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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

Popular Examples

integral of t^3e^{-4t}

\int t^{3} e^{- 4 t} d t

integral of 6/13 x^{13/7}

\int \frac{6}{13} x^{\frac{13}{7}} d x

integral of (5x^2+x)/((20x^3+6x^2)^2)

\int \frac{5 x ^{2} + x}{( 20 x ^{3} + 6 x ^{2} ) ^{2}} d x

integral of (-1)/(x^6)

\int \frac{- 1}{x ^{6}} d x

integral of x^3(x^2-5)^{1/2}

\int x^{3} (x^{2} - 5)^{\frac{1}{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