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Resolución de integrales/ x*sqrt/ log(x)/ 1/(x*sqrt(1-(log(x))^2))

Integral de 1/(x*sqrt(1-(log(x))^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                      
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |       _____________   
 |      /        2       
 |  x*\/  1 - log (x)    
 |                       
/                        
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{1 - \log{\left(x \right)}^{2}}}\, dx$$ 
Integral(1/(x*sqrt(1 - log(x)^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                              /                                    
 |                              |                                     
 |         1                    |                 1                   
 | ------------------ dx = C +  | --------------------------------- dx
 |      _____________           |     _____________________________   
 |     /        2               | x*\/ -(1 + log(x))*(-1 + log(x))    
 | x*\/  1 - log (x)            |                                     
 |                             /                                      
/
$$\int \frac{1}{x \sqrt{1 - \log{\left(x \right)}^{2}}}\, dx = C + \int \frac{1}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}\, dx$$
Simplificar
Respuesta [src] 
  1                                     
  /                                     
 |                                      
 |                  1                   
 |  --------------------------------- dx
 |      _____________________________   
 |  x*\/ -(1 + log(x))*(-1 + log(x))    
 |                                      
/                                       
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}\, dx$$ 
=
= 
  1                                     
  /                                     
 |                                      
 |                  1                   
 |  --------------------------------- dx
 |      _____________________________   
 |  x*\/ -(1 + log(x))*(-1 + log(x))    
 |                                      
/                                       
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}}\, dx$$ 
Integral(1/(x*sqrt(-(1 + log(x))*(-1 + log(x)))), (x, 0, 1))
Respuesta numérica [src] 
(1.39206658078322 - 5.06878125385943j)
(1.39206658078322 - 5.06878125385943j)

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

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