Mister Exam

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Identical expressions
(two xy^2-2x^ three)
(2xy squared minus 2x cubed )
(two xy squared minus 2x to the power of three)
(2xy2-2x3)
2xy2-2x3
(2xy²-2x³)
(2xy to the power of 2-2x to the power of 3)
2xy^2-2x^3
(2xy^2-2x^3)dx
Similar expressions
(2xy^2+2x^3)

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

The solution

You have entered [src]

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$x^2\,y^2-{{x^4}\over{2}}$$

Simplify

The answer [src]

  1    2
- - + y 
  2

$${{2\,y^2-1}\over{2}}$$

  1    2
- - + y 
  2

$$y^{2} - \frac{1}{2}$$

Simplify

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

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

Limits of integration:

The graph:

Piecewise:

The solution