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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+2*x+6)/2-atan((2*x+2)/(2*sqrt(5)))/sqrt(5)

¿Cómo vas a descomponer esta log(x^2+2*x+6)/2-atan((2*x+2)/(2*sqrt(5)))/sqrt(5) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                        /2*x + 2\
                    atan|-------|
   / 2          \       |    ___|
log\x  + 2*x + 6/       \2*\/ 5 /
----------------- - -------------
        2                 ___    
                        \/ 5
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 6 \right)}}{2} - \frac{\operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{5}} \right)}}{\sqrt{5}}$$ 
log(x^2 + 2*x + 6)/2 - atan((2*x + 2)/((2*sqrt(5))))/sqrt(5)
Simplificación general [src] 
                              /  ___        \
                      ___     |\/ 5 *(1 + x)|
   /     2      \   \/ 5 *atan|-------------|
log\6 + x  + 2*x/             \      5      /
----------------- - -------------------------
        2                       5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 1\right)}{5} \right)}}{5}$$ 
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(1 + x)/5)/5
Respuesta numérica [src] 
0.5*log(x^2 + 2*x + 6) - 0.447213595499958*atan((2*x + 2)/((2*sqrt(5))))
0.5*log(x^2 + 2*x + 6) - 0.447213595499958*atan((2*x + 2)/((2*sqrt(5))))
Parte trigonométrica [src] 
                              /  ___          \
                      ___     |\/ 5 *(2 + 2*x)|
   /     2      \   \/ 5 *atan|---------------|
log\6 + x  + 2*x/             \       10      /
----------------- - ---------------------------
        2                        5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 2\right)}{10} \right)}}{5}$$ 
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(2 + 2*x)/10)/5
Denominador racional [src] 
                                  /  ___       ___\
     /     2      \       ___     |\/ 5    x*\/ 5 |
5*log\6 + x  + 2*x/ - 2*\/ 5 *atan|----- + -------|
                                  \  5        5   /
---------------------------------------------------
                         10
$$\frac{5 \log{\left(x^{2} + 2 x + 6 \right)} - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{10}$$ 
(5*log(6 + x^2 + 2*x) - 2*sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5))/10
Potencias [src] 
                      ___     /  ___ /1   x\\
   /     2      \   \/ 5 *atan|\/ 5 *|- + -||
log\6 + x  + 2*x/             \      \5   5//
----------------- - -------------------------
        2                       5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \left(\frac{x}{5} + \frac{1}{5}\right) \right)}}{5}$$ 
                              /  ___          \
                      ___     |\/ 5 *(2 + 2*x)|
   /     2      \   \/ 5 *atan|---------------|
log\6 + x  + 2*x/             \       10      /
----------------- - ---------------------------
        2                        5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 2\right)}{10} \right)}}{5}$$ 
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)*(2 + 2*x)/10)/5
Denominador común [src] 
                              /  ___       ___\
                      ___     |\/ 5    x*\/ 5 |
   /     2      \   \/ 5 *atan|----- + -------|
log\6 + x  + 2*x/             \  5        5   /
----------------- - ---------------------------
        2                        5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{5}$$ 
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5)/5
Combinatoria [src] 
                              /  ___       ___\
                      ___     |\/ 5    x*\/ 5 |
   /     2      \   \/ 5 *atan|----- + -------|
log\6 + x  + 2*x/             \  5        5   /
----------------- - ---------------------------
        2                        5
$$\frac{\log{\left(x^{2} + 2 x + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \right)}}{5}$$ 
log(6 + x^2 + 2*x)/2 - sqrt(5)*atan(sqrt(5)/5 + x*sqrt(5)/5)/5
Unión de expresiones racionales [src] 
                                   /  ___        \
                           ___     |\/ 5 *(1 + x)|
5*log(6 + x*(2 + x)) - 2*\/ 5 *atan|-------------|
                                   \      5      /
--------------------------------------------------
                        10
$$\frac{5 \log{\left(x \left(x + 2\right) + 6 \right)} - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 1\right)}{5} \right)}}{10}$$ 
(5*log(6 + x*(2 + x)) - 2*sqrt(5)*atan(sqrt(5)*(1 + x)/5))/10
Compilar la expresión [src] 
                      ___     /2*x + 2\
                    \/ 5 *atan|-------|
   / 2          \             |    ___|
log\x  + 2*x + 6/             \2*\/ 5 /
----------------- - -------------------
        2                    5
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 6 \right)}}{2} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 x + 2}{2 \sqrt{5}} \right)}}{5}$$ 
log(x^2 + 2*x + 6)/2 - sqrt(5)*atan((2*x + 2)/((2*sqrt(5))))/5
Abrimos la expresión [src] 
   / 2          \     ___     /  ___          \
log\x  + 2*x + 6/   \/ 5      |\/ 5 *(2*x + 2)|
----------------- - -----*atan|---------------|
        2             5       \       10      /
$$\frac{\log{\left(\left(x^{2} + 2 x\right) + 6 \right)}}{2} - \frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 2\right)}{10} \right)}$$ 
log(x^2 + 2*x + 6)/2 - sqrt(5)/5*atan(sqrt(5)*(2*x + 2)/10)
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