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Popular >

integral of x^2-x-2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

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f (x) = \frac{sin ( x )}{x ^{3}}

xy^'+y=6x^2,y(1)=2

x y^{^{'}} + y = 6 x^{2}, y (1) = 2

limit as n approaches infinity of n^{10}

n \to \infty lim (n^{10})

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f (x) = 2 x - x ln ∣ x ∣

Frequently Asked Questions (FAQ)

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