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Solving integrals/ x/sqrt(x^2-4x-1)

Integral of x/sqrt(x^2-4x-1) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |          x           
 |  ----------------- dx
 |     ______________   
 |    /  2              
 |  \/  x  - 4*x - 1    
 |                      
/                       
0
∫01x(x2−4x)−1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{\left(x^{2} - 4 x\right) - 1}}\, dx 
Integral(x/sqrt(x^2 - 4*x - 1), (x, 0, 1))
The answer (Indefinite) [src] 
  /                             /                     
 |                             |                      
 |         x                   |         x            
 | ----------------- dx = C +  | ------------------ dx
 |    ______________           |    _______________   
 |   /  2                      |   /       2          
 | \/  x  - 4*x - 1            | \/  -1 + x  - 4*x    
 |                             |                      
/                             /
∫x(x2−4x)−1 dx=C+∫xx2−4x−1 dx\int \frac{x}{\sqrt{\left(x^{2} - 4 x\right) - 1}}\, dx = C + \int \frac{x}{\sqrt{x^{2} - 4 x - 1}}\, dx
Simplify
The answer [src] 
  1                      
  /                      
 |                       
 |          x            
 |  ------------------ dx
 |     _______________   
 |    /       2          
 |  \/  -1 + x  - 4*x    
 |                       
/                        
0
∫01xx2−4x−1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{x^{2} - 4 x - 1}}\, dx 
=
= 
  1                      
  /                      
 |                       
 |          x            
 |  ------------------ dx
 |     _______________   
 |    /       2          
 |  \/  -1 + x  - 4*x    
 |                       
/                        
0
∫01xx2−4x−1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{x^{2} - 4 x - 1}}\, dx 
Integral(x/sqrt(-1 + x^2 - 4*x), (x, 0, 1))
Numerical answer [src] 
(0.0 - 0.287002217586569j)
(0.0 - 0.287002217586569j)

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

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