Mister Exam

Other calculators

1÷(x^2-1)
Solving integrals/ 1÷(x^2-1)

Integral of 1÷(x^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |   2       
 |  x  - 1   
 |           
/            
0
∫011x2−1 dx\int\limits_{0}^{1} \frac{1}{x^{2} - 1}\, dx 
Integral(1/(x^2 - 1), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

    {−acoth⁡(x)for x2>1−atanh⁡(x)for x2<1+constant\begin{cases} - \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\- \operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases}+ \mathrm{constant}

The answer is:

{−acoth⁡(x)for x2>1−atanh⁡(x)for x2<1+constant\begin{cases} - \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\- \operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                        
 |                 //                2    \
 |   1             ||-acoth(x)  for x  > 1|
 | ------ dx = C + |<                     |
 |  2              ||                2    |
 | x  - 1          \\-atanh(x)  for x  < 1/
 |                                         
/
∫1x2−1 dx=C+{−acoth⁡(x)for x2>1−atanh⁡(x)for x2<1\int \frac{1}{x^{2} - 1}\, dx = C + \begin{cases} - \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\- \operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-50005000
Plot the graph f(x)
The answer [src] 
      pi*I
-oo - ----
       2
−∞−iπ2-\infty - \frac{i \pi}{2} 
=
= 
      pi*I
-oo - ----
       2
−∞−iπ2-\infty - \frac{i \pi}{2} 
-oo - pi*i/2
Numerical answer [src] 
-22.3920519833869
-22.3920519833869
The graph
Integral of 1÷(x^2-1) dx

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

    © Mister Exam – Calculator