Integral of xy(z+2)dx dx

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  4               
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 |  x*y*(z + 2) dx
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\int\limits_{0}^{4} x y \left(z + 2\right)\, dx

Integral((x*y)*(z + 2), (x, 0, 4))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int x y \left(z + 2\right)\, dx = \left(z + 2\right) \int x y\, dx$
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: $\frac{x^{2} y}{2}$
So, the result is: $\frac{x^{2} y \left(z + 2\right)}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                        2        
 |                      y*x *(z + 2)
 | x*y*(z + 2) dx = C + ------------
 |                           2      
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\int x y \left(z + 2\right)\, dx = C + \frac{x^{2} y \left(z + 2\right)}{2}

Simplify

The answer [src]

16*y + 8*y*z

8 y z + 16 y

16*y + 8*y*z

8 y z + 16 y

16*y + 8*y*z

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