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Popular Calculus >

integral of (x-x^3)/x

Solution

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

Solution

x - \frac{x ^{3}}{3} + C

Solution steps

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

Expand

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

\int \frac{x}{x} d x = x

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

= x - \frac{x ^{3}}{3}

Add a constant to the solution

= x - \frac{x ^{3}}{3} + C

Graph

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Frequently Asked Questions (FAQ)

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