What is the integral of (a+x-x^2) ?

The integral of (a+x-x^2) is ax+(x^2)/2-(x^3)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (a+x-x^2)

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

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

Solution steps

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

\int a d x = a x

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

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

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

Add a constant to the solution

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

\int 7 x^{\frac{2}{5}} + 8 x^{- \frac{4}{5}} d x

\frac{\partial}{\partial x} (\frac{( 2 x - y )}{5 x + 3 y})

x^{2} y^{^{''}} + x y^{^{'}} - y = ln (x)

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

\frac{d}{d x} (\frac{1}{1 + 24 e ^{- 0.28 x}})

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