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

The integral of (x-1)^3(x+2) is (x^5)/5-(x^4)/4-x^3+(5x^2)/2-2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{x ^{5}}{5} - \frac{x ^{4}}{4} - x^{3} + \frac{5 x ^{2}}{2} - 2 x + C

Solution steps

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

Expand

(x - 1)^{3} (x + 2) : x^{4} - x^{3} - 3 x^{2} + 5 x - 2

= \int x^{4} - x^{3} - 3 x^{2} + 5 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^{4} d x - \int x^{3} d x - \int 3 x^{2} d x + \int 5 x d x - \int 2 d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int x^{3} d x = \frac{x ^{4}}{4}

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 2 d x = 2 x

= \frac{x ^{5}}{5} - \frac{x ^{4}}{4} - x^{3} + \frac{5 x ^{2}}{2} - 2 x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{x ^{4}}{4} - x^{3} + \frac{5 x ^{2}}{2} - 2 x + C

\int \frac{e ^{6 x} + 3}{e ^{6 x} + e ^{- 6 x}} d x

\int cos (x) e^{- 2 x} d x

\int \frac{1}{6 + x} d x

\int x^{3} arccot (x) d x

\int \frac{1}{( x + 2 ) ( x + 3 ) ( x + 4 )} d x

What is the integral of (x-1)^3(x+2) ?
The integral of (x-1)^3(x+2) is (x^5)/5-(x^4)/4-x^3+(5x^2)/2-2x+C