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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                        /2*x + 2\
                    atan|-------|
   / 2          \       |    ___|
log\x  + 2*x + 4/       \2*\/ 3 /
----------------- - -------------
        2                 ___    
                        \/ 3
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 4 \right)}}{2} - \frac{\operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
log(x^2 + 2*x + 4)/2 - atan((2*x + 2)/((2*sqrt(3))))/sqrt(3)
Simplificación general [src] 
                              /  ___        \
                      ___     |\/ 3 *(1 + x)|
   /     2      \   \/ 3 *atan|-------------|
log\4 + x  + 2*x/             \      3      /
----------------- - -------------------------
        2                       3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{3}$$ 
log(4 + x^2 + 2*x)/2 - sqrt(3)*atan(sqrt(3)*(1 + x)/3)/3
Respuesta numérica [src] 
0.5*log(x^2 + 2*x + 4) - 0.577350269189626*atan((2*x + 2)/((2*sqrt(3))))
0.5*log(x^2 + 2*x + 4) - 0.577350269189626*atan((2*x + 2)/((2*sqrt(3))))
Combinatoria [src] 
                              /  ___       ___\
                      ___     |\/ 3    x*\/ 3 |
   /     2      \   \/ 3 *atan|----- + -------|
log\4 + x  + 2*x/             \  3        3   /
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$ 
log(4 + x^2 + 2*x)/2 - sqrt(3)*atan(sqrt(3)/3 + x*sqrt(3)/3)/3
Potencias [src] 
                      ___     /  ___ /1   x\\
   /     2      \   \/ 3 *atan|\/ 3 *|- + -||
log\4 + x  + 2*x/             \      \3   3//
----------------- - -------------------------
        2                       3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{x}{3} + \frac{1}{3}\right) \right)}}{3}$$ 
                              /  ___          \
                      ___     |\/ 3 *(2 + 2*x)|
   /     2      \   \/ 3 *atan|---------------|
log\4 + x  + 2*x/             \       6       /
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 2\right)}{6} \right)}}{3}$$ 
log(4 + x^2 + 2*x)/2 - sqrt(3)*atan(sqrt(3)*(2 + 2*x)/6)/3
Denominador racional [src] 
                                  /  ___       ___\
     /     2      \       ___     |\/ 3    x*\/ 3 |
3*log\4 + x  + 2*x/ - 2*\/ 3 *atan|----- + -------|
                                  \  3        3   /
---------------------------------------------------
                         6
$$\frac{3 \log{\left(x^{2} + 2 x + 4 \right)} - 2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{6}$$ 
(3*log(4 + x^2 + 2*x) - 2*sqrt(3)*atan(sqrt(3)/3 + x*sqrt(3)/3))/6
Denominador común [src] 
                              /  ___       ___\
                      ___     |\/ 3    x*\/ 3 |
   /     2      \   \/ 3 *atan|----- + -------|
log\4 + x  + 2*x/             \  3        3   /
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3}$$ 
log(4 + x^2 + 2*x)/2 - sqrt(3)*atan(sqrt(3)/3 + x*sqrt(3)/3)/3
Unión de expresiones racionales [src] 
                                   /  ___        \
                           ___     |\/ 3 *(1 + x)|
3*log(4 + x*(2 + x)) - 2*\/ 3 *atan|-------------|
                                   \      3      /
--------------------------------------------------
                        6
$$\frac{3 \log{\left(x \left(x + 2\right) + 4 \right)} - 2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 1\right)}{3} \right)}}{6}$$ 
(3*log(4 + x*(2 + x)) - 2*sqrt(3)*atan(sqrt(3)*(1 + x)/3))/6
Parte trigonométrica [src] 
                              /  ___          \
                      ___     |\/ 3 *(2 + 2*x)|
   /     2      \   \/ 3 *atan|---------------|
log\4 + x  + 2*x/             \       6       /
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 2 x + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 2\right)}{6} \right)}}{3}$$ 
log(4 + x^2 + 2*x)/2 - sqrt(3)*atan(sqrt(3)*(2 + 2*x)/6)/3
Compilar la expresión [src] 
                      ___     /2*x + 2\
                    \/ 3 *atan|-------|
   / 2          \             |    ___|
log\x  + 2*x + 4/             \2*\/ 3 /
----------------- - -------------------
        2                    3
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 4 \right)}}{2} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{3}} \right)}}{3}$$ 
log(x^2 + 2*x + 4)/2 - sqrt(3)*atan((2*x + 2)/((2*sqrt(3))))/3
Abrimos la expresión [src] 
   / 2          \     ___     /  ___          \
log\x  + 2*x + 4/   \/ 3      |\/ 3 *(2*x + 2)|
----------------- - -----*atan|---------------|
        2             3       \       6       /
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 4 \right)}}{2} - \frac{\sqrt{3}}{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 2\right)}{6} \right)}$$ 
log(x^2 + 2*x + 4)/2 - sqrt(3)/3*atan(sqrt(3)*(2*x + 2)/6)
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