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Popular >

integral of-x^2-x+6

Solution

\int - x^{2} - x + 6 d x

Solution

- \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x + C

Solution steps

\int - x^{2} - x + 6 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^{2} d x - \int x d x + \int 6 d x

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

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

\int 6 d x = 6 x

= - \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x

Add a constant to the solution

= - \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + 6 x + C

Graph

Popular Examples

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

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\int x^{2} 9 - x^{2} d x

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\int_{1}^{3} \frac{2}{x ^{2}} d x

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\frac{d}{d x} (5 sin (x) cos (x) + 4 csc (x))

integral of 1/(2x-x^2-10)

\int \frac{1}{2 x - x ^{2} - 10} d x

Frequently Asked Questions (FAQ)

What is the integral of-x^2-x+6 ?
The integral of-x^2-x+6 is -(x^3)/3-(x^2)/2+6x+C