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Popular Calculus >

integral of-x^3+9x

Solution

\int - x^{3} + 9 x d x

Solution

- \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

Solution steps

\int - x^{3} + 9 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 x^{3} d x + \int 9 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 9 x d x = \frac{9 x ^{2}}{2}

= - \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= - \frac{x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of-x^3+9x ?
The integral of-x^3+9x is -(x^4)/4+(9x^2)/2+C