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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   cos(x)      /                          cos(x)  \
log      (2*x)*|-log(log(2*x))*sin(x) + ----------|
               \                        x*log(2*x)/
(−log⁡(log⁡(2x))sin⁡(x)+cos⁡(x)xlog⁡(2x))log⁡(2x)cos⁡(x)\left(- \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)}} 
log(2*x)^cos(x)*((-log(log(2*x)))*sin(x) + cos(x)/((x*log(2*x))))
Simplificación general [src] 
   -1 + cos(x)                                                 
log           (2*x)*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))
---------------------------------------------------------------
                               x
(−xlog⁡(2x)log⁡(log⁡(2x))sin⁡(x)+cos⁡(x))log⁡(2x)cos⁡(x)−1x\frac{\left(- x \log{\left(2 x \right)} \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \cos{\left(x \right)}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)} - 1}}{x} 
log(2*x)^(-1 + cos(x))*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))/x
Respuesta numérica [src] 
log(2*x)^cos(x)*(-log(log(2*x))*sin(x) + cos(x)/(x*log(2*x)))
log(2*x)^cos(x)*(-log(log(2*x))*sin(x) + cos(x)/(x*log(2*x)))
Unión de expresiones racionales [src] 
   cos(x)                                                 
log      (2*x)*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))
----------------------------------------------------------
                        x*log(2*x)
(−xlog⁡(2x)log⁡(log⁡(2x))sin⁡(x)+cos⁡(x))log⁡(2x)cos⁡(x)xlog⁡(2x)\frac{\left(- x \log{\left(2 x \right)} \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \cos{\left(x \right)}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)}}}{x \log{\left(2 x \right)}} 
log(2*x)^cos(x)*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))/(x*log(2*x))
Denominador racional [src] 
   cos(x)                                                 
log      (2*x)*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))
----------------------------------------------------------
                        x*log(2*x)
(−xlog⁡(2x)log⁡(log⁡(2x))sin⁡(x)+cos⁡(x))log⁡(2x)cos⁡(x)xlog⁡(2x)\frac{\left(- x \log{\left(2 x \right)} \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \cos{\left(x \right)}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)}}}{x \log{\left(2 x \right)}} 
log(2*x)^cos(x)*(-x*log(2*x)*log(log(2*x))*sin(x) + cos(x))/(x*log(2*x))
Denominador común [src] 
                 cos(x)                                                             
(log(2) + log(x))      *cos(x)                    cos(x)                            
------------------------------ - (log(2) + log(x))      *log(log(2) + log(x))*sin(x)
     x*log(2) + x*log(x)
−(log⁡(x)+log⁡(2))cos⁡(x)log⁡(log⁡(x)+log⁡(2))sin⁡(x)+(log⁡(x)+log⁡(2))cos⁡(x)cos⁡(x)xlog⁡(x)+xlog⁡(2)- \left(\log{\left(x \right)} + \log{\left(2 \right)}\right)^{\cos{\left(x \right)}} \log{\left(\log{\left(x \right)} + \log{\left(2 \right)} \right)} \sin{\left(x \right)} + \frac{\left(\log{\left(x \right)} + \log{\left(2 \right)}\right)^{\cos{\left(x \right)}} \cos{\left(x \right)}}{x \log{\left(x \right)} + x \log{\left(2 \right)}} 
(log(2) + log(x))^cos(x)*cos(x)/(x*log(2) + x*log(x)) - (log(2) + log(x))^cos(x)*log(log(2) + log(x))*sin(x)
Potencias [src] 
           I*x    -I*x / I*x    -I*x                                   \
          e      e     |e      e                                       |
          ---- + ----- |---- + -----     /   -I*x    I*x\              |
           2       2   | 2       2     I*\- e     + e   /*log(log(2*x))|
(log(2*x))            *|------------ + --------------------------------|
                       \ x*log(2*x)                   2                /
(i(eix−e−ix)log⁡(log⁡(2x))2+eix2+e−ix2xlog⁡(2x))log⁡(2x)eix2+e−ix2\left(\frac{i \left(e^{i x} - e^{- i x}\right) \log{\left(\log{\left(2 x \right)} \right)}}{2} + \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{x \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}} 
log(2*x)^(exp(i*x)/2 + exp(-i*x)/2)*((exp(i*x)/2 + exp(-i*x)/2)/(x*log(2*x)) + i*(-exp(-i*x) + exp(i*x))*log(log(2*x))/2)
Abrimos la expresión [src] 
                 cos(x)                                                             
(log(2) + log(x))      *cos(x)                    cos(x)                            
------------------------------ - (log(2) + log(x))      *log(log(2) + log(x))*sin(x)
     x*log(2) + x*log(x)
−(log⁡(x)+log⁡(2))cos⁡(x)log⁡(log⁡(x)+log⁡(2))sin⁡(x)+(log⁡(x)+log⁡(2))cos⁡(x)cos⁡(x)xlog⁡(x)+xlog⁡(2)- \left(\log{\left(x \right)} + \log{\left(2 \right)}\right)^{\cos{\left(x \right)}} \log{\left(\log{\left(x \right)} + \log{\left(2 \right)} \right)} \sin{\left(x \right)} + \frac{\left(\log{\left(x \right)} + \log{\left(2 \right)}\right)^{\cos{\left(x \right)}} \cos{\left(x \right)}}{x \log{\left(x \right)} + x \log{\left(2 \right)}} 
(log(2) + log(x))^cos(x)*cos(x)/(x*log(2) + x*log(x)) - (log(2) + log(x))^cos(x)*log(log(2) + log(x))*sin(x)
Combinatoria [src] 
                  cos(x)                                                                                         
-(log(2) + log(x))      *(-cos(x) + x*log(2)*log(log(2) + log(x))*sin(x) + x*log(x)*log(log(2) + log(x))*sin(x)) 
-----------------------------------------------------------------------------------------------------------------
                                               x*(log(2) + log(x))
−(log⁡(x)+log⁡(2))cos⁡(x)(xlog⁡(x)log⁡(log⁡(x)+log⁡(2))sin⁡(x)+xlog⁡(2)log⁡(log⁡(x)+log⁡(2))sin⁡(x)−cos⁡(x))x(log⁡(x)+log⁡(2))- \frac{\left(\log{\left(x \right)} + \log{\left(2 \right)}\right)^{\cos{\left(x \right)}} \left(x \log{\left(x \right)} \log{\left(\log{\left(x \right)} + \log{\left(2 \right)} \right)} \sin{\left(x \right)} + x \log{\left(2 \right)} \log{\left(\log{\left(x \right)} + \log{\left(2 \right)} \right)} \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x \left(\log{\left(x \right)} + \log{\left(2 \right)}\right)} 
-(log(2) + log(x))^cos(x)*(-cos(x) + x*log(2)*log(log(2) + log(x))*sin(x) + x*log(x)*log(log(2) + log(x))*sin(x))/(x*(log(2) + log(x)))
Parte trigonométrica [src] 
                 2/x\                                                      
          1 - tan |-|                                                      
                  \2/                                                      
          -----------                                                      
                 2/x\ /                     /x\                2/x\       \
          1 + tan |-| |  2*log(log(2*x))*tan|-|         1 - tan |-|       |
                  \2/ |                     \2/                 \2/       |
(log(2*x))           *|- ---------------------- + ------------------------|
                      |              2/x\           /       2/x\\         |
                      |       1 + tan |-|         x*|1 + tan |-||*log(2*x)|
                      \               \2/           \        \2//         /
(−2log⁡(log⁡(2x))tan⁡(x2)tan⁡2(x2)+1+1−tan⁡2(x2)x(tan⁡2(x2)+1)log⁡(2x))log⁡(2x)1−tan⁡2(x2)tan⁡2(x2)+1\left(- \frac{2 \log{\left(\log{\left(2 x \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} 
            1                                         
          ------                                      
          sec(x) /  log(log(2*x))           1        \
(log(2*x))      *|- ------------- + -----------------|
                 \      csc(x)      x*log(2*x)*sec(x)/
(−log⁡(log⁡(2x))csc⁡(x)+1xlog⁡(2x)sec⁡(x))log⁡(2x)1sec⁡(x)\left(- \frac{\log{\left(\log{\left(2 x \right)} \right)}}{\csc{\left(x \right)}} + \frac{1}{x \log{\left(2 x \right)} \sec{\left(x \right)}}\right) \log{\left(2 x \right)}^{\frac{1}{\sec{\left(x \right)}}} 
             /    pi\ /                           /    pi\\
          sin|x + --| |                        sin|x + --||
             \    2 / |                           \    2 /|
(log(2*x))           *|-log(log(2*x))*sin(x) + -----------|
                      \                         x*log(2*x)/
(−log⁡(log⁡(2x))sin⁡(x)+sin⁡(x+π2)xlog⁡(2x))log⁡(2x)sin⁡(x+π2)\left(- \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{x \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\sin{\left(x + \frac{\pi}{2} \right)}} 
   cos(x)      /     /    pi\                   cos(x)  \
log      (2*x)*|- cos|x - --|*log(log(2*x)) + ----------|
               \     \    2 /                 x*log(2*x)/
(−log⁡(log⁡(2x))cos⁡(x−π2)+cos⁡(x)xlog⁡(2x))log⁡(2x)cos⁡(x)\left(- \log{\left(\log{\left(2 x \right)} \right)} \cos{\left(x - \frac{\pi}{2} \right)} + \frac{\cos{\left(x \right)}}{x \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)}} 
                  2/x\                                                      
          -1 + cot |-|                                                      
                   \2/                                                      
          ------------                                                      
                 2/x\  /       /x\                               2/x\      \
          1 + cot |-|  |  2*cot|-|*log(log(2*x))         -1 + cot |-|      |
                  \2/  |       \2/                                \2/      |
(log(2*x))            *|- ---------------------- + ------------------------|
                       |              2/x\           /       2/x\\         |
                       |       1 + cot |-|         x*|1 + cot |-||*log(2*x)|
                       \               \2/           \        \2//         /
(−2log⁡(log⁡(2x))cot⁡(x2)cot⁡2(x2)+1+cot⁡2(x2)−1x(cot⁡2(x2)+1)log⁡(2x))log⁡(2x)cot⁡2(x2)−1cot⁡2(x2)+1\left(- \frac{2 \log{\left(\log{\left(2 x \right)} \right)} \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{x \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(2 x \right)}}\right) \log{\left(2 x \right)}^{\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} 
               1                                                
          -----------                                           
             /pi    \                                           
          csc|-- - x|                                           
             \2     / /  log(log(2*x))             1           \
(log(2*x))           *|- ------------- + ----------------------|
                      |      csc(x)           /pi    \         |
                      |                  x*csc|-- - x|*log(2*x)|
                      \                       \2     /         /
(−log⁡(log⁡(2x))csc⁡(x)+1xlog⁡(2x)csc⁡(−x+π2))log⁡(2x)1csc⁡(−x+π2)\left(- \frac{\log{\left(\log{\left(2 x \right)} \right)}}{\csc{\left(x \right)}} + \frac{1}{x \log{\left(2 x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}\right) \log{\left(2 x \right)}^{\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}} 
   cos(x)      /    1                                   \
log      (2*x)*|----------*cos(x) - log(log(2*x))*sin(x)|
               \x*log(2*x)                              /
(−log⁡(log⁡(2x))sin⁡(x)+1xlog⁡(2x)cos⁡(x))log⁡(2x)cos⁡(x)\left(- \log{\left(\log{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{1}{x \log{\left(2 x \right)}} \cos{\left(x \right)}\right) \log{\left(2 x \right)}^{\cos{\left(x \right)}} 
            1                                         
          ------                                      
          sec(x) /  log(log(2*x))           1        \
(log(2*x))      *|- ------------- + -----------------|
                 |      /    pi\    x*log(2*x)*sec(x)|
                 |   sec|x - --|                     |
                 \      \    2 /                     /
(−log⁡(log⁡(2x))sec⁡(x−π2)+1xlog⁡(2x)sec⁡(x))log⁡(2x)1sec⁡(x)\left(- \frac{\log{\left(\log{\left(2 x \right)} \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{x \log{\left(2 x \right)} \sec{\left(x \right)}}\right) \log{\left(2 x \right)}^{\frac{1}{\sec{\left(x \right)}}} 
log(2*x)^(1/sec(x))*(-log(log(2*x))/sec(x - pi/2) + 1/(x*log(2*x)*sec(x)))
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