Mister Exam

Other calculators

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |       ________   
 |      /     1     
 |     /  2 - --    
 |    /        2    
 |  \/        x     
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \frac{1}{\sqrt{2 - \frac{1}{x^{2}}}}\, dx$$
Integral(1/(sqrt(2 - 1/x^2)), (x, 0, 1))
The answer (Indefinite) [src]
                          //   ___________                 \
                          ||  /         2                  |
  /                       ||\/  -1 + 2*x           | 2|    |
 |                        ||--------------   for 2*|x | > 1|
 |       1                ||      2                        |
 | ------------- dx = C + |<                               |
 |      ________          ||     __________                |
 |     /     1            ||    /        2                 |
 |    /  2 - --           ||I*\/  1 - 2*x                  |
 |   /        2           ||---------------    otherwise   |
 | \/        x            \\       2                       /
 |                                                          
/                                                           
$$\int \frac{1}{\sqrt{2 - \frac{1}{x^{2}}}}\, dx = C + \begin{cases} \frac{\sqrt{2 x^{2} - 1}}{2} & \text{for}\: 2 \left|{x^{2}}\right| > 1 \\\frac{i \sqrt{1 - 2 x^{2}}}{2} & \text{otherwise} \end{cases}$$
The graph
The answer [src]
  1                                 
  /                                 
 |                                  
 |  /      x                2       
 |  |--------------  for 2*x  > 1   
 |  |   ___________                 
 |  |  /         2                  
 |  |\/  -1 + 2*x                   
 |  <                             dx
 |  |    -I*x                       
 |  |-------------    otherwise     
 |  |   __________                  
 |  |  /        2                   
 |  \\/  1 - 2*x                    
 |                                  
/                                   
0                                   
$$\int\limits_{0}^{1} \begin{cases} \frac{x}{\sqrt{2 x^{2} - 1}} & \text{for}\: 2 x^{2} > 1 \\- \frac{i x}{\sqrt{1 - 2 x^{2}}} & \text{otherwise} \end{cases}\, dx$$
=
=
  1                                 
  /                                 
 |                                  
 |  /      x                2       
 |  |--------------  for 2*x  > 1   
 |  |   ___________                 
 |  |  /         2                  
 |  |\/  -1 + 2*x                   
 |  <                             dx
 |  |    -I*x                       
 |  |-------------    otherwise     
 |  |   __________                  
 |  |  /        2                   
 |  \\/  1 - 2*x                    
 |                                  
/                                   
0                                   
$$\int\limits_{0}^{1} \begin{cases} \frac{x}{\sqrt{2 x^{2} - 1}} & \text{for}\: 2 x^{2} > 1 \\- \frac{i x}{\sqrt{1 - 2 x^{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((x/sqrt(-1 + 2*x^2), 2*x^2 > 1), (-i*x/sqrt(1 - 2*x^2), True)), (x, 0, 1))
Numerical answer [src]
(0.505674648770025 - 0.454284972789841j)
(0.505674648770025 - 0.454284972789841j)

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