What is the integral of ((1-2x^3)/(x^3)) ?

The integral of ((1-2x^3)/(x^3)) is -1/(2x^2)-2x+C

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integral of ((1-2x^3)/(x^3))

\int (\frac{1 - 2 x ^{3}}{x ^{3}}) d x

- \frac{1}{2 x ^{2}} - 2 x + C

Solution steps

\int \frac{1 - 2 x ^{3}}{x ^{3}} d x

Expand

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

= \int \frac{1}{x ^{3}} - 2 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 \frac{1}{x ^{3}} d x - \int 2 d x

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

\int 2 d x = 2 x

= - \frac{1}{2 x ^{2}} - 2 x

Add a constant to the solution

= - \frac{1}{2 x ^{2}} - 2 x + C

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What is the integral of ((1-2x^3)/(x^3)) ?
The integral of ((1-2x^3)/(x^3)) is -1/(2x^2)-2x+C