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  • Identical expressions

  • z- one /(x*y*z^ two)
  • z minus 1 divide by (x multiply by y multiply by z squared )
  • z minus one divide by (x multiply by y multiply by z to the power of two)
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  • z-1/(xyz^2)
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  • z-1/(x*y*z^2)dx

  • Similar expressions

  • z+1/(x*y*z^2)
Solving integrals/ z-1/(x*y*z^2)

Integral of z-1/(x*y*z^2) dz

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  z                
  /                
 |                 
 |  /      1   \   
 |  |z - ------| dz
 |  |         2|   
 |  \    x*y*z /   
 |                 
/                  
0
$$\int\limits_{0}^{z} \left(z - \frac{1}{z^{2} x y}\right)\, dz$$ 
Integral(z - 1/((x*y)*z^2), (z, 0, z))
Detail solution

  1. Integrate term-by-term:

    1. The integral of is when :

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

      1. The integral of is .

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                          
 |                        2                  
 | /      1   \          z    zoo*atan(zoo*z)
 | |z - ------| dz = C + -- + ---------------
 | |         2|          2          x*y      
 | \    x*y*z /                              
 |                                           
/
$$\int \left(z - \frac{1}{z^{2} x y}\right)\, dz = C + \frac{z^{2}}{2} + \frac{\tilde{\infty} \operatorname{atan}{\left(\tilde{\infty} z \right)}}{x y}$$
Simplify
The answer [src] 
                          2
                 1   x*y*z 
                 - + ------
         / 1 \   z     2   
- oo*sign|---| + ----------
         \x*y/      x*y
$$- \infty \operatorname{sign}{\left(\frac{1}{x y} \right)} + \frac{\frac{x y z^{2}}{2} + \frac{1}{z}}{x y}$$ 
=
= 
                          2
                 1   x*y*z 
                 - + ------
         / 1 \   z     2   
- oo*sign|---| + ----------
         \x*y/      x*y
$$- \infty \operatorname{sign}{\left(\frac{1}{x y} \right)} + \frac{\frac{x y z^{2}}{2} + \frac{1}{z}}{x y}$$ 
-oo*sign(1/(x*y)) + (1/z + x*y*z^2/2)/(x*y)

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

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