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Simplificación de expresiones/ Descomposición en fracciones simples/ ln(1/(2x))^tgx

¿Cómo vas a descomponer esta ln(1/(2x))^tgx expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   tan(x)/ 1 \
log      |---|
         \2*x/
log⁡(12x)tan⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\tan{\left(x \right)}} 
log(1/(2*x))^tan(x)
Descomposición de una fracción [src] 
(-log(2) + log(1/x))^tan(x)
(log⁡(1x)−log⁡(2))tan⁡(x)\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}} 
                  tan(x)
/             /1\\      
|-log(2) + log|-||      
\             \x//
Respuesta numérica [src] 
log(1/(2*x))^tan(x)
log(1/(2*x))^tan(x)
Potencias [src] 
            /   I*x    -I*x\
          I*\- e    + e    /
          ------------------
              I*x    -I*x   
             e    + e       
/   / 1 \\                  
|log|---||                  
\   \2*x//
log⁡(12x)i(−eix+e−ix)eix+e−ix\log{\left(\frac{1}{2 x} \right)}^{\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}} 
log(1/(2*x))^(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))
Combinatoria [src] 
                  tan(x)
/             /1\\      
|-log(2) + log|-||      
\             \x//
(log⁡(1x)−log⁡(2))tan⁡(x)\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}} 
(-log(2) + log(1/x))^tan(x)
Denominador común [src] 
                  tan(x)
/             /1\\      
|-log(2) + log|-||      
\             \x//
(log⁡(1x)−log⁡(2))tan⁡(x)\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}} 
(-log(2) + log(1/x))^tan(x)
Parte trigonométrica [src] 
             /    pi\
          cos|x - --|
             \    2 /
          -----------
             cos(x)  
/   / 1 \\           
|log|---||           
\   \2*x//
log⁡(12x)cos⁡(x−π2)cos⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}} 
          sin(x)
          ------
          cos(x)
/   / 1 \\      
|log|---||      
\   \2*x//
log⁡(12x)sin⁡(x)cos⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}} 
          sec(x)
          ------
          csc(x)
/   / 1 \\      
|log|---||      
\   \2*x//
log⁡(12x)sec⁡(x)csc⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}} 
            1   
          ------
          cot(x)
/   / 1 \\      
|log|---||      
\   \2*x//
log⁡(12x)1cot⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\frac{1}{\cot{\left(x \right)}}} 
               2   
          2*sin (x)
          ---------
           sin(2*x)
/   / 1 \\         
|log|---||         
\   \2*x//
log⁡(12x)2sin⁡2(x)sin⁡(2x)\log{\left(\frac{1}{2 x} \right)}^{\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}} 
             sec(x)  
          -----------
             /    pi\
          sec|x - --|
             \    2 /
/   / 1 \\           
|log|---||           
\   \2*x//
log⁡(12x)sec⁡(x)sec⁡(x−π2)\log{\left(\frac{1}{2 x} \right)}^{\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}} 
             /pi    \
          csc|-- - x|
             \2     /
          -----------
             csc(x)  
/   / 1 \\           
|log|---||           
\   \2*x//
log⁡(12x)csc⁡(−x+π2)csc⁡(x)\log{\left(\frac{1}{2 x} \right)}^{\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}} 
log(1/(2*x))^(csc(pi/2 - x)/csc(x))
Abrimos la expresión [src] 
                  tan(x)
/             /1\\      
|-log(2) + log|-||      
\             \x//
(log⁡(1x)−log⁡(2))tan⁡(x)\left(\log{\left(\frac{1}{x} \right)} - \log{\left(2 \right)}\right)^{\tan{\left(x \right)}} 
(-log(2) + log(1/x))^tan(x)
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