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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x^2+1)*exp(x)/(1+exp(2*x))-2*x*atan(E^x)*sin(x^2+1)

¿Cómo vas a descomponer esta cos(x^2+1)*exp(x)/(1+exp(2*x))-2*x*atan(E^x)*sin(x^2+1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 2    \  x                           
cos\x  + 1/*e            / x\    / 2    \
-------------- - 2*x*atan\E /*sin\x  + 1/
        2*x                              
   1 + e
$$- 2 x \operatorname{atan}{\left(e^{x} \right)} \sin{\left(x^{2} + 1 \right)} + \frac{e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
(cos(x^2 + 1)*exp(x))/(1 + exp(2*x)) - (2*x)*atan(E^x)*sin(x^2 + 1)
Simplificación general [src] 
   /     2\  x       /     2*x\     / x\    /     2\
cos\1 + x /*e  - 2*x*\1 + e   /*atan\e /*sin\1 + x /
----------------------------------------------------
                           2*x                      
                      1 + e
$$\frac{- 2 x \left(e^{2 x} + 1\right) \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
(cos(1 + x^2)*exp(x) - 2*x*(1 + exp(2*x))*atan(exp(x))*sin(1 + x^2))/(1 + exp(2*x))
Respuesta numérica [src] 
cos(x^2 + 1)*exp(x)/(1.0 + exp(2*x)) - 2.0*x*atan(E^x)*sin(x^2 + 1)
cos(x^2 + 1)*exp(x)/(1.0 + exp(2*x)) - 2.0*x*atan(E^x)*sin(x^2 + 1)
Denominador racional [src] 
   /     2\  x           / x\    /     2\           / x\  2*x    /     2\
cos\1 + x /*e  - 2*x*atan\e /*sin\1 + x / - 2*x*atan\e /*e   *sin\1 + x /
-------------------------------------------------------------------------
                                      2*x                                
                                 1 + e
$$\frac{- 2 x e^{2 x} \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} - 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
(cos(1 + x^2)*exp(x) - 2*x*atan(exp(x))*sin(1 + x^2) - 2*x*atan(exp(x))*exp(2*x)*sin(1 + x^2))/(1 + exp(2*x))
Denominador común [src] 
   /     2\  x                           
cos\1 + x /*e            / x\    /     2\
-------------- - 2*x*atan\e /*sin\1 + x /
        2*x                              
   1 + e
$$- 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + \frac{e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
cos(1 + x^2)*exp(x)/(1 + exp(2*x)) - 2*x*atan(exp(x))*sin(1 + x^2)
Combinatoria [src] 
 /     /     2\  x           / x\    /     2\           / x\  2*x    /     2\\ 
-\- cos\1 + x /*e  + 2*x*atan\e /*sin\1 + x / + 2*x*atan\e /*e   *sin\1 + x // 
-------------------------------------------------------------------------------
                                         2*x                                   
                                    1 + e
$$- \frac{2 x e^{2 x} \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} - e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
-(-cos(1 + x^2)*exp(x) + 2*x*atan(exp(x))*sin(1 + x^2) + 2*x*atan(exp(x))*exp(2*x)*sin(1 + x^2))/(1 + exp(2*x))
Abrimos la expresión [src] 
          / 2\  x    x           / 2\                                                            
cos(1)*cos\x /*e    e *sin(1)*sin\x /           / x\           / 2\           / x\    / 2\       
----------------- - ----------------- - 2*x*atan\e /*cos(1)*sin\x / - 2*x*atan\e /*cos\x /*sin(1)
          2*x                 2*x                                                                
     1 + e               1 + e
$$- 2 x \sin{\left(x^{2} \right)} \cos{\left(1 \right)} \operatorname{atan}{\left(e^{x} \right)} - 2 x \sin{\left(1 \right)} \cos{\left(x^{2} \right)} \operatorname{atan}{\left(e^{x} \right)} - \frac{e^{x} \sin{\left(1 \right)} \sin{\left(x^{2} \right)}}{e^{2 x} + 1} + \frac{e^{x} \cos{\left(1 \right)} \cos{\left(x^{2} \right)}}{e^{2 x} + 1}$$ 
cos(1)*cos(x^2)*exp(x)/(1 + exp(2*x)) - exp(x)*sin(1)*sin(x^2)/(1 + exp(2*x)) - 2*x*atan(exp(x))*cos(1)*sin(x^2) - 2*x*atan(exp(x))*cos(x^2)*sin(1)
Compilar la expresión [src] 
   / 2    \  x                           
cos\x  + 1/*e            / x\    / 2    \
-------------- - 2*x*atan\e /*sin\x  + 1/
        2*x                              
   1 + e
$$- 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + \frac{e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
   / 2    \  x                           
cos\x  + 1/*e            / x\    / 2    \
-------------- - 2*x*atan\E /*sin\x  + 1/
        2*x                              
   1 + e
$$- 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + \frac{e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
cos(x^2 + 1)*exp(x)/(1 + exp(2*x)) - 2*x*atan(E^x)*sin(x^2 + 1)
Potencias [src] 
   /     2\  x                           
cos\1 + x /*e            / x\    /     2\
-------------- - 2*x*atan\e /*sin\1 + x /
        2*x                              
   1 + e
$$- 2 x \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + \frac{e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
/   /     2\      /      2\\                                                 
| I*\1 + x /    I*\-1 - x /|                                                 
|e             e           |  x                                              
|----------- + ------------|*e        /     /      2\      /     2\\         
\     2             2      /          |   I*\-1 - x /    I*\1 + x /|     / x\
------------------------------- + I*x*\- e            + e          /*atan\e /
                 2*x                                                         
            1 + e
$$i x \left(- e^{i \left(- x^{2} - 1\right)} + e^{i \left(x^{2} + 1\right)}\right) \operatorname{atan}{\left(e^{x} \right)} + \frac{\left(\frac{e^{i \left(- x^{2} - 1\right)}}{2} + \frac{e^{i \left(x^{2} + 1\right)}}{2}\right) e^{x}}{e^{2 x} + 1}$$ 
(exp(i*(1 + x^2))/2 + exp(i*(-1 - x^2))/2)*exp(x)/(1 + exp(2*x)) + i*x*(-exp(i*(-1 - x^2)) + exp(i*(1 + x^2)))*atan(exp(x))
Unión de expresiones racionales [src] 
   /     2\  x       /     2*x\     / x\    /     2\
cos\1 + x /*e  - 2*x*\1 + e   /*atan\e /*sin\1 + x /
----------------------------------------------------
                           2*x                      
                      1 + e
$$\frac{- 2 x \left(e^{2 x} + 1\right) \sin{\left(x^{2} + 1 \right)} \operatorname{atan}{\left(e^{x} \right)} + e^{x} \cos{\left(x^{2} + 1 \right)}}{e^{2 x} + 1}$$ 
(cos(1 + x^2)*exp(x) - 2*x*(1 + exp(2*x))*atan(exp(x))*sin(1 + x^2))/(1 + exp(2*x))
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