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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2-8*x+28)/2+(2*atan((2*x-8)/(4*sqrt(3))))/sqrt(3)

¿Cómo vas a descomponer esta log(x^2-8*x+28)/2+(2*atan((2*x-8)/(4*sqrt(3))))/sqrt(3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           /2*x - 8\
                     2*atan|-------|
   / 2           \         |    ___|
log\x  - 8*x + 28/         \4*\/ 3 /
------------------ + ---------------
        2                   ___     
                          \/ 3
$$\frac{\log{\left(\left(x^{2} - 8 x\right) + 28 \right)}}{2} + \frac{2 \operatorname{atan}{\left(\frac{2 x - 8}{4 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
log(x^2 - 8*x + 28)/2 + (2*atan((2*x - 8)/((4*sqrt(3)))))/sqrt(3)
Simplificación general [src] 
                                 /  ___         \
                         ___     |\/ 3 *(-4 + x)|
   /      2      \   2*\/ 3 *atan|--------------|
log\28 + x  - 8*x/               \      6       /
------------------ + ----------------------------
        2                         3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x - 4\right)}{6} \right)}}{3}$$ 
log(28 + x^2 - 8*x)/2 + 2*sqrt(3)*atan(sqrt(3)*(-4 + x)/6)/3
Respuesta numérica [src] 
0.5*log(x^2 - 8*x + 28) + 1.15470053837925*atan((2*x - 8)/((4*sqrt(3))))
0.5*log(x^2 - 8*x + 28) + 1.15470053837925*atan((2*x - 8)/((4*sqrt(3))))
Parte trigonométrica [src] 
                                 /  ___           \
                         ___     |\/ 3 *(-8 + 2*x)|
   /      2      \   2*\/ 3 *atan|----------------|
log\28 + x  - 8*x/               \       12       /
------------------ + ------------------------------
        2                          3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 8\right)}{12} \right)}}{3}$$ 
log(28 + x^2 - 8*x)/2 + 2*sqrt(3)*atan(sqrt(3)*(-8 + 2*x)/12)/3
Denominador común [src] 
                                 /      ___       ___\
                         ___     |  2*\/ 3    x*\/ 3 |
   /      2      \   2*\/ 3 *atan|- ------- + -------|
log\28 + x  - 8*x/               \     3         6   /
------------------ + ---------------------------------
        2                            3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{6} - \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
log(28 + x^2 - 8*x)/2 + 2*sqrt(3)*atan(-2*sqrt(3)/3 + x*sqrt(3)/6)/3
Combinatoria [src] 
                                 /      ___       ___\
                         ___     |  2*\/ 3    x*\/ 3 |
   /      2      \   2*\/ 3 *atan|- ------- + -------|
log\28 + x  - 8*x/               \     3         6   /
------------------ + ---------------------------------
        2                            3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{6} - \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
log(28 + x^2 - 8*x)/2 + 2*sqrt(3)*atan(-2*sqrt(3)/3 + x*sqrt(3)/6)/3
Compilar la expresión [src] 
                         ___     /2*x - 8\
                     2*\/ 3 *atan|-------|
   / 2           \               |    ___|
log\x  - 8*x + 28/               \4*\/ 3 /
------------------ + ---------------------
        2                      3
$$\frac{\log{\left(\left(x^{2} - 8 x\right) + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 x - 8}{4 \sqrt{3}} \right)}}{3}$$ 
log(x^2 - 8*x + 28)/2 + 2*sqrt(3)*atan((2*x - 8)/((4*sqrt(3))))/3
Potencias [src] 
                                 /  ___           \
                         ___     |\/ 3 *(-8 + 2*x)|
   /      2      \   2*\/ 3 *atan|----------------|
log\28 + x  - 8*x/               \       12       /
------------------ + ------------------------------
        2                          3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 8\right)}{12} \right)}}{3}$$ 
                         ___     /  ___ /  2   x\\
   /      2      \   2*\/ 3 *atan|\/ 3 *|- - + -||
log\28 + x  - 8*x/               \      \  3   6//
------------------ + -----------------------------
        2                          3
$$\frac{\log{\left(x^{2} - 8 x + 28 \right)}}{2} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{x}{6} - \frac{2}{3}\right) \right)}}{3}$$ 
log(28 + x^2 - 8*x)/2 + 2*sqrt(3)*atan(sqrt(3)*(-2/3 + x/6))/3
Unión de expresiones racionales [src] 
                                     /  ___         \
                             ___     |\/ 3 *(-4 + x)|
3*log(28 + x*(-8 + x)) + 4*\/ 3 *atan|--------------|
                                     \      6       /
-----------------------------------------------------
                          6
$$\frac{3 \log{\left(x \left(x - 8\right) + 28 \right)} + 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x - 4\right)}{6} \right)}}{6}$$ 
(3*log(28 + x*(-8 + x)) + 4*sqrt(3)*atan(sqrt(3)*(-4 + x)/6))/6
Denominador racional [src] 
                                   /      ___       ___\
     /      2      \       ___     |  2*\/ 3    x*\/ 3 |
3*log\28 + x  - 8*x/ + 4*\/ 3 *atan|- ------- + -------|
                                   \     3         6   /
--------------------------------------------------------
                           6
$$\frac{3 \log{\left(x^{2} - 8 x + 28 \right)} + 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{6} - \frac{2 \sqrt{3}}{3} \right)}}{6}$$ 
(3*log(28 + x^2 - 8*x) + 4*sqrt(3)*atan(-2*sqrt(3)/3 + x*sqrt(3)/6))/6
Abrimos la expresión [src] 
   / 2           \       ___     /  ___          \
log\x  - 8*x + 28/     \/ 3      |\/ 3 *(2*x - 8)|
------------------ + 2*-----*atan|---------------|
        2                3       \       12      /
$$\frac{\log{\left(\left(x^{2} - 8 x\right) + 28 \right)}}{2} + 2 \frac{\sqrt{3}}{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x - 8\right)}{12} \right)}$$ 
log(x^2 - 8*x + 28)/2 + 2*(sqrt(3)/3)*atan(sqrt(3)*(2*x - 8)/12)
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