Mister Exam

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Integral of d{x}:
Integral of 2
Integral of 1/(x^2)
Integral of e^x^2
Integral of exp(-x^2)
Identical expressions
(xy-y^ two)dx+x*d*y
(xy minus y squared )dx plus x multiply by d multiply by y
(xy minus y to the power of two)dx plus x multiply by d multiply by y
(xy-y2)dx+x*d*y
xy-y2dx+x*d*y
(xy-y²)dx+x*d*y
(xy-y to the power of 2)dx+x*d*y
(xy-y^2)dx+xdy
(xy-y2)dx+xdy
xy-y2dx+xdy
xy-y^2dx+xdy
Similar expressions
(xy+y^2)dx+x*d*y
(xy-y^2)dx-x*d*y

Integral of (xy-y^2)dx+xdy dx

The solution

You have entered [src]

  1                      
  /                      
 |                       
 |  /       2        \   
 |  \x*y - y  + x*d*y/ dx
 |                       
/                        
0

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(y d x + \left(x y - y^{2}\right)\right)\, dx = C + \frac{d x^{2} y}{2} + \frac{x^{2} y}{2} - x y^{2}$$

Simplify

The answer [src]

y    2   d*y
- - y  + ---
2         2

$$\frac{d y}{2} - y^{2} + \frac{y}{2}$$

y    2   d*y
- - y  + ---
2         2

$$\frac{d y}{2} - y^{2} + \frac{y}{2}$$

y/2 - y^2 + d*y/2

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

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Integral of (xy-y^2)dx+xdy dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (xy-y^2)dx+x*d*y dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of (xy-y^2)dx+xdy dx