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

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

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

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

2 x - ln ∣ x ∣ + C

Solution steps

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

Simplify

\frac{2 x ^{3} - x ^{2}}{x ^{3}} : \frac{2 x - 1}{x}

= \int \frac{2 x - 1}{x} d x

Expand

\frac{2 x - 1}{x} : 2 - \frac{1}{x}

= \int 2 - \frac{1}{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 d x - \int \frac{1}{x} d x

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x - ln ∣ x ∣

Add a constant to the solution

= 2 x - ln ∣ x ∣ + C

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