 x ^{3} - 3}{x} : 2 x^{2} - \frac{3}{x}

= \int 2 x^{2} - \frac{3}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{2} d x - \int \frac{3}{x} d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{2 x ^{3}}{3} - 3 ln ∣ x ∣

Add a constant to the solution

= \frac{2 x ^{3}}{3} - 3 ln ∣ x ∣ + C

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What is the integral of ((2x^3-3)/x) ?
The integral of ((2x^3-3)/x) is (2x^3)/3-3ln|x|+C