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Popular >

integral of-x^2+5x-6

Solution

\int - x^{2} + 5 x - 6 d x

Solution

- \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 6 x + C

Solution steps

\int - x^{2} + 5 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 5 x d x - \int 6 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= - \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 6 x

Add a constant to the solution

= - \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} - 6 x + C

Popular Examples

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

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\int (6 \frac{sin ( 2 x )}{sin ( x )}) d x

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\int x e^{c x} d x

integral of (3000)/(sqrt(200x))

\int \frac{3000}{200 x} d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of-x^2+5x-6 ?
The integral of-x^2+5x-6 is -(x^3)/3+(5x^2)/2-6x+C