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

The integral of x(x-3)^2(x+1) is (x^5)/5-(5x^4)/4+x^3+(9x^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{x ^{5}}{5} - \frac{5 x ^{4}}{4} + x^{3} + \frac{9 x ^{2}}{2} + C

Solution steps

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

Expand

x (x - 3)^{2} (x + 1) : x^{4} - 5 x^{3} + 3 x^{2} + 9 x

= \int x^{4} - 5 x^{3} + 3 x^{2} + 9 x 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 5 x^{3} d x + \int 3 x^{2} d x + \int 9 x d x

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

\int 9 x d x = \frac{9 x ^{2}}{2}

= \frac{x ^{5}}{5} - \frac{5 x ^{4}}{4} + x^{3} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{5 x ^{4}}{4} + x^{3} + \frac{9 x ^{2}}{2} + C

\int x (x^{\frac{3}{2}} - 10)^{4} d x

\int x^{(- 1)} d x

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

\frac{1}{x 1 - x} d x

\int sin (v) cos (v) d v

What is the integral of x(x-3)^2(x+1) ?
The integral of x(x-3)^2(x+1) is (x^5)/5-(5x^4)/4+x^3+(9x^2)/2+C