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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)^(1/x)*(1/(x^2*log(x))-log(log(x))/x^2)

¿Cómo vas a descomponer esta log(x)^(1/x)*(1/(x^2*log(x))-log(log(x))/x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
x ________ /    1       log(log(x))\
\/ log(x) *|--------- - -----------|
           | 2                2    |
           \x *log(x)        x     /
(1x2log⁡(x)−log⁡(log⁡(x))x2)log⁡(x)1x\left(\frac{1}{x^{2} \log{\left(x \right)}} - \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)}^{\frac{1}{x}} 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
Simplificación general [src] 
        1 - x                         
        -----                         
          x                           
(log(x))     *(1 - log(x)*log(log(x)))
--------------------------------------
                   2                  
                  x
(−log⁡(x)log⁡(log⁡(x))+1)log⁡(x)1−xxx2\frac{\left(- \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\frac{1 - x}{x}}}{x^{2}} 
log(x)^((1 - x)/x)*(1 - log(x)*log(log(x)))/x^2
Respuesta numérica [src] 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
Unión de expresiones racionales [src] 
x ________                         
\/ log(x) *(1 - log(x)*log(log(x)))
-----------------------------------
              2                    
             x *log(x)
(−log⁡(x)log⁡(log⁡(x))+1)log⁡(x)1xx2log⁡(x)\frac{\left(- \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}} 
log(x)^(1/x)*(1 - log(x)*log(log(x)))/(x^2*log(x))
Potencias [src] 
x ________ /    1       log(log(x))\
\/ log(x) *|--------- - -----------|
           | 2                2    |
           \x *log(x)        x     /
(−log⁡(log⁡(x))x2+1x2log⁡(x))log⁡(x)1x\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}} 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
Combinatoria [src] 
 x ________                           
-\/ log(x) *(-1 + log(x)*log(log(x))) 
--------------------------------------
               2                      
              x *log(x)
−(log⁡(x)log⁡(log⁡(x))−1)log⁡(x)1xx2log⁡(x)- \frac{\left(\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} - 1\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}} 
-log(x)^(1/x)*(-1 + log(x)*log(log(x)))/(x^2*log(x))
Denominador común [src] 
 /  x ________   x ________                   \ 
-\- \/ log(x)  + \/ log(x) *log(x)*log(log(x))/ 
------------------------------------------------
                    2                           
                   x *log(x)
−log⁡(x)log⁡(x)1xlog⁡(log⁡(x))−log⁡(x)1xx2log⁡(x)- \frac{\log{\left(x \right)} \log{\left(x \right)}^{\frac{1}{x}} \log{\left(\log{\left(x \right)} \right)} - \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}} 
-(-log(x)^(1/x) + log(x)^(1/x)*log(x)*log(log(x)))/(x^2*log(x))
Denominador racional [src] 
x ________ / 2    2                   \
\/ log(x) *\x  - x *log(x)*log(log(x))/
---------------------------------------
                4                      
               x *log(x)
(−x2log⁡(x)log⁡(log⁡(x))+x2)log⁡(x)1xx4log⁡(x)\frac{\left(- x^{2} \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + x^{2}\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{4} \log{\left(x \right)}} 
log(x)^(1/x)*(x^2 - x^2*log(x)*log(log(x)))/(x^4*log(x))
Parte trigonométrica [src] 
x ________ /    1       log(log(x))\
\/ log(x) *|--------- - -----------|
           | 2                2    |
           \x *log(x)        x     /
(−log⁡(log⁡(x))x2+1x2log⁡(x))log⁡(x)1x\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}} 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
Compilar la expresión [src] 
x ________ /    1       log(log(x))\
\/ log(x) *|--------- - -----------|
           | 2                2    |
           \x *log(x)        x     /
(−log⁡(log⁡(x))x2+1x2log⁡(x))log⁡(x)1x\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}} 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
Abrimos la expresión [src] 
x ________ /    1       log(log(x))\
\/ log(x) *|--------- - -----------|
           | 2                2    |
           \x *log(x)        x     /
(−log⁡(log⁡(x))x2+1x2log⁡(x))log⁡(x)1x\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}} 
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)
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