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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2-x+1)/2+(7*atan((2*x-1)/sqrt(3)))/sqrt(3)+3/(1+x)

¿Cómo vas a descomponer esta log(x^2-x+1)/2+(7*atan((2*x-1)/sqrt(3)))/sqrt(3)+3/(1+x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                        /2*x - 1\        
                  7*atan|-------|        
   / 2        \         |   ___ |        
log\x  - x + 1/         \ \/ 3  /     3  
--------------- + --------------- + -----
       2                 ___        1 + x
                       \/ 3
$$\left(\frac{\log{\left(\left(x^{2} - x\right) + 1 \right)}}{2} + \frac{7 \operatorname{atan}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{\sqrt{3}}\right) + \frac{3}{x + 1}$$ 
log(x^2 - x + 1)/2 + (7*atan((2*x - 1)/sqrt(3)))/sqrt(3) + 3/(1 + x)
Simplificación general [src] 
             /                                 /  ___           \\
             |     /     2    \        ___     |\/ 3 *(-1 + 2*x)||
18 + (1 + x)*|3*log\1 + x  - x/ + 14*\/ 3 *atan|----------------||
             \                                 \       3        //
------------------------------------------------------------------
                            6*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}\right) + 18}{6 \left(x + 1\right)}$$ 
(18 + (1 + x)*(3*log(1 + x^2 - x) + 14*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)))/(6*(1 + x))
Denominador común [src] 
                                      /    ___         ___\
                              ___     |  \/ 3    2*x*\/ 3 |
   /     2    \           7*\/ 3 *atan|- ----- + ---------|
log\1 + x  - x/     3                 \    3         3    /
--------------- + ----- + ---------------------------------
       2          1 + x                   3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)}}{3} + \frac{3}{x + 1}$$ 
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3)/3
Combinatoria [src] 
                                                            /    ___         ___\                  /    ___         ___\
          /     2    \          /     2    \        ___     |  \/ 3    2*x*\/ 3 |          ___     |  \/ 3    2*x*\/ 3 |
18 + 3*log\1 + x  - x/ + 3*x*log\1 + x  - x/ + 14*\/ 3 *atan|- ----- + ---------| + 14*x*\/ 3 *atan|- ----- + ---------|
                                                            \    3         3    /                  \    3         3    /
------------------------------------------------------------------------------------------------------------------------
                                                       6*(1 + x)
$$\frac{3 x \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 18}{6 \left(x + 1\right)}$$ 
(18 + 3*log(1 + x^2 - x) + 3*x*log(1 + x^2 - x) + 14*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 14*x*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3))/(6*(1 + x))
Unión de expresiones racionales [src] 
             /                                     /  ___           \\
             |                             ___     |\/ 3 *(-1 + 2*x)||
18 + (1 + x)*|3*log(1 + x*(-1 + x)) + 14*\/ 3 *atan|----------------||
             \                                     \       3        //
----------------------------------------------------------------------
                              6*(1 + x)
$$\frac{\left(x + 1\right) \left(3 \log{\left(x \left(x - 1\right) + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}\right) + 18}{6 \left(x + 1\right)}$$ 
(18 + (1 + x)*(3*log(1 + x*(-1 + x)) + 14*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)))/(6*(1 + x))
Denominador racional [src] 
                                                            /    ___         ___\                  /    ___         ___\
          /     2    \          /     2    \        ___     |  \/ 3    2*x*\/ 3 |          ___     |  \/ 3    2*x*\/ 3 |
18 + 3*log\1 + x  - x/ + 3*x*log\1 + x  - x/ + 14*\/ 3 *atan|- ----- + ---------| + 14*x*\/ 3 *atan|- ----- + ---------|
                                                            \    3         3    /                  \    3         3    /
------------------------------------------------------------------------------------------------------------------------
                                                        6 + 6*x
$$\frac{3 x \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} x \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 3 \log{\left(x^{2} - x + 1 \right)} + 14 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} x}{3} - \frac{\sqrt{3}}{3} \right)} + 18}{6 x + 6}$$ 
(18 + 3*log(1 + x^2 - x) + 3*x*log(1 + x^2 - x) + 14*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3) + 14*x*sqrt(3)*atan(-sqrt(3)/3 + 2*x*sqrt(3)/3))/(6 + 6*x)
Parte trigonométrica [src] 
                                      /  ___           \
                              ___     |\/ 3 *(-1 + 2*x)|
   /     2    \           7*\/ 3 *atan|----------------|
log\1 + x  - x/     3                 \       3        /
--------------- + ----- + ------------------------------
       2          1 + x                 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{3} + \frac{3}{x + 1}$$ 
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(sqrt(3)*(-1 + 2*x)/3)/3
Compilar la expresión [src] 
                              ___     /2*x - 1\
                          7*\/ 3 *atan|-------|
   / 2        \                       |   ___ |
log\x  - x + 1/     3                 \ \/ 3  /
--------------- + ----- + ---------------------
       2          1 + x             3
$$\frac{\log{\left(\left(x^{2} - x\right) + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}}{3} + \frac{3}{x + 1}$$ 
log(x^2 - x + 1)/2 + 3/(1 + x) + 7*sqrt(3)*atan((2*x - 1)/sqrt(3))/3
Respuesta numérica [src] 
0.5*log(x^2 - x + 1) + 3.0/(1.0 + x) + 4.04145188432738*atan((2*x - 1)/sqrt(3))
0.5*log(x^2 - x + 1) + 3.0/(1.0 + x) + 4.04145188432738*atan((2*x - 1)/sqrt(3))
Potencias [src] 
                                      /  ___           \
                              ___     |\/ 3 *(-1 + 2*x)|
   /     2    \           7*\/ 3 *atan|----------------|
log\1 + x  - x/     3                 \       3        /
--------------- + ----- + ------------------------------
       2          1 + x                 3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 1\right)}{3} \right)}}{3} + \frac{3}{x + 1}$$ 
                              ___     /  ___ /  1   2*x\\
   /     2    \           7*\/ 3 *atan|\/ 3 *|- - + ---||
log\1 + x  - x/     3                 \      \  3    3 //
--------------- + ----- + -------------------------------
       2          1 + x                  3
$$\frac{\log{\left(x^{2} - x + 1 \right)}}{2} + \frac{7 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{2 x}{3} - \frac{1}{3}\right) \right)}}{3} + \frac{3}{x + 1}$$ 
log(1 + x^2 - x)/2 + 3/(1 + x) + 7*sqrt(3)*atan(sqrt(3)*(-1/3 + 2*x/3))/3
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