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Popular >

integral of x^2-x-12

Solution

\int x^{2} - x - 12 d x

Solution

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 12 x + C

Solution steps

\int x^{2} - x - 12 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 12 d x

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

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

\int 12 d x = 12 x

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 12 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 12 x + C

Graph

Popular Examples

integral of 2/((2x+1)^2)

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

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\int \frac{27 x ^{3} - 1}{4 x} d x

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

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

integral of e^{-0.03x}

\int e^{- 0.03 x} d x

integral of 1/((xln(x^2)))

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

Frequently Asked Questions (FAQ)

What is the integral of x^2-x-12 ?
The integral of x^2-x-12 is (x^3)/3-(x^2)/2-12x+C