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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                      x
 x    / 2    \   2*x*e 
e *log\x  + 2/ + ------
                  2    
                 x  + 2
2xexx2+2+exlog⁡(x2+2)\frac{2 x e^{x}}{x^{2} + 2} + e^{x} \log{\left(x^{2} + 2 \right)} 
exp(x)*log(x^2 + 2) + ((2*x)*exp(x))/(x^2 + 2)
Simplificación general [src] 
/      /     2\    /     2\\  x
\2*x + \2 + x /*log\2 + x //*e 
-------------------------------
                  2            
             2 + x
(2x+(x2+2)log⁡(x2+2))exx2+2\frac{\left(2 x + \left(x^{2} + 2\right) \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2} 
(2*x + (2 + x^2)*log(2 + x^2))*exp(x)/(2 + x^2)
Respuesta numérica [src] 
exp(x)*log(x^2 + 2) + 2.0*x*exp(x)/(2.0 + x^2)
exp(x)*log(x^2 + 2) + 2.0*x*exp(x)/(2.0 + x^2)
Combinatoria [src] 
/           /     2\    2    /     2\\  x
\2*x + 2*log\2 + x / + x *log\2 + x //*e 
-----------------------------------------
                       2                 
                  2 + x
(x2log⁡(x2+2)+2x+2log⁡(x2+2))exx2+2\frac{\left(x^{2} \log{\left(x^{2} + 2 \right)} + 2 x + 2 \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2} 
(2*x + 2*log(2 + x^2) + x^2*log(2 + x^2))*exp(x)/(2 + x^2)
Denominador racional [src] 
/           /     2\    2    /     2\\  x
\2*x + 2*log\2 + x / + x *log\2 + x //*e 
-----------------------------------------
                       2                 
                  2 + x
(x2log⁡(x2+2)+2x+2log⁡(x2+2))exx2+2\frac{\left(x^{2} \log{\left(x^{2} + 2 \right)} + 2 x + 2 \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2} 
(2*x + 2*log(2 + x^2) + x^2*log(2 + x^2))*exp(x)/(2 + x^2)
Unión de expresiones racionales [src] 
/      /     2\    /     2\\  x
\2*x + \2 + x /*log\2 + x //*e 
-------------------------------
                  2            
             2 + x
(2x+(x2+2)log⁡(x2+2))exx2+2\frac{\left(2 x + \left(x^{2} + 2\right) \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2} 
(2*x + (2 + x^2)*log(2 + x^2))*exp(x)/(2 + x^2)
Parte trigonométrica [src] 
                       /     2\   2*x*(cosh(x) + sinh(x))
(cosh(x) + sinh(x))*log\2 + x / + -----------------------
                                                2        
                                           2 + x
2x(sinh⁡(x)+cosh⁡(x))x2+2+(sinh⁡(x)+cosh⁡(x))log⁡(x2+2)\frac{2 x \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{x^{2} + 2} + \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \log{\left(x^{2} + 2 \right)} 
(cosh(x) + sinh(x))*log(2 + x^2) + 2*x*(cosh(x) + sinh(x))/(2 + x^2)
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