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1/(-1+y^2)
Solving integrals/ 1/(-1+y^2)

Integral of 1/(-1+y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
 |                  //                2    \
 |    1             ||-acoth(y)  for y  > 1|
 | ------- dy = C + |<                     |
 |       2          ||                2    |
 | -1 + y           \\-atanh(y)  for y  < 1/
 |                                          
/
$$\int \frac{1}{y^{2} - 1}\, dy = C + \begin{cases} - \operatorname{acoth}{\left(y \right)} & \text{for}\: y^{2} > 1 \\- \operatorname{atanh}{\left(y \right)} & \text{for}\: y^{2} < 1 \end{cases}$$
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
The graph
Integral of 1/(-1+y^2) dy

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

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