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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 2    \                              
log\x  + 1/            atan(x)    x - 2  
----------- - log(x) + ------- + --------
     2                    2             2
                                 2 + 2*x
x−22x2+2+((−log⁡(x)+log⁡(x2+1)2)+atan⁡(x)2)\frac{x - 2}{2 x^{2} + 2} + \left(\left(- \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}\right) + \frac{\operatorname{atan}{\left(x \right)}}{2}\right) 
log(x^2 + 1)/2 - log(x) + atan(x)/2 + (x - 2)/(2 + 2*x^2)
Simplificación general [src] 
         /     2\ /                         /     2\\
-2 + x + \1 + x /*\-2*log(x) + atan(x) + log\1 + x //
-----------------------------------------------------
                        /     2\                     
                      2*\1 + x /
x+(x2+1)(−2log⁡(x)+log⁡(x2+1)+atan⁡(x))−22(x2+1)\frac{x + \left(x^{2} + 1\right) \left(- 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x^{2} + 1\right)} 
(-2 + x + (1 + x^2)*(-2*log(x) + atan(x) + log(1 + x^2)))/(2*(1 + x^2))
Respuesta numérica [src] 
-log(x) + 0.5*atan(x) + 0.5*log(x^2 + 1) + (-2.0 + x)/(2.0 + 2.0*x^2)
-log(x) + 0.5*atan(x) + 0.5*log(x^2 + 1) + (-2.0 + x)/(2.0 + 2.0*x^2)
Parte trigonométrica [src] 
             /     2\                    
atan(x)   log\1 + x /             -2 + x 
------- + ----------- - log(x) + --------
   2           2                        2
                                 2 + 2*x
x−22x2+2−log⁡(x)+log⁡(x2+1)2+atan⁡(x)2\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2} 
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Denominador común [src] 
             /     2\                    
atan(x)   log\1 + x /             -2 + x 
------- + ----------- - log(x) + --------
   2           2                        2
                                 2 + 2*x
x−22x2+2−log⁡(x)+log⁡(x2+1)2+atan⁡(x)2\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2} 
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Potencias [src] 
             /     2\                    
atan(x)   log\1 + x /             -2 + x 
------- + ----------- - log(x) + --------
   2           2                        2
                                 2 + 2*x
x−22x2+2−log⁡(x)+log⁡(x2+1)2+atan⁡(x)2\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2} 
atan(x)/2 + log(1 + x^2)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Denominador racional [src] 
                     2            2    /     2\      2                       /     2\
-2 + x - 2*log(x) + x *atan(x) + x *log\1 + x / - 2*x *log(x) + atan(x) + log\1 + x /
-------------------------------------------------------------------------------------
                                              2                                      
                                       2 + 2*x
−2x2log⁡(x)+x2log⁡(x2+1)+x2atan⁡(x)+x−2log⁡(x)+log⁡(x2+1)+atan⁡(x)−22x2+2\frac{- 2 x^{2} \log{\left(x \right)} + x^{2} \log{\left(x^{2} + 1 \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} - 2}{2 x^{2} + 2} 
(-2 + x - 2*log(x) + x^2*atan(x) + x^2*log(1 + x^2) - 2*x^2*log(x) + atan(x) + log(1 + x^2))/(2 + 2*x^2)
Unión de expresiones racionales [src] 
         /     2\ /                         /     2\\
-2 + x + \1 + x /*\-2*log(x) + atan(x) + log\1 + x //
-----------------------------------------------------
                        /     2\                     
                      2*\1 + x /
x+(x2+1)(−2log⁡(x)+log⁡(x2+1)+atan⁡(x))−22(x2+1)\frac{x + \left(x^{2} + 1\right) \left(- 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x^{2} + 1\right)} 
(-2 + x + (1 + x^2)*(-2*log(x) + atan(x) + log(1 + x^2)))/(2*(1 + x^2))
Compilar la expresión [src] 
             / 2    \                    
atan(x)   log\x  + 1/             -2 + x 
------- + ----------- - log(x) + --------
   2           2                        2
                                 2 + 2*x
x−22x2+2−log⁡(x)+log⁡(x2+1)2+atan⁡(x)2\frac{x - 2}{2 x^{2} + 2} - \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}{\left(x \right)}}{2} 
atan(x)/2 + log(x^2 + 1)/2 - log(x) + (-2 + x)/(2 + 2*x^2)
Combinatoria [src] 
                     2            2    /     2\      2                       /     2\
-2 + x - 2*log(x) + x *atan(x) + x *log\1 + x / - 2*x *log(x) + atan(x) + log\1 + x /
-------------------------------------------------------------------------------------
                                        /     2\                                     
                                      2*\1 + x /
−2x2log⁡(x)+x2log⁡(x2+1)+x2atan⁡(x)+x−2log⁡(x)+log⁡(x2+1)+atan⁡(x)−22(x2+1)\frac{- 2 x^{2} \log{\left(x \right)} + x^{2} \log{\left(x^{2} + 1 \right)} + x^{2} \operatorname{atan}{\left(x \right)} + x - 2 \log{\left(x \right)} + \log{\left(x^{2} + 1 \right)} + \operatorname{atan}{\left(x \right)} - 2}{2 \left(x^{2} + 1\right)} 
(-2 + x - 2*log(x) + x^2*atan(x) + x^2*log(1 + x^2) - 2*x^2*log(x) + atan(x) + log(1 + x^2))/(2*(1 + x^2))
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