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

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

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       x        
 |  ----------- dx
 |     ________   
 |    /      4    
 |  \/  4 - x     
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{4 - x^{4}}}\, dx$$ 
Integral(x/sqrt(4 - x^4), (x, 0, 1))
The answer (Indefinite) [src] 
                        //        / 2\               \
                        ||        |x |               |
                        ||-I*acosh|--|       | 4|    |
  /                     ||        \2 /       |x |    |
 |                      ||-------------  for ---- > 1|
 |      x               ||      2             4      |
 | ----------- dx = C + |<                           |
 |    ________          ||      / 2\                 |
 |   /      4           ||      |x |                 |
 | \/  4 - x            ||  asin|--|                 |
 |                      ||      \2 /                 |
/                       ||  --------      otherwise  |
                        \\     2                     /
$$\int \frac{x}{\sqrt{4 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{2}}{2} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{4} > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{2}}{2} \right)}}{2} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                                 
  /                                 
 |                                  
 |  /                       4       
 |  |     -I*x             x        
 |  |----------------  for -- > 1   
 |  |       _________      4        
 |  |      /       4                
 |  |     /       x                 
 |  |2*  /   -1 + --                
 |  |  \/         4                 
 |  <                             dx
 |  |       x                       
 |  |---------------   otherwise    
 |  |       ________                
 |  |      /      4                 
 |  |     /      x                  
 |  |2*  /   1 - --                 
 |  |  \/        4                  
 |  \                               
 |                                  
/                                   
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{2 \sqrt{\frac{x^{4}}{4} - 1}} & \text{for}\: \frac{x^{4}}{4} > 1 \\\frac{x}{2 \sqrt{1 - \frac{x^{4}}{4}}} & \text{otherwise} \end{cases}\, dx$$ 
=
= 
  1                                 
  /                                 
 |                                  
 |  /                       4       
 |  |     -I*x             x        
 |  |----------------  for -- > 1   
 |  |       _________      4        
 |  |      /       4                
 |  |     /       x                 
 |  |2*  /   -1 + --                
 |  |  \/         4                 
 |  <                             dx
 |  |       x                       
 |  |---------------   otherwise    
 |  |       ________                
 |  |      /      4                 
 |  |     /      x                  
 |  |2*  /   1 - --                 
 |  |  \/        4                  
 |  \                               
 |                                  
/                                   
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{2 \sqrt{\frac{x^{4}}{4} - 1}} & \text{for}\: \frac{x^{4}}{4} > 1 \\\frac{x}{2 \sqrt{1 - \frac{x^{4}}{4}}} & \text{otherwise} \end{cases}\, dx$$ 
Integral(Piecewise((-i*x/(2*sqrt(-1 + x^4/4)), x^4/4 > 1), (x/(2*sqrt(1 - x^4/4)), True)), (x, 0, 1))
Numerical answer [src] 
0.261799387799149
0.261799387799149
The graph
Integral of x/sqrt(4-x^4) dx

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

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