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Simplificación de expresiones/ Descomposición en fracciones simples/ cosh(x)/(1+sinh(x)^2)+sinh(x)^2/cosh(x)+cosh(x)*log(cosh(x))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                   2                          
  cosh(x)      sinh (x)                       
------------ + -------- + cosh(x)*log(cosh(x))
        2      cosh(x)                        
1 + sinh (x)
$$\left(\frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}\right) + \log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)}$$ 
cosh(x)/(1 + sinh(x)^2) + sinh(x)^2/cosh(x) + cosh(x)*log(cosh(x))
Simplificación general [src] 
(1 + log(cosh(x)))*cosh(x)
$$\left(\log{\left(\cosh{\left(x \right)} \right)} + 1\right) \cosh{\left(x \right)}$$ 
(1 + log(cosh(x)))*cosh(x)
Denominador racional [src] 
    2          2    /        2   \       2    /        2   \             
cosh (x) + sinh (x)*\1 + sinh (x)/ + cosh (x)*\1 + sinh (x)/*log(cosh(x))
-------------------------------------------------------------------------
                          /        2   \                                 
                          \1 + sinh (x)/*cosh(x)
$$\frac{\left(\sinh^{2}{\left(x \right)} + 1\right) \log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)} + \left(\sinh^{2}{\left(x \right)} + 1\right) \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right) \cosh{\left(x \right)}}$$ 
(cosh(x)^2 + sinh(x)^2*(1 + sinh(x)^2) + cosh(x)^2*(1 + sinh(x)^2)*log(cosh(x)))/((1 + sinh(x)^2)*cosh(x))
Respuesta numérica [src] 
cosh(x)/(1.0 + sinh(x)^2) + sinh(x)^2/cosh(x) + cosh(x)*log(cosh(x))
cosh(x)/(1.0 + sinh(x)^2) + sinh(x)^2/cosh(x) + cosh(x)*log(cosh(x))
Potencias [src] 
                   2                          
  cosh(x)      sinh (x)                       
------------ + -------- + cosh(x)*log(cosh(x))
        2      cosh(x)                        
1 + sinh (x)
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$ 
cosh(x)/(1 + sinh(x)^2) + sinh(x)^2/cosh(x) + cosh(x)*log(cosh(x))
Combinatoria [src] 
    2          2          4          2                       2        2                
cosh (x) + sinh (x) + sinh (x) + cosh (x)*log(cosh(x)) + cosh (x)*sinh (x)*log(cosh(x))
---------------------------------------------------------------------------------------
                                 /        2   \                                        
                                 \1 + sinh (x)/*cosh(x)
$$\frac{\log{\left(\cosh{\left(x \right)} \right)} \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)} + \log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)} + \sinh^{4}{\left(x \right)} + \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right) \cosh{\left(x \right)}}$$ 
(cosh(x)^2 + sinh(x)^2 + sinh(x)^4 + cosh(x)^2*log(cosh(x)) + cosh(x)^2*sinh(x)^2*log(cosh(x)))/((1 + sinh(x)^2)*cosh(x))
Compilar la expresión [src] 
                   2                          
  cosh(x)      sinh (x)                       
------------ + -------- + cosh(x)*log(cosh(x))
        2      cosh(x)                        
1 + sinh (x)
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$ 
cosh(x)/(1 + sinh(x)^2) + sinh(x)^2/cosh(x) + cosh(x)*log(cosh(x))
Unión de expresiones racionales [src] 
    2          2    /        2   \       2    /        2   \             
cosh (x) + sinh (x)*\1 + sinh (x)/ + cosh (x)*\1 + sinh (x)/*log(cosh(x))
-------------------------------------------------------------------------
                          /        2   \                                 
                          \1 + sinh (x)/*cosh(x)
$$\frac{\left(\sinh^{2}{\left(x \right)} + 1\right) \log{\left(\cosh{\left(x \right)} \right)} \cosh^{2}{\left(x \right)} + \left(\sinh^{2}{\left(x \right)} + 1\right) \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right) \cosh{\left(x \right)}}$$ 
(cosh(x)^2 + sinh(x)^2*(1 + sinh(x)^2) + cosh(x)^2*(1 + sinh(x)^2)*log(cosh(x)))/((1 + sinh(x)^2)*cosh(x))
Denominador común [src] 
    2          2          4                          
cosh (x) + sinh (x) + sinh (x)                       
------------------------------ + cosh(x)*log(cosh(x))
      2                                              
  sinh (x)*cosh(x) + cosh(x)
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{4}{\left(x \right)} + \sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} \cosh{\left(x \right)} + \cosh{\left(x \right)}}$$ 
(cosh(x)^2 + sinh(x)^2 + sinh(x)^4)/(sinh(x)^2*cosh(x) + cosh(x)) + cosh(x)*log(cosh(x))
Parte trigonométrica [src] 
                   2                          
  cosh(x)      sinh (x)                       
------------ + -------- + cosh(x)*log(cosh(x))
        2      cosh(x)                        
1 + sinh (x)
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$ 
(1 + log(cosh(x)))*cosh(x)
$$\left(\log{\left(\cosh{\left(x \right)} \right)} + 1\right) \cosh{\left(x \right)}$$ 
(1 + log(cosh(x)))*cosh(x)
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