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(x^ two -3x)^ two
(x squared minus 3x) squared
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Similar expressions
(x^2+3x)^2

Solving integrals/ (x^2-3x)^2

Integral of (x^2-3x)^2 dx

The solution

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  1               
  /               
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 |            2   
 |  / 2      \    
 |  \x  - 3*x/  dx
 |                
/                 
0

$$\int\limits_{0}^{1} \left(x^{2} - 3 x\right)^{2}\, dx$$

Integral((x^2 - 3*x)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x^{2} - 3 x\right)^{2} = x^{4} - 6 x^{3} + 9 x^{2}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 6 x^{3}\right)\, dx = - 6 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $- \frac{3 x^{4}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 9 x^{2}\, dx = 9 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $3 x^{3}$
The result is: $\frac{x^{5}}{5} - \frac{3 x^{4}}{2} + 3 x^{3}$
Now simplify:

$\frac{x^{3} \cdot \left(2 x^{2} - 15 x + 30\right)}{10}$
Add the constant of integration:

$\frac{x^{3} \cdot \left(2 x^{2} - 15 x + 30\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \cdot \left(2 x^{2} - 15 x + 30\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 |           2                    4    5
 | / 2      \              3   3*x    x 
 | \x  - 3*x/  dx = C + 3*x  - ---- + --
 |                              2     5 
/

$${{x^5}\over{5}}-{{3\,x^4}\over{2}}+3\,x^3$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

17
--
10

$${{17}\over{10}}$$

17
--
10

$$\frac{17}{10}$$

Упростить

Numerical answer [src]

1.7

1.7

The graph

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

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Integral of (x^2-3x)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution