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Popular >

integral of-x^2+8x

Solution

\int - x^{2} + 8 x d x

Solution

- \frac{x ^{3}}{3} + 4 x^{2} + C

Solution steps

\int - x^{2} + 8 x 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 8 x d x

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

\int 8 x d x = 4 x^{2}

= - \frac{x ^{3}}{3} + 4 x^{2}

Add a constant to the solution

= - \frac{x ^{3}}{3} + 4 x^{2} + C

Popular Examples

limit as x approaches 3 of-1/(x-3)

x \to 3 lim (- \frac{1}{x - 3})

derivative of 50x-0.5x^2

\frac{d}{d x} (50 x - 0.5 x^{2})

limit as x approaches-5-of (3x+8)/(x+5)

x \to - 5 - lim (\frac{3 x + 8}{x + 5})

derivative of (cos(x)/(sin(x)))

\frac{d}{d x} (\frac{cos ( x )}{sin ( x )})

limit as x approaches infinity of x-x^2

x \to \infty lim (x - x^{2})

Frequently Asked Questions (FAQ)

What is the integral of-x^2+8x ?
The integral of-x^2+8x is -(x^3)/3+4x^2+C