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+2

Solution

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

Solution

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

Solution steps

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

t(dx)/(dt)+2x=3t

t \frac{d x}{d t} + 2 x = 3 t

derivative of (10)/(x^2+1)derivative of

\frac{10}{x ^{2} + 1}

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

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

y^'+t/(t^2-16)y=(e^t)/(t-9),y(-7)=-0.5

y^{^{'}} + \frac{t}{t ^{2} - 16} y = \frac{e ^{t}}{t - 9}, y (- 7) = - 0.5

(dy)/(dx)=x(1+x)(1+y)

\frac{d y}{d x} = x (1 + x) (1 + y)

Frequently Asked Questions (FAQ)

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