What is the integral of (x^2-x-6) ?

The integral of (x^2-x-6) is (x^3)/3-(x^2)/2-6x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2-x-6)

\int (x^{2} - x - 6) d x

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

Solution steps

\int x^{2} - x - 6 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 x d x - \int 6 d x

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

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

\int 6 d x = 6 x

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + C

\int \frac{x + 19}{x ^{2} - 7 x - 8} d x

\int e^{- x} f (e^{- x}) d x

\int 3 x^{\frac{1}{2}} - x^{\frac{3}{2}} + 2 x^{- \frac{1}{2}} d x

\int 2 sin (x) + 4 d x

\int \frac{π}{4 W} cos (\frac{π x}{2 W}) d x

What is the integral of (x^2-x-6) ?
The integral of (x^2-x-6) is (x^3)/3-(x^2)/2-6x+C