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¿Cómo vas a descomponer esta cosh(2*x)^(1/(x^2))*(-2*log(cosh(2*x))/x^3+2*sinh(2*x)/(x^2*cosh(2*x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
           1                                    
           --                                   
            2                                   
           x  /-2*log(cosh(2*x))   2*sinh(2*x) \
(cosh(2*x))  *|----------------- + ------------|
              |         3           2          |
              \        x           x *cosh(2*x)/
$$\left(\frac{2 \sinh{\left(2 x \right)}}{x^{2} \cosh{\left(2 x \right)}} + \frac{\left(-1\right) 2 \log{\left(\cosh{\left(2 x \right)} \right)}}{x^{3}}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}$$
cosh(2*x)^(1/(x^2))*((-2*log(cosh(2*x)))/x^3 + (2*sinh(2*x))/((x^2*cosh(2*x))))
Simplificación general [src]
                  1                                          
             -1 + --                                         
                   2                                         
                  x                                          
2*(cosh(2*x))       *(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))
-------------------------------------------------------------
                               3                             
                              x                              
$$\frac{2 \left(x \sinh{\left(2 x \right)} - \log{\left(\cosh{\left(2 x \right)} \right)} \cosh{\left(2 x \right)}\right) \cosh^{-1 + \frac{1}{x^{2}}}{\left(2 x \right)}}{x^{3}}$$
2*cosh(2*x)^(-1 + x^(-2))*(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))/x^3
Respuesta numérica [src]
cosh(2*x)^(x^(-2))*(-2.0*log(cosh(2*x))/x^3 + 2.0*sinh(2*x)/(x^2*cosh(2*x)))
cosh(2*x)^(x^(-2))*(-2.0*log(cosh(2*x))/x^3 + 2.0*sinh(2*x)/(x^2*cosh(2*x)))
Unión de expresiones racionales [src]
             1                                          
             --                                         
              2                                         
             x                                          
2*(cosh(2*x))  *(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))
--------------------------------------------------------
                       3                                
                      x *cosh(2*x)                      
$$\frac{2 \left(x \sinh{\left(2 x \right)} - \log{\left(\cosh{\left(2 x \right)} \right)} \cosh{\left(2 x \right)}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}}{x^{3} \cosh{\left(2 x \right)}}$$
2*cosh(2*x)^(x^(-2))*(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))/(x^3*cosh(2*x))
Denominador común [src]
               1                                            1           
               --                                           --          
                2                                            2          
               x                                            x           
- 2*(cosh(2*x))  *cosh(2*x)*log(cosh(2*x)) + 2*x*(cosh(2*x))  *sinh(2*x)
------------------------------------------------------------------------
                               3                                        
                              x *cosh(2*x)                              
$$\frac{2 x \sinh{\left(2 x \right)} \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)} - 2 \log{\left(\cosh{\left(2 x \right)} \right)} \cosh{\left(2 x \right)} \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}}{x^{3} \cosh{\left(2 x \right)}}$$
(-2*cosh(2*x)^(x^(-2))*cosh(2*x)*log(cosh(2*x)) + 2*x*cosh(2*x)^(x^(-2))*sinh(2*x))/(x^3*cosh(2*x))
Potencias [src]
           1                                     
           --                                    
            2                                    
           x  /  2*log(cosh(2*x))   2*sinh(2*x) \
(cosh(2*x))  *|- ---------------- + ------------|
              |          3           2          |
              \         x           x *cosh(2*x)/
$$\left(\frac{2 \sinh{\left(2 x \right)}}{x^{2} \cosh{\left(2 x \right)}} - \frac{2 \log{\left(\cosh{\left(2 x \right)} \right)}}{x^{3}}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}$$
cosh(2*x)^(x^(-2))*(-2*log(cosh(2*x))/x^3 + 2*sinh(2*x)/(x^2*cosh(2*x)))
Denominador racional [src]
                     1                                   1                          
                -1 + --                             -1 + --                         
                      2                                   2                         
   3                 x                 2                 x                          
2*x *(cosh(2*x))       *sinh(2*x) - 2*x *(cosh(2*x))       *cosh(2*x)*log(cosh(2*x))
------------------------------------------------------------------------------------
                                          5                                         
                                         x                                          
$$\frac{2 x^{3} \sinh{\left(2 x \right)} \cosh^{-1 + \frac{1}{x^{2}}}{\left(2 x \right)} - 2 x^{2} \log{\left(\cosh{\left(2 x \right)} \right)} \cosh{\left(2 x \right)} \cosh^{-1 + \frac{1}{x^{2}}}{\left(2 x \right)}}{x^{5}}$$
(2*x^3*cosh(2*x)^(-1 + x^(-2))*sinh(2*x) - 2*x^2*cosh(2*x)^(-1 + x^(-2))*cosh(2*x)*log(cosh(2*x)))/x^5
Abrimos la expresión [src]
           1                                    
           --                                   
            2                                   
           x  /-2*log(cosh(2*x))   2*sinh(2*x) \
(cosh(2*x))  *|----------------- + ------------|
              |         3           2          |
              \        x           x *cosh(2*x)/
$$\left(\frac{\left(-1\right) 2 \log{\left(\cosh{\left(2 x \right)} \right)}}{x^{3}} + \frac{2 \sinh{\left(2 x \right)}}{x^{2} \cosh{\left(2 x \right)}}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}$$
cosh(2*x)^(1/(x^2))*((-2*log(cosh(2*x)))/x^3 + 2*sinh(2*x)/(x^2*cosh(2*x)))
Compilar la expresión [src]
           1                                     
           --                                    
            2                                    
           x  /  2*log(cosh(2*x))   2*sinh(2*x) \
(cosh(2*x))  *|- ---------------- + ------------|
              |          3           2          |
              \         x           x *cosh(2*x)/
$$\left(\frac{2 \sinh{\left(2 x \right)}}{x^{2} \cosh{\left(2 x \right)}} - \frac{2 \log{\left(\cosh{\left(2 x \right)} \right)}}{x^{3}}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}$$
cosh(2*x)^(1/(x^2))*(-2*log(cosh(2*x))/x^3 + 2*sinh(2*x)/(x^2*cosh(2*x)))
Parte trigonométrica [src]
           1                                     
           --                                    
            2                                    
           x  /  2*log(cosh(2*x))   2*sinh(2*x) \
(cosh(2*x))  *|- ---------------- + ------------|
              |          3           2          |
              \         x           x *cosh(2*x)/
$$\left(\frac{2 \sinh{\left(2 x \right)}}{x^{2} \cosh{\left(2 x \right)}} - \frac{2 \log{\left(\cosh{\left(2 x \right)} \right)}}{x^{3}}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}$$
             1                                
             --                               
              2                               
             x  /  log(cosh(2*x))            \
2*(cosh(2*x))  *|- -------------- + tanh(2*x)|
                \        x                   /
----------------------------------------------
                       2                      
                      x                       
$$\frac{2 \left(\tanh{\left(2 x \right)} - \frac{\log{\left(\cosh{\left(2 x \right)} \right)}}{x}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}}{x^{2}}$$
2*cosh(2*x)^(x^(-2))*(-log(cosh(2*x))/x + tanh(2*x))/x^2
Combinatoria [src]
             1                                          
             --                                         
              2                                         
             x                                          
2*(cosh(2*x))  *(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))
--------------------------------------------------------
                       3                                
                      x *cosh(2*x)                      
$$\frac{2 \left(x \sinh{\left(2 x \right)} - \log{\left(\cosh{\left(2 x \right)} \right)} \cosh{\left(2 x \right)}\right) \cosh^{\frac{1}{x^{2}}}{\left(2 x \right)}}{x^{3} \cosh{\left(2 x \right)}}$$
2*cosh(2*x)^(x^(-2))*(x*sinh(2*x) - cosh(2*x)*log(cosh(2*x)))/(x^3*cosh(2*x))