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Identical expressions
xy- four (x^ three)y^ three
xy minus 4(x cubed )y cubed
xy minus four (x to the power of three)y to the power of three
xy-4(x3)y3
xy-4x3y3
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xy-4(x to the power of 3)y to the power of 3
xy-4x^3y^3
xy-4(x^3)y^3dx
Similar expressions
xy+4(x^3)y^3

Integral of xy-4(x^3)y^3 dy

The solution

You have entered [src]

    3                    
   x                     
    /                    
   |                     
   |   /         3  3\   
   |   \x*y - 4*x *y / dy
   |                     
  /                      
   ___                   
-\/ x

$$\int\limits_{- \sqrt{x}}^{x^{3}} \left(- 4 x^{3} y^{3} + x y\right)\, dy$$

Integral(x*y - 4*x^3*y^3, (y, -sqrt(x), x^3))

Detail solution

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

$- x^{3} y^{4} + \frac{x y^{2}}{2}+ \mathrm{constant}$

The answer is:

$- x^{3} y^{4} + \frac{x y^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

      7          2
 5   x     15   x 
x  + -- - x   - --
     2          2

$${{2\,x^5-x^2}\over{2}}-{{2\,x^{15}-x^7}\over{2}}$$

      7          2
 5   x     15   x 
x  + -- - x   - --
     2          2

$$- x^{15} + \frac{x^{7}}{2} + x^{5} - \frac{x^{2}}{2}$$

Упростить

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

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Similar expressions

Integral of xy-4(x^3)y^3 dy

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The graph:

Piecewise:

The solution