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Integral of d{x}:
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Identical expressions
(two *x- three *y)-(x-y)
(2 multiply by x minus 3 multiply by y) minus (x minus y)
(two multiply by x minus three multiply by y) minus (x minus y)
(2x-3y)-(x-y)
2x-3y-x-y
(2*x-3*y)-(x-y)dx
Similar expressions
(2*x-3*y)-(x+y)
(2*x+3*y)-(x-y)
(2*x-3*y)+(x-y)

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

The solution

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  1                        
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 |  (2*x - 3*y + -x + y) dx
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0

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

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

Detail solution

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

$\frac{x \left(x - 4 y\right)}{2}$
Add the constant of integration:

$\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               2        
 |                               x         
 | (2*x - 3*y + -x + y) dx = C + -- - 2*x*y
 |                               2         
/

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

Simplify

The answer [src]

1/2 - 2*y

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

1/2 - 2*y

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

1/2 - 2*y

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (2*x-3*y)-(x-y) dx

Limits of integration:

The graph:

Piecewise:

The solution

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