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Resolución de integrales/ dx/(x*(1-4ln(x)*ln(x))^(1/2))

Integral de dx/(x*(1-4ln(x)*ln(x))^(1/2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                             
  /                             
 |                              
 |              1               
 |  ------------------------- dx
 |      _____________________   
 |  x*\/ 1 - 4*log(x)*log(x)    
 |                              
/                               
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \log{\left(x \right)} 4 \log{\left(x \right)} + 1}}\, dx$$ 
Integral(1/(x*sqrt(1 - 4*log(x)*log(x))), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                     /                                        
 |                                     |                                         
 |             1                       |                   1                     
 | ------------------------- dx = C +  | ------------------------------------- dx
 |     _____________________           |     _________________________________   
 | x*\/ 1 - 4*log(x)*log(x)            | x*\/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 |                                     |                                         
/                                     /
$$\int \frac{1}{x \sqrt{- \log{\left(x \right)} 4 \log{\left(x \right)} + 1}}\, dx = C + \int \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}\, dx$$
Simplificar
Respuesta [src] 
  1                                         
  /                                         
 |                                          
 |                    1                     
 |  ------------------------------------- dx
 |      _________________________________   
 |  x*\/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 |                                          
/                                           
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}\, dx$$ 
=
= 
  1                                         
  /                                         
 |                                          
 |                    1                     
 |  ------------------------------------- dx
 |      _________________________________   
 |  x*\/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 |                                          
/                                           
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}\, dx$$ 
Integral(1/(x*sqrt(-(1 + 2*log(x))*(-1 + 2*log(x)))), (x, 0, 1))
Respuesta numérica [src] 
(0.817188089183674 - 2.50540983536595j)
(0.817188089183674 - 2.50540983536595j)

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

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