Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of x^e Integral of x^e
  • Integral of √(x+4) Integral of √(x+4)
  • Integral of sin(2x)cos(2x) Integral of sin(2x)cos(2x)
  • Integral of cos2 Integral of cos2

  • Identical expressions

  • one /(sqrt(one /(x^ two)- one))
  • 1 divide by ( square root of (1 divide by (x squared ) minus 1))
  • one divide by ( square root of (one divide by (x to the power of two) minus one))
  • 1/(√(1/(x^2)-1))
  • 1/(sqrt(1/(x2)-1))
  • 1/sqrt1/x2-1
  • 1/(sqrt(1/(x²)-1))
  • 1/(sqrt(1/(x to the power of 2)-1))
  • 1/sqrt1/x^2-1
  • 1 divide by (sqrt(1 divide by (x^2)-1))
  • 1/(sqrt(1/(x^2)-1))dx

  • Similar expressions

  • 1/(sqrt(1/(x^2)+1))
Solving integrals/ 1/(sqrt(1/(x^2)-1))

Integral of 1/(sqrt(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
 |       ________   
 |      / 1         
 |     /  -- - 1    
 |    /    2        
 |  \/    x         
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{-1 + \frac{1}{x^{2}}}}\, dx$$ 
Integral(1/(sqrt(1/(x^2) - 1)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                       //      _________              \
 |                        ||     /       2       | 2|    |
 |       1                ||-I*\/  -1 + x    for |x | > 1|
 | ------------- dx = C + |<                             |
 |      ________          ||     ________                |
 |     / 1                ||    /      2                 |
 |    /  -- - 1           \\ -\/  1 - x       otherwise  /
 |   /    2                                               
 | \/    x                                                
 |                                                        
/
$$\int \frac{1}{\sqrt{-1 + \frac{1}{x^{2}}}}\, dx = C + \begin{cases} - i \sqrt{x^{2} - 1} & \text{for}\: \left|{x^{2}}\right| > 1 \\- \sqrt{1 - x^{2}} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                             
  /                             
 |                              
 |  /   -I*x            2       
 |  |------------  for x  > 1   
 |  |   _________               
 |  |  /       2                
 |  |\/  -1 + x                 
 |  <                         dx
 |  |     x                     
 |  |-----------   otherwise    
 |  |   ________                
 |  |  /      2                 
 |  \\/  1 - x                  
 |                              
/                               
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{x}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$ 
=
= 
  1                             
  /                             
 |                              
 |  /   -I*x            2       
 |  |------------  for x  > 1   
 |  |   _________               
 |  |  /       2                
 |  |\/  -1 + x                 
 |  <                         dx
 |  |     x                     
 |  |-----------   otherwise    
 |  |   ________                
 |  |  /      2                 
 |  \\/  1 - x                  
 |                              
/                               
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{2} - 1}} & \text{for}\: x^{2} > 1 \\\frac{x}{\sqrt{1 - x^{2}}} & \text{otherwise} \end{cases}\, dx$$ 
Integral(Piecewise((-i*x/sqrt(-1 + x^2), x^2 > 1), (x/sqrt(1 - x^2), True)), (x, 0, 1))
Numerical answer [src] 
0.999999999624892
0.999999999624892

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

    © Mister Exam – Calculator