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

Integral of dx/(1-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Add the constant of integration:

The answer is:

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

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

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