Integral of x(x-5)dx dx

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 |  x*(x - 5) dx
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$$\int\limits_{0}^{1} x \left(x - 5\right)\, dx$$

Integral(x*(x - 5), (x, 0, 1))

Detail solution

Rewrite the integrand:

$x \left(x - 5\right) = x^{2} - 5 x$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 5 x\right)\, dx = - 5 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{5 x^{2}}{2}$
The result is: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x - 15\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x - 15\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x - 15\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      2    3
 |                    5*x    x 
 | x*(x - 5) dx = C - ---- + --
 |                     2     3 
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$$\int x \left(x - 5\right)\, dx = C + \frac{x^{3}}{3} - \frac{5 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-13/6

$$- \frac{13}{6}$$

-13/6

$$- \frac{13}{6}$$

-13/6

Numerical answer [src]

-2.16666666666667

-2.16666666666667

The graph

Use the examples entering the upper and lower limits of integration.