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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |     ____________   
 |    /          2    
 |  \/  1 + x - x     
 |                    
/                     
0
∫01x−x2+(x+1) dx\int\limits_{0}^{1} \frac{x}{\sqrt{- x^{2} + \left(x + 1\right)}}\, dx 
Integral(x/sqrt(1 + x - x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                           /                  
 |                           |                   
 |        x                  |        x          
 | --------------- dx = C +  | --------------- dx
 |    ____________           |    ____________   
 |   /          2            |   /          2    
 | \/  1 + x - x             | \/  1 + x - x     
 |                           |                   
/                           /
∫x−x2+(x+1) dx=C+∫x−x2+x+1 dx\int \frac{x}{\sqrt{- x^{2} + \left(x + 1\right)}}\, dx = C + \int \frac{x}{\sqrt{- x^{2} + x + 1}}\, dx
Simplify
The answer [src] 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |     ____________   
 |    /          2    
 |  \/  1 + x - x     
 |                    
/                     
0
∫01x−x2+x+1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{- x^{2} + x + 1}}\, dx 
=
= 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |     ____________   
 |    /          2    
 |  \/  1 + x - x     
 |                    
/                     
0
∫01x−x2+x+1 dx\int\limits_{0}^{1} \frac{x}{\sqrt{- x^{2} + x + 1}}\, dx 
Integral(x/sqrt(1 + x - x^2), (x, 0, 1))
Numerical answer [src] 
0.463647609000806
0.463647609000806

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

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