Mister Exam

Other calculators

x/sqrt(16-x^4)
Solving integrals/ x/sqrt(16-x^4)

Integral of x/sqrt(16-x^4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                
  /                
 |                 
 |       x         
 |  ------------ dx
 |     _________   
 |    /       4    
 |  \/  16 - x     
 |                 
/                  
0
$$\int\limits_{0}^{2} \frac{x}{\sqrt{16 - x^{4}}}\, dx$$ 
Integral(x/sqrt(16 - x^4), (x, 0, 2))
The answer (Indefinite) [src] 
                         //        / 2\               \
                         ||        |x |               |
                         ||-I*acosh|--|       | 4|    |
  /                      ||        \4 /       |x |    |
 |                       ||-------------  for ---- > 1|
 |      x                ||      2             16     |
 | ------------ dx = C + |<                           |
 |    _________          ||      / 2\                 |
 |   /       4           ||      |x |                 |
 | \/  16 - x            ||  asin|--|                 |
 |                       ||      \4 /                 |
/                        ||  --------      otherwise  |
                         \\     2                     /
$$\int \frac{x}{\sqrt{16 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{16} > 1 \\\frac{\operatorname{asin}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  2                                 
  /                                 
 |                                  
 |  /                       4       
 |  |     -I*x             x        
 |  |----------------  for -- > 1   
 |  |       _________      16       
 |  |      /       4                
 |  |     /       x                 
 |  |4*  /   -1 + --                
 |  |  \/         16                
 |  <                             dx
 |  |       x                       
 |  |---------------   otherwise    
 |  |       ________                
 |  |      /      4                 
 |  |     /      x                  
 |  |4*  /   1 - --                 
 |  |  \/        16                 
 |  \                               
 |                                  
/                                   
0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$ 
=
= 
  2                                 
  /                                 
 |                                  
 |  /                       4       
 |  |     -I*x             x        
 |  |----------------  for -- > 1   
 |  |       _________      16       
 |  |      /       4                
 |  |     /       x                 
 |  |4*  /   -1 + --                
 |  |  \/         16                
 |  <                             dx
 |  |       x                       
 |  |---------------   otherwise    
 |  |       ________                
 |  |      /      4                 
 |  |     /      x                  
 |  |4*  /   1 - --                 
 |  |  \/        16                 
 |  \                               
 |                                  
/                                   
0
$$\int\limits_{0}^{2} \begin{cases} - \frac{i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$ 
Integral(Piecewise((-i*x/(4*sqrt(-1 + x^4/16)), x^4/16 > 1), (x/(4*sqrt(1 - x^4/16)), True)), (x, 0, 2))
Numerical answer [src] 
0.785398163062549
0.785398163062549
The graph
Integral of x/sqrt(16-x^4) dx

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

    © Mister Exam – Calculator