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Solving integrals/ 1/(sqrt(abs(x^2-1)))

Integral of 1/(sqrt(abs(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
∫011∣x2−1∣ dx\int\limits_{0}^{1} \frac{1}{\sqrt{\left|{x^{2} - 1}\right|}}\, dx 
Integral(1/(sqrt(|x^2 - 1|)), (x, 0, 1))
The answer (Indefinite) [src] 
                          //                 ___                                  \
                          ||            pi*\/ 2 *asin(x)                  | 2|    |
  /                       ||         ---------------------            for |x | < 1|
 |                        ||         Gamma(1/4)*Gamma(3/4)                        |
 |       1                ||                                                      |
 | ------------- dx = C + |<  ___   ____  __1, 2 /1, 1   3/4   |  2\              |
 |    __________          ||\/ 2 *\/ pi */__     |             | x |              |
 |   / | 2    |           ||             \_|3, 3 \1/2   3/4, 0 |   /              |
 | \/  |x  - 1|           ||----------------------------------------   otherwise  |
 |                        ||                   2                                  |
/                         \\                                                      /
∫1∣x2−1∣ dx=C+{2πasin⁡(x)Γ(14)Γ(34)for ∣x2∣<12πG3,31,2(1,1341234,0|x2)2otherwise\int \frac{1}{\sqrt{\left|{x^{2} - 1}\right|}}\, dx = C + \begin{cases} \frac{\sqrt{2} \pi \operatorname{asin}{\left(x \right)}}{\Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right)} & \text{for}\: \left|{x^{2}}\right| < 1 \\\frac{\sqrt{2} \sqrt{\pi} {G_{3, 3}^{1, 2}\left(\begin{matrix} 1, 1 & \frac{3}{4} \\\frac{1}{2} & \frac{3}{4}, 0 \end{matrix} \middle| {x^{2}} \right)}}{2} & \text{otherwise} \end{cases}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900100
Plot the graph f(x)
The answer [src] 
  1                                   
  /                                   
 |                                    
 |  /     1                  2        
 |  |------------  for -1 + x  >= 0   
 |  |   _________                     
 |  |  /       2                      
 |  |\/  -1 + x                       
 |  <                               dx
 |  |     1                           
 |  |-----------      otherwise       
 |  |   ________                      
 |  |  /      2                       
 |  \\/  1 - x                        
 |                                    
/                                     
0
∫01{1x2−1for x2−1≥011−x2otherwise dx\int\limits_{0}^{1} \begin{cases} \frac{1}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} - 1 \geq 0 \\\frac{1}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx 
=
= 
  1                                   
  /                                   
 |                                    
 |  /     1                  2        
 |  |------------  for -1 + x  >= 0   
 |  |   _________                     
 |  |  /       2                      
 |  |\/  -1 + x                       
 |  <                               dx
 |  |     1                           
 |  |-----------      otherwise       
 |  |   ________                      
 |  |  /      2                       
 |  \\/  1 - x                        
 |                                    
/                                     
0
∫01{1x2−1for x2−1≥011−x2otherwise dx\int\limits_{0}^{1} \begin{cases} \frac{1}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} - 1 \geq 0 \\\frac{1}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((1/sqrt(-1 + x^2), -1 + x^2 >= 0), (1/sqrt(1 - x^2), True)), (x, 0, 1))
Numerical answer [src] 
1.57079632641979
1.57079632641979

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

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