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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1/2                     
 e                        
   /                      
  |                       
  |       _____________   
  |      /        2       
  |  x*\/  1 - log (x)  dx
  |                       
 /                        
 1
∫1e12x1−log⁡(x)2 dx\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{1 - \log{\left(x \right)}^{2}}\, dx 
Integral(x*sqrt(1 - log(x)^2), (x, 1, exp(1/2)))
Respuesta (Indefinida) [src] 
  /                                                                   
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 |      _____________           |                                     
 |     /        2               |     _____________________________   
 | x*\/  1 - log (x)  dx = C +  | x*\/ -(1 + log(x))*(-1 + log(x))  dx
 |                              |                                     
/                              /
∫x1−log⁡(x)2 dx=C+∫x−(log⁡(x)−1)(log⁡(x)+1) dx\int x \sqrt{1 - \log{\left(x \right)}^{2}}\, dx = C + \int x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx
Simplificar
Respuesta [src] 
  1/2                                    
 e                                       
   /                                     
  |                                      
  |      _____________________________   
  |  x*\/ -(1 + log(x))*(-1 + log(x))  dx
  |                                      
 /                                       
 1
∫1e12x−(log⁡(x)−1)(log⁡(x)+1) dx\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx 
=
= 
  1/2                                    
 e                                       
   /                                     
  |                                      
  |      _____________________________   
  |  x*\/ -(1 + log(x))*(-1 + log(x))  dx
  |                                      
 /                                       
 1
∫1e12x−(log⁡(x)−1)(log⁡(x)+1) dx\int\limits_{1}^{e^{\frac{1}{2}}} x \sqrt{- \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}\, dx 
Integral(x*sqrt(-(1 + log(x))*(-1 + log(x))), (x, 1, exp(1/2)))
Respuesta numérica [src] 
0.812240834235589
0.812240834235589

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

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