Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x)^sin(x)*(cos(x)*log(log(x))+sin(x)/(x*log(x)))
¿Cómo vas a descomponer esta log(x)^sin(x)*(cos(x)*log(log(x))+sin(x)/(x*log(x))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x) / sin(x) \
log (x)*|cos(x)*log(log(x)) + --------|
\ x*log(x)/
$$\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
log(x)^sin(x)*(cos(x)*log(log(x)) + sin(x)/((x*log(x))))
Simplificación general
[src]
-1 + sin(x)
log (x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))
--------------------------------------------------------
x
$$\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}^{\sin{\left(x \right)} - 1}}{x}$$
log(x)^(-1 + sin(x))*(x*cos(x)*log(x)*log(log(x)) + sin(x))/x
Respuesta numérica
[src]
log(x)^sin(x)*(cos(x)*log(log(x)) + sin(x)/(x*log(x)))
log(x)^sin(x)*(cos(x)*log(log(x)) + sin(x)/(x*log(x)))
Potencias
[src]
/ -I*x I*x\
-I*\- e + e /
-------------------- // I*x -I*x\ / -I*x I*x\\
2 ||e e | I*\- e + e /|
(log(x)) *||---- + -----|*log(log(x)) - ------------------|
\\ 2 2 / 2*x*log(x) /
$$\left(\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(\log{\left(x \right)} \right)} - \frac{i \left(e^{i x} - e^{- i x}\right)}{2 x \log{\left(x \right)}}\right) \log{\left(x \right)}^{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2}}$$
log(x)^(-i*(-exp(-i*x) + exp(i*x))/2)*((exp(i*x)/2 + exp(-i*x)/2)*log(log(x)) - i*(-exp(-i*x) + exp(i*x))/(2*x*log(x)))
Combinatoria
[src]
sin(x)
log (x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))
---------------------------------------------------
x*log(x)
$$\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}}{x \log{\left(x \right)}}$$
log(x)^sin(x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))/(x*log(x))
Denominador racional
[src]
sin(x)
log (x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))
---------------------------------------------------
x*log(x)
$$\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}}{x \log{\left(x \right)}}$$
log(x)^sin(x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))/(x*log(x))
Denominador común
[src]
sin(x)
sin(x) log (x)*sin(x)
log (x)*cos(x)*log(log(x)) + -------------------
x*log(x)
$$\log{\left(x \right)}^{\sin{\left(x \right)}} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\log{\left(x \right)}^{\sin{\left(x \right)}} \sin{\left(x \right)}}{x \log{\left(x \right)}}$$
log(x)^sin(x)*cos(x)*log(log(x)) + log(x)^sin(x)*sin(x)/(x*log(x))
Unión de expresiones racionales
[src]
sin(x)
log (x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))
---------------------------------------------------
x*log(x)
$$\frac{\left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}}{x \log{\left(x \right)}}$$
log(x)^sin(x)*(x*cos(x)*log(x)*log(log(x)) + sin(x))/(x*log(x))
Parte trigonométrica
[src]
1
------
csc(x) /log(log(x)) 1 \
(log(x)) *|----------- + ---------------|
| /pi \ x*csc(x)*log(x)|
|csc|-- - x| |
\ \2 / /
$$\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{x \log{\left(x \right)} \csc{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{\csc{\left(x \right)}}}$$
1
-----------
/ pi\
sec|x - --|
\ 2 / /log(log(x)) 1 \
(log(x)) *|----------- + --------------------|
| sec(x) / pi\|
| x*log(x)*sec|x - --||
\ \ 2 //
$$\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{\sec{\left(x \right)}} + \frac{1}{x \log{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}\right) \log{\left(x \right)}^{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}}$$
/x\
2*tan|-|
\2/
-----------
2/x\ // 2/x\\ /x\ \
1 + tan |-| ||1 - tan |-||*log(log(x)) 2*tan|-| |
\2/ |\ \2// \2/ |
(log(x)) *|------------------------- + ----------------------|
| 2/x\ / 2/x\\ |
| 1 + tan |-| x*|1 + tan |-||*log(x)|
\ \2/ \ \2// /
$$\left(\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(\log{\left(x \right)} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}$$
/x\
2*cot|-|
\2/
-----------
2/x\ // 2/x\\ /x\ \
1 + cot |-| ||-1 + cot |-||*log(log(x)) 2*cot|-| |
\2/ |\ \2// \2/ |
(log(x)) *|-------------------------- + ----------------------|
| 2/x\ / 2/x\\ |
| 1 + cot |-| x*|1 + cot |-||*log(x)|
\ \2/ \ \2// /
$$\left(\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \log{\left(\log{\left(x \right)} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}$$
/ pi\ / / pi\\
cos|x - --| | cos|x - --||
\ 2 / | \ 2 /|
(log(x)) *|cos(x)*log(log(x)) + -----------|
\ x*log(x) /
$$\left(\log{\left(\log{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\cos{\left(x - \frac{\pi}{2} \right)}}$$
1
------
csc(x) /log(log(x)) 1 \
(log(x)) *|----------- + ---------------|
\ sec(x) x*csc(x)*log(x)/
$$\left(\frac{\log{\left(\log{\left(x \right)} \right)}}{\sec{\left(x \right)}} + \frac{1}{x \log{\left(x \right)} \csc{\left(x \right)}}\right) \log{\left(x \right)}^{\frac{1}{\csc{\left(x \right)}}}$$
sin(x) / / pi\ sin(x) \
log (x)*|log(log(x))*sin|x + --| + --------|
\ \ 2 / x*log(x)/
$$\left(\log{\left(\log{\left(x \right)} \right)} \sin{\left(x + \frac{\pi}{2} \right)} + \frac{\sin{\left(x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(x \right)}}$$
log(x)^sin(x)*(log(log(x))*sin(x + pi/2) + sin(x)/(x*log(x)))