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Resolución de integrales/ ln(x)/ (x)^4/ x*sqrt/ lnx/(x*sqrt(1-(ln(x)^4)))

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0                      
  /                      
 |                       
 |        log(x)         
 |  ------------------ dx
 |       _____________   
 |      /        4       
 |  x*\/  1 - log (x)    
 |                       
/                        
4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{1 - \log{\left(x \right)}^{4}}}\, dx$$ 
Integral(log(x)/((x*sqrt(1 - log(x)^4))), (x, 4, 0))
Respuesta (Indefinida) [src] 
  /                              /                                                   
 |                              |                                                    
 |       log(x)                 |                      log(x)                        
 | ------------------ dx = C +  | ------------------------------------------------ dx
 |      _____________           |      ___________________________________________   
 |     /        4               |     /  /       2   \                               
 | x*\/  1 - log (x)            | x*\/  -\1 + log (x)/*(1 + log(x))*(-1 + log(x))    
 |                              |                                                    
/                              /
$$\int \frac{\log{\left(x \right)}}{x \sqrt{1 - \log{\left(x \right)}^{4}}}\, dx = C + \int \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right) \left(\log{\left(x \right)}^{2} + 1\right)}}\, dx$$
Simplificar
Respuesta [src] 
  0                                                      
  /                                                      
 |                                                       
 |                        log(x)                         
 |  -------------------------------------------------- dx
 |                                       _____________   
 |      _____________________________   /        2       
 |  x*\/ -(1 + log(x))*(-1 + log(x)) *\/  1 + log (x)    
 |                                                       
/                                                        
4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$ 
=
= 
  0                                                      
  /                                                      
 |                                                       
 |                        log(x)                         
 |  -------------------------------------------------- dx
 |                                       _____________   
 |      _____________________________   /        2       
 |  x*\/ -(1 + log(x))*(-1 + log(x)) *\/  1 + log (x)    
 |                                                       
/                                                        
4
$$\int\limits_{4}^{0} \frac{\log{\left(x \right)}}{x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)} \sqrt{\log{\left(x \right)}^{2} + 1}}\, dx$$ 
Integral(log(x)/(x*sqrt(-(1 + log(x))*(-1 + log(x)))*sqrt(1 + log(x)^2)), (x, 4, 0))
Respuesta numérica [src] 
(-0.0323884442358661 - 3.41887875976503j)
(-0.0323884442358661 - 3.41887875976503j)

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

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