Sr Examen
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?
Solución
Ha introducido
[src]
x ________ / 1 log(log(x))\
\/ log(x) *|--------- - -----------|
| 2 2 |
\x *log(x) x /
$$\left(\frac{1}{x^{2} \log{\left(x \right)}} - \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)}^{\frac{1}{x}}$$
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
$$\frac{\left(- \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\frac{1 - x}{x}}}{x^{2}}$$
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)
$$\frac{\left(- \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + 1\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}}$$
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 /
$$\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}}$$
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)
$$- \frac{\left(\log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} - 1\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}}$$
-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)
$$- \frac{\log{\left(x \right)} \log{\left(x \right)}^{\frac{1}{x}} \log{\left(\log{\left(x \right)} \right)} - \log{\left(x \right)}^{\frac{1}{x}}}{x^{2} \log{\left(x \right)}}$$
-(-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)
$$\frac{\left(- x^{2} \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} + x^{2}\right) \log{\left(x \right)}^{\frac{1}{x}}}{x^{4} \log{\left(x \right)}}$$
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 /
$$\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}}$$
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 /
$$\left(- \frac{\log{\left(\log{\left(x \right)} \right)}}{x^{2}} + \frac{1}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{x}}$$
log(x)^(1/x)*(1/(x^2*log(x)) - log(log(x))/x^2)