Mister Exam

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Canonical form:
x+y+z
Expression:
x+y+z
Limit of the function:
x+y+z
Identical expressions
x+y+z
x plus y plus z
x+y+zdx
Similar expressions
x+y-z
x-y+z

Integral of x+y+z dy

The solution

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  1               
  /               
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 |  (x + y + z) dy
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0

$$\int\limits_{0}^{1} \left(z + \left(x + y\right)\right)\, dy$$

Integral(x + y + z, (y, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int z\, dy = y z$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int x\, dy = x y$
  1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int y\, dy = \frac{y^{2}}{2}$
  The result is: $x y + \frac{y^{2}}{2}$
The result is: $x y + \frac{y^{2}}{2} + y z$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                      2            
 |                      y             
 | (x + y + z) dy = C + -- + x*y + y*z
 |                      2             
/

$$\int \left(z + \left(x + y\right)\right)\, dy = C + x y + \frac{y^{2}}{2} + y z$$

Simplify

The answer [src]

1/2 + x + z

$$x + z + \frac{1}{2}$$

1/2 + x + z

$$x + z + \frac{1}{2}$$

1/2 + x + z

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

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Integral of x+y+z dy

Limits of integration:

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Piecewise:

The solution