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Resolución de integrales/ 1/x*(√(1-Log(x)*Log(x)))

Integral de 1/x*(√(1-Log(x)*Log(x))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |    ___________________   
 |  \/ 1 - log(x)*log(x)    
 |  --------------------- dx
 |            x             
 |                          
/                           
0
$$\int\limits_{0}^{1} \frac{\sqrt{- \log{\left(x \right)} \log{\left(x \right)} + 1}}{x}\, dx$$ 
Integral(sqrt(1 - log(x)*log(x))/x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                 /                                  
 |                                 |                                   
 |   ___________________           |   _____________________________   
 | \/ 1 - log(x)*log(x)            | \/ -(1 + log(x))*(-1 + log(x))    
 | --------------------- dx = C +  | ------------------------------- dx
 |           x                     |                x                  
 |                                 |                                   
/                                 /
$$\int \frac{\sqrt{- \log{\left(x \right)} \log{\left(x \right)} + 1}}{x}\, dx = C + \int \frac{\sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}{x}\, dx$$
Simplificar
Respuesta [src] 
  1                                   
  /                                   
 |                                    
 |    _____________________________   
 |  \/ -(1 + log(x))*(-1 + log(x))    
 |  ------------------------------- dx
 |                 x                  
 |                                    
/                                     
0
$$\int\limits_{0}^{1} \frac{\sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}{x}\, dx$$ 
=
= 
  1                                   
  /                                   
 |                                    
 |    _____________________________   
 |  \/ -(1 + log(x))*(-1 + log(x))    
 |  ------------------------------- dx
 |                 x                  
 |                                    
/                                     
0
$$\int\limits_{0}^{1} \frac{\sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}{x}\, dx$$ 
Integral(sqrt(-(1 + log(x))*(-1 + log(x)))/x, (x, 0, 1))
Respuesta numérica [src] 
(0.783909061216611 + 969.473668425502j)
(0.783909061216611 + 969.473668425502j)

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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