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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+8*x+21)/2+(8*atan((2*x+8)/(2*sqrt(5))))/sqrt(5)

¿Cómo vas a descomponer esta log(x^2+8*x+21)/2+(8*atan((2*x+8)/(2*sqrt(5))))/sqrt(5) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           /2*x + 8\
                     8*atan|-------|
   / 2           \         |    ___|
log\x  + 8*x + 21/         \2*\/ 5 /
------------------ + ---------------
        2                   ___     
                          \/ 5
$$\frac{\log{\left(\left(x^{2} + 8 x\right) + 21 \right)}}{2} + \frac{8 \operatorname{atan}{\left(\frac{2 x + 8}{2 \sqrt{5}} \right)}}{\sqrt{5}}$$ 
log(x^2 + 8*x + 21)/2 + (8*atan((2*x + 8)/((2*sqrt(5)))))/sqrt(5)
Simplificación general [src] 
                                 /  ___        \
                         ___     |\/ 5 *(4 + x)|
   /      2      \   8*\/ 5 *atan|-------------|
log\21 + x  + 8*x/               \      5      /
------------------ + ---------------------------
        2                         5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 4\right)}{5} \right)}}{5}$$ 
log(21 + x^2 + 8*x)/2 + 8*sqrt(5)*atan(sqrt(5)*(4 + x)/5)/5
Denominador común [src] 
                                 /    ___       ___\
                         ___     |4*\/ 5    x*\/ 5 |
   /      2      \   8*\/ 5 *atan|------- + -------|
log\21 + x  + 8*x/               \   5         5   /
------------------ + -------------------------------
        2                           5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{4 \sqrt{5}}{5} \right)}}{5}$$ 
log(21 + x^2 + 8*x)/2 + 8*sqrt(5)*atan(4*sqrt(5)/5 + x*sqrt(5)/5)/5
Respuesta numérica [src] 
0.5*log(x^2 + 8*x + 21) + 3.57770876399966*atan((2*x + 8)/((2*sqrt(5))))
0.5*log(x^2 + 8*x + 21) + 3.57770876399966*atan((2*x + 8)/((2*sqrt(5))))
Parte trigonométrica [src] 
                                 /  ___          \
                         ___     |\/ 5 *(8 + 2*x)|
   /      2      \   8*\/ 5 *atan|---------------|
log\21 + x  + 8*x/               \       10      /
------------------ + -----------------------------
        2                          5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 8\right)}{10} \right)}}{5}$$ 
log(21 + x^2 + 8*x)/2 + 8*sqrt(5)*atan(sqrt(5)*(8 + 2*x)/10)/5
Potencias [src] 
                                 /  ___          \
                         ___     |\/ 5 *(8 + 2*x)|
   /      2      \   8*\/ 5 *atan|---------------|
log\21 + x  + 8*x/               \       10      /
------------------ + -----------------------------
        2                          5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 8\right)}{10} \right)}}{5}$$ 
                         ___     /  ___ /4   x\\
   /      2      \   8*\/ 5 *atan|\/ 5 *|- + -||
log\21 + x  + 8*x/               \      \5   5//
------------------ + ---------------------------
        2                         5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\sqrt{5} \left(\frac{x}{5} + \frac{4}{5}\right) \right)}}{5}$$ 
log(21 + x^2 + 8*x)/2 + 8*sqrt(5)*atan(sqrt(5)*(4/5 + x/5))/5
Unión de expresiones racionales [src] 
                                     /  ___        \
                             ___     |\/ 5 *(4 + x)|
5*log(21 + x*(8 + x)) + 16*\/ 5 *atan|-------------|
                                     \      5      /
----------------------------------------------------
                         10
$$\frac{5 \log{\left(x \left(x + 8\right) + 21 \right)} + 16 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(x + 4\right)}{5} \right)}}{10}$$ 
(5*log(21 + x*(8 + x)) + 16*sqrt(5)*atan(sqrt(5)*(4 + x)/5))/10
Denominador racional [src] 
                                    /    ___       ___\
     /      2      \        ___     |4*\/ 5    x*\/ 5 |
5*log\21 + x  + 8*x/ + 16*\/ 5 *atan|------- + -------|
                                    \   5         5   /
-------------------------------------------------------
                           10
$$\frac{5 \log{\left(x^{2} + 8 x + 21 \right)} + 16 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{4 \sqrt{5}}{5} \right)}}{10}$$ 
(5*log(21 + x^2 + 8*x) + 16*sqrt(5)*atan(4*sqrt(5)/5 + x*sqrt(5)/5))/10
Combinatoria [src] 
                                 /    ___       ___\
                         ___     |4*\/ 5    x*\/ 5 |
   /      2      \   8*\/ 5 *atan|------- + -------|
log\21 + x  + 8*x/               \   5         5   /
------------------ + -------------------------------
        2                           5
$$\frac{\log{\left(x^{2} + 8 x + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} + \frac{4 \sqrt{5}}{5} \right)}}{5}$$ 
log(21 + x^2 + 8*x)/2 + 8*sqrt(5)*atan(4*sqrt(5)/5 + x*sqrt(5)/5)/5
Abrimos la expresión [src] 
   / 2           \       ___     /  ___          \
log\x  + 8*x + 21/     \/ 5      |\/ 5 *(2*x + 8)|
------------------ + 8*-----*atan|---------------|
        2                5       \       10      /
$$\frac{\log{\left(\left(x^{2} + 8 x\right) + 21 \right)}}{2} + 8 \frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 x + 8\right)}{10} \right)}$$ 
log(x^2 + 8*x + 21)/2 + 8*(sqrt(5)/5)*atan(sqrt(5)*(2*x + 8)/10)
Compilar la expresión [src] 
                         ___     /2*x + 8\
                     8*\/ 5 *atan|-------|
   / 2           \               |    ___|
log\x  + 8*x + 21/               \2*\/ 5 /
------------------ + ---------------------
        2                      5
$$\frac{\log{\left(\left(x^{2} + 8 x\right) + 21 \right)}}{2} + \frac{8 \sqrt{5} \operatorname{atan}{\left(\frac{2 x + 8}{2 \sqrt{5}} \right)}}{5}$$ 
log(x^2 + 8*x + 21)/2 + 8*sqrt(5)*atan((2*x + 8)/((2*sqrt(5))))/5
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