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Resolución de integrales/ ln(x)/ 1/(x*ln(x)/x*ln(ln(x))/x)

Integral de 1/(x*ln(x)/x*ln(ln(x))/x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                          
  /                          
 |                           
 |            1              
 |  ---------------------- dx
 |  /x*log(x)            \   
 |  |--------*log(log(x))|   
 |  |   x                |   
 |  |--------------------|   
 |  \         x          /   
 |                           
/                            
0
$$\int\limits_{0}^{1} \frac{1}{\frac{1}{x} \frac{x \log{\left(x \right)}}{x} \log{\left(\log{\left(x \right)} \right)}}\, dx$$ 
Integral(1/((((x*log(x))/x)*log(log(x)))/x), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                  /                     
 |                                  |                      
 |           1                      |         x            
 | ---------------------- dx = C +  | ------------------ dx
 | /x*log(x)            \           | log(x)*log(log(x))   
 | |--------*log(log(x))|           |                      
 | |   x                |          /                       
 | |--------------------|                                  
 | \         x          /                                  
 |                                                         
/
$$\int \frac{1}{\frac{1}{x} \frac{x \log{\left(x \right)}}{x} \log{\left(\log{\left(x \right)} \right)}}\, dx = C + \int \frac{x}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}\, dx$$
Simplificar
Respuesta [src] 
  1                      
  /                      
 |                       
 |          x            
 |  ------------------ dx
 |  log(x)*log(log(x))   
 |                       
/                        
0
$$\int\limits_{0}^{1} \frac{x}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}\, dx$$ 
=
= 
  1                      
  /                      
 |                       
 |          x            
 |  ------------------ dx
 |  log(x)*log(log(x))   
 |                       
/                        
0
$$\int\limits_{0}^{1} \frac{x}{\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)}}\, dx$$ 
Integral(x/(log(x)*log(log(x))), (x, 0, 1))
Respuesta numérica [src] 
(2.52951549208342 + 1.15872870294113j)
(2.52951549208342 + 1.15872870294113j)

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

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