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Popular >

integral of-x^2+5x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

(\partial)/(\partial x)((3y-6x)/(y^2+7x^2))

\frac{\partial}{\partial x} (\frac{3 y - 6 x}{y ^{2} + 7 x ^{2}})

integral of sqrt(1-100x^2)

\int 1 - 100 x^{2} d x

integral from 0 to pi/2 of 10sin^2(3x)

\int_{0}^{\frac{π}{2}} 10 sin^{2} (3 x) d x

limit as x approaches 1+of xln(x)

x \to 1 + lim (x ln (x))

derivative of \sqrt[3]{3x^2}

\frac{d}{d x} (3 3 x^{2})

Frequently Asked Questions (FAQ)

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