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xdx/(sqrt(1-x^4))
Solving integrals/ xdx/(sqrt(1-x^4))

Integral of xdx/(sqrt(1-x^4)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       x        
 |  ----------- dx
 |     ________   
 |    /      4    
 |  \/  1 - x     
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{1 - x^{4}}}\, dx$$ 
Integral(x/sqrt(1 - x^4), (x, 0, 1))
The answer (Indefinite) [src] 
                        //        / 2\               \
  /                     ||-I*acosh\x /       | 4|    |
 |                      ||-------------  for |x | > 1|
 |      x               ||      2                    |
 | ----------- dx = C + |<                           |
 |    ________          ||      / 2\                 |
 |   /      4           ||  asin\x /                 |
 | \/  1 - x            ||  --------      otherwise  |
 |                      \\     2                     /
/
$$\int \frac{x}{\sqrt{1 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(x^{2} \right)}}{2} & \text{for}\: \left|{x^{4}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{2} \right)}}{2} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                             
  /                             
 |                              
 |  /   -I*x            4       
 |  |------------  for x  > 1   
 |  |   _________               
 |  |  /       4                
 |  |\/  -1 + x                 
 |  <                         dx
 |  |     x                     
 |  |-----------   otherwise    
 |  |   ________                
 |  |  /      4                 
 |  \\/  1 - x                  
 |                              
/                               
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{4} - 1}} & \text{for}\: x^{4} > 1 \\\frac{x}{\sqrt{1 - x^{4}}} & \text{otherwise} \end{cases}\, dx$$ 
=
= 
  1                             
  /                             
 |                              
 |  /   -I*x            4       
 |  |------------  for x  > 1   
 |  |   _________               
 |  |  /       4                
 |  |\/  -1 + x                 
 |  <                         dx
 |  |     x                     
 |  |-----------   otherwise    
 |  |   ________                
 |  |  /      4                 
 |  \\/  1 - x                  
 |                              
/                               
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{x^{4} - 1}} & \text{for}\: x^{4} > 1 \\\frac{x}{\sqrt{1 - x^{4}}} & \text{otherwise} \end{cases}\, dx$$ 
Integral(Piecewise((-i*x/sqrt(-1 + x^4), x^4 > 1), (x/sqrt(1 - x^4), True)), (x, 0, 1))
Numerical answer [src] 
0.785398163062549
0.785398163062549
The graph
Integral of xdx/(sqrt(1-x^4)) dx

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

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