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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+2*x+2)/2-(5*atan((2*x+2)/2))/2+(x-2)/(4+4*x+2*x^2)

¿Cómo vas a descomponer esta log(x^2+2*x+2)/2-(5*atan((2*x+2)/2))/2+(x-2)/(4+4*x+2*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                          /2*x + 2\                 
   / 2          \   5*atan|-------|                 
log\x  + 2*x + 2/         \   2   /       x - 2     
----------------- - --------------- + --------------
        2                  2                       2
                                      4 + 4*x + 2*x
x−22x2+(4x+4)+(log⁡((x2+2x)+2)2−5atan⁡(2x+22)2)\frac{x - 2}{2 x^{2} + \left(4 x + 4\right)} + \left(\frac{\log{\left(\left(x^{2} + 2 x\right) + 2 \right)}}{2} - \frac{5 \operatorname{atan}{\left(\frac{2 x + 2}{2} \right)}}{2}\right) 
log(x^2 + 2*x + 2)/2 - 5*atan((2*x + 2)/2)/2 + (x - 2)/(4 + 4*x + 2*x^2)
Simplificación general [src] 
         /                    /     2      \\ /     2      \
-2 + x + \-5*atan(1 + x) + log\2 + x  + 2*x//*\2 + x  + 2*x/
------------------------------------------------------------
                        /     2      \                      
                      2*\2 + x  + 2*x/
x+(log⁡(x2+2x+2)−5atan⁡(x+1))(x2+2x+2)−22(x2+2x+2)\frac{x + \left(\log{\left(x^{2} + 2 x + 2 \right)} - 5 \operatorname{atan}{\left(x + 1 \right)}\right) \left(x^{2} + 2 x + 2\right) - 2}{2 \left(x^{2} + 2 x + 2\right)} 
(-2 + x + (-5*atan(1 + x) + log(2 + x^2 + 2*x))*(2 + x^2 + 2*x))/(2*(2 + x^2 + 2*x))
Respuesta numérica [src] 
0.5*log(x^2 + 2*x + 2) - 2.5*atan((2*x + 2)/2) + (-2.0 + x)/(4.0 + 2.0*x^2 + 4.0*x)
0.5*log(x^2 + 2*x + 2) - 2.5*atan((2*x + 2)/2) + (-2.0 + x)/(4.0 + 2.0*x^2 + 4.0*x)
Combinatoria [src] 
 /             /     2      \                     2    /     2      \          /     2      \      2                               \ 
-\2 - x - 2*log\2 + x  + 2*x/ + 10*atan(1 + x) - x *log\2 + x  + 2*x/ - 2*x*log\2 + x  + 2*x/ + 5*x *atan(1 + x) + 10*x*atan(1 + x)/ 
-------------------------------------------------------------------------------------------------------------------------------------
                                                             /     2      \                                                          
                                                           2*\2 + x  + 2*x/
−−x2log⁡(x2+2x+2)+5x2atan⁡(x+1)−2xlog⁡(x2+2x+2)+10xatan⁡(x+1)−x−2log⁡(x2+2x+2)+10atan⁡(x+1)+22(x2+2x+2)- \frac{- x^{2} \log{\left(x^{2} + 2 x + 2 \right)} + 5 x^{2} \operatorname{atan}{\left(x + 1 \right)} - 2 x \log{\left(x^{2} + 2 x + 2 \right)} + 10 x \operatorname{atan}{\left(x + 1 \right)} - x - 2 \log{\left(x^{2} + 2 x + 2 \right)} + 10 \operatorname{atan}{\left(x + 1 \right)} + 2}{2 \left(x^{2} + 2 x + 2\right)} 
-(2 - x - 2*log(2 + x^2 + 2*x) + 10*atan(1 + x) - x^2*log(2 + x^2 + 2*x) - 2*x*log(2 + x^2 + 2*x) + 5*x^2*atan(1 + x) + 10*x*atan(1 + x))/(2*(2 + x^2 + 2*x))
Unión de expresiones racionales [src] 
                                               /     2      \
-2 + x + (-5*atan(1 + x) + log(2 + x*(2 + x)))*\2 + x  + 2*x/
-------------------------------------------------------------
                         /     2      \                      
                       2*\2 + x  + 2*x/
x+(log⁡(x(x+2)+2)−5atan⁡(x+1))(x2+2x+2)−22(x2+2x+2)\frac{x + \left(\log{\left(x \left(x + 2\right) + 2 \right)} - 5 \operatorname{atan}{\left(x + 1 \right)}\right) \left(x^{2} + 2 x + 2\right) - 2}{2 \left(x^{2} + 2 x + 2\right)} 
(-2 + x + (-5*atan(1 + x) + log(2 + x*(2 + x)))*(2 + x^2 + 2*x))/(2*(2 + x^2 + 2*x))
Parte trigonométrica [src] 
   /     2      \                                 
log\2 + x  + 2*x/   5*atan(1 + x)       -2 + x    
----------------- - ------------- + --------------
        2                 2                2      
                                    4 + 2*x  + 4*x
x−22x2+4x+4+log⁡(x2+2x+2)2−5atan⁡(x+1)2\frac{x - 2}{2 x^{2} + 4 x + 4} + \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} - \frac{5 \operatorname{atan}{\left(x + 1 \right)}}{2} 
log(2 + x^2 + 2*x)/2 - 5*atan(1 + x)/2 + (-2 + x)/(4 + 2*x^2 + 4*x)
Denominador racional [src] 
                               /     2      \    2    /     2      \                         2                      /     2      \
-2 + x - 10*atan(1 + x) + 2*log\2 + x  + 2*x/ + x *log\2 + x  + 2*x/ - 10*x*atan(1 + x) - 5*x *atan(1 + x) + 2*x*log\2 + x  + 2*x/
----------------------------------------------------------------------------------------------------------------------------------
                                                                 2                                                                
                                                          4 + 2*x  + 4*x
x2log⁡(x2+2x+2)−5x2atan⁡(x+1)+2xlog⁡(x2+2x+2)−10xatan⁡(x+1)+x+2log⁡(x2+2x+2)−10atan⁡(x+1)−22x2+4x+4\frac{x^{2} \log{\left(x^{2} + 2 x + 2 \right)} - 5 x^{2} \operatorname{atan}{\left(x + 1 \right)} + 2 x \log{\left(x^{2} + 2 x + 2 \right)} - 10 x \operatorname{atan}{\left(x + 1 \right)} + x + 2 \log{\left(x^{2} + 2 x + 2 \right)} - 10 \operatorname{atan}{\left(x + 1 \right)} - 2}{2 x^{2} + 4 x + 4} 
(-2 + x - 10*atan(1 + x) + 2*log(2 + x^2 + 2*x) + x^2*log(2 + x^2 + 2*x) - 10*x*atan(1 + x) - 5*x^2*atan(1 + x) + 2*x*log(2 + x^2 + 2*x))/(4 + 2*x^2 + 4*x)
Denominador común [src] 
   /     2      \                                 
log\2 + x  + 2*x/   5*atan(1 + x)       -2 + x    
----------------- - ------------- + --------------
        2                 2                2      
                                    4 + 2*x  + 4*x
x−22x2+4x+4+log⁡(x2+2x+2)2−5atan⁡(x+1)2\frac{x - 2}{2 x^{2} + 4 x + 4} + \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} - \frac{5 \operatorname{atan}{\left(x + 1 \right)}}{2} 
log(2 + x^2 + 2*x)/2 - 5*atan(1 + x)/2 + (-2 + x)/(4 + 2*x^2 + 4*x)
Compilar la expresión [src] 
                          /2*x + 2\                 
   / 2          \   5*atan|-------|                 
log\x  + 2*x + 2/         \   2   /       -2 + x    
----------------- - --------------- + --------------
        2                  2                 2      
                                      4 + 2*x  + 4*x
x−22x2+4x+4+log⁡((x2+2x)+2)2−5atan⁡(2x+22)2\frac{x - 2}{2 x^{2} + 4 x + 4} + \frac{\log{\left(\left(x^{2} + 2 x\right) + 2 \right)}}{2} - \frac{5 \operatorname{atan}{\left(\frac{2 x + 2}{2} \right)}}{2} 
log(x^2 + 2*x + 2)/2 - 5*atan((2*x + 2)/2)/2 + (-2 + x)/(4 + 2*x^2 + 4*x)
Potencias [src] 
   /     2      \                                 
log\2 + x  + 2*x/   5*atan(1 + x)       -2 + x    
----------------- - ------------- + --------------
        2                 2                2      
                                    4 + 2*x  + 4*x
x−22x2+4x+4+log⁡(x2+2x+2)2−5atan⁡(x+1)2\frac{x - 2}{2 x^{2} + 4 x + 4} + \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} - \frac{5 \operatorname{atan}{\left(x + 1 \right)}}{2} 
log(2 + x^2 + 2*x)/2 - 5*atan(1 + x)/2 + (-2 + x)/(4 + 2*x^2 + 4*x)
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