en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-x^2+2x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of (x^6/3)

\frac{d}{d x} (\frac{x ^{6}}{3})

integral of 6x^2cos(2x^3+1)

\int 6 x^{2} cos (2 x^{3} + 1) d x

derivative of x+3 derivative of

x + 3

(dy)/(dx)=y(1-0.0004y)

\frac{d y}{d x} = y (1 - 0.0004 y)

(e^x-2xy)dx-x^2dy=0

(e^{x} - 2 x y) d x - x^{2} d y = 0

Frequently Asked Questions (FAQ)

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