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Solving integrals/ dz/(z^2-1)

Integral of dz/(z^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=-1, context=1/(z**2 - 1), symbol=z), False), (ArccothRule(a=1, b=1, c=-1, context=1/(z**2 - 1), symbol=z), z**2 > 1), (ArctanhRule(a=1, b=1, c=-1, context=1/(z**2 - 1), symbol=z), z**2 < 1)], context=1/(z**2 - 1), symbol=z)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                        
 |                 //                2    \
 |   1             ||-acoth(z)  for z  > 1|
 | ------ dz = C + |<                     |
 |  2              ||                2    |
 | z  - 1          \\-atanh(z)  for z  < 1/
 |                                         
/
$$\int \frac{1}{z^{2} - 1}\, dz = C + \begin{cases} - \operatorname{acoth}{\left(z \right)} & \text{for}\: z^{2} > 1 \\- \operatorname{atanh}{\left(z \right)} & \text{for}\: z^{2} < 1 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
      pi*I
-oo - ----
       2
$$-\infty - \frac{i \pi}{2}$$ 
=
= 
      pi*I
-oo - ----
       2
$$-\infty - \frac{i \pi}{2}$$ 
-oo - pi*i/2
Numerical answer [src] 
-22.3920519833869
-22.3920519833869

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

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