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Solving integrals/ x*y*z/((3*m))

Integral of x*y*z/((3*m)) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |  x*y*z   
 |  ----- dx
 |   3*m    
 |          
/           
0
∫01zxy3m dx\int\limits_{0}^{1} \frac{z x y}{3 m}\, dx 
Integral(((x*y)*z)/((3*m)), (x, 0, 1))
Detail solution

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

    ∫zxy3m dx=13m∫xyz dx\int \frac{z x y}{3 m}\, dx = \frac{1}{3 m} \int x y z\, dx

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

      ∫xyz dx=yz∫x dx\int x y z\, dx = y z \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: x2yz2\frac{x^{2} y z}{2}

    So, the result is: 13mx2yz2\frac{\frac{1}{3 m} x^{2} y z}{2}

  2. Now simplify:

    x2yz6m\frac{x^{2} y z}{6 m}

  3. Add the constant of integration:

    x2yz6m+constant\frac{x^{2} y z}{6 m}+ \mathrm{constant}

The answer is:

x2yz6m+constant\frac{x^{2} y z}{6 m}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    2  1 
 |                y*z*x *---
 | x*y*z                 3*m
 | ----- dx = C + ----------
 |  3*m               2     
 |                          
/
∫zxy3m dx=C+13mx2yz2\int \frac{z x y}{3 m}\, dx = C + \frac{\frac{1}{3 m} x^{2} y z}{2}
Simplify
The answer [src] 
y*z
---
6*m
yz6m\frac{y z}{6 m} 
=
= 
y*z
---
6*m
yz6m\frac{y z}{6 m} 
y*z/(6*m)

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

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