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)(x+1)

Solution

\int (x - 2) (x + 1) d x

Solution

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

Solution steps

\int (x - 2) (x + 1) d x

Expand

(x - 2) (x + 1) : x^{2} - x - 2

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

integral of 6/(sqrt(2-4x^2))

\int \frac{6}{2 - 4 x ^{2}} d x

integral of sec(4x+2)tan(4x+2)

\int sec (4 x + 2) tan (4 x + 2) d x

integral of 1/(x^2+3x-1)

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

integral of 8x^{3/2}

\int 8 x^{\frac{3}{2}} d x

integral of (e^{tan(x)})/(1-sin^2(x))

\int \frac{e ^{t a n (x)}}{1 - sin ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of (x-2)(x+1) ?
The integral of (x-2)(x+1) is (x^3)/3-(x^2)/2-2x+C