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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 4(sin(x))^2

\int 4 (sin (x))^{2} d x

integral of x^{3/2}-x

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

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\int \frac{( x + 3 )}{x} d x

integral of 5/(e^{3x+1)}

\int \frac{5}{e ^{3 x + 1}} 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