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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+4*x+7)/2-(2*atan((2*x+4)/(2*sqrt(3))))/sqrt(3)

¿Cómo vas a descomponer esta log(x^2+4*x+7)/2-(2*atan((2*x+4)/(2*sqrt(3))))/sqrt(3) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                          /2*x + 4\
                    2*atan|-------|
   / 2          \         |    ___|
log\x  + 4*x + 7/         \2*\/ 3 /
----------------- - ---------------
        2                  ___     
                         \/ 3
$$\frac{\log{\left(\left(x^{2} + 4 x\right) + 7 \right)}}{2} - \frac{2 \operatorname{atan}{\left(\frac{2 x + 4}{2 \sqrt{3}} \right)}}{\sqrt{3}}$$ 
log(x^2 + 4*x + 7)/2 - 2*atan((2*x + 4)/((2*sqrt(3))))/sqrt(3)
Simplificación general [src] 
                                /  ___        \
                        ___     |\/ 3 *(2 + x)|
   /     2      \   2*\/ 3 *atan|-------------|
log\7 + x  + 4*x/               \      3      /
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3} \right)}}{3}$$ 
log(7 + x^2 + 4*x)/2 - 2*sqrt(3)*atan(sqrt(3)*(2 + x)/3)/3
Respuesta numérica [src] 
0.5*log(x^2 + 4*x + 7) - 1.15470053837925*atan((2*x + 4)/((2*sqrt(3))))
0.5*log(x^2 + 4*x + 7) - 1.15470053837925*atan((2*x + 4)/((2*sqrt(3))))
Denominador racional [src] 
                                  /    ___       ___\
     /     2      \       ___     |2*\/ 3    x*\/ 3 |
3*log\7 + x  + 4*x/ - 4*\/ 3 *atan|------- + -------|
                                  \   3         3   /
-----------------------------------------------------
                          6
$$\frac{3 \log{\left(x^{2} + 4 x + 7 \right)} - 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{6}$$ 
(3*log(7 + x^2 + 4*x) - 4*sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3))/6
Parte trigonométrica [src] 
                                /  ___          \
                        ___     |\/ 3 *(4 + 2*x)|
   /     2      \   2*\/ 3 *atan|---------------|
log\7 + x  + 4*x/               \       6       /
----------------- - -----------------------------
        2                         3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}}{3}$$ 
log(7 + x^2 + 4*x)/2 - 2*sqrt(3)*atan(sqrt(3)*(4 + 2*x)/6)/3
Denominador común [src] 
                                /    ___       ___\
                        ___     |2*\/ 3    x*\/ 3 |
   /     2      \   2*\/ 3 *atan|------- + -------|
log\7 + x  + 4*x/               \   3         3   /
----------------- - -------------------------------
        2                          3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
log(7 + x^2 + 4*x)/2 - 2*sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3)/3
Unión de expresiones racionales [src] 
                                   /  ___        \
                           ___     |\/ 3 *(2 + x)|
3*log(7 + x*(4 + x)) - 4*\/ 3 *atan|-------------|
                                   \      3      /
--------------------------------------------------
                        6
$$\frac{3 \log{\left(x \left(x + 4\right) + 7 \right)} - 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(x + 2\right)}{3} \right)}}{6}$$ 
(3*log(7 + x*(4 + x)) - 4*sqrt(3)*atan(sqrt(3)*(2 + x)/3))/6
Combinatoria [src] 
                                /    ___       ___\
                        ___     |2*\/ 3    x*\/ 3 |
   /     2      \   2*\/ 3 *atan|------- + -------|
log\7 + x  + 4*x/               \   3         3   /
----------------- - -------------------------------
        2                          3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} + \frac{2 \sqrt{3}}{3} \right)}}{3}$$ 
log(7 + x^2 + 4*x)/2 - 2*sqrt(3)*atan(2*sqrt(3)/3 + x*sqrt(3)/3)/3
Potencias [src] 
                        ___     /  ___ /2   x\\
   /     2      \   2*\/ 3 *atan|\/ 3 *|- + -||
log\7 + x  + 4*x/               \      \3   3//
----------------- - ---------------------------
        2                        3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\sqrt{3} \left(\frac{x}{3} + \frac{2}{3}\right) \right)}}{3}$$ 
                                /  ___          \
                        ___     |\/ 3 *(4 + 2*x)|
   /     2      \   2*\/ 3 *atan|---------------|
log\7 + x  + 4*x/               \       6       /
----------------- - -----------------------------
        2                         3
$$\frac{\log{\left(x^{2} + 4 x + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}}{3}$$ 
log(7 + x^2 + 4*x)/2 - 2*sqrt(3)*atan(sqrt(3)*(4 + 2*x)/6)/3
Compilar la expresión [src] 
                        ___     /2*x + 4\
                    2*\/ 3 *atan|-------|
   / 2          \               |    ___|
log\x  + 4*x + 7/               \2*\/ 3 /
----------------- - ---------------------
        2                     3
$$\frac{\log{\left(\left(x^{2} + 4 x\right) + 7 \right)}}{2} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 x + 4}{2 \sqrt{3}} \right)}}{3}$$ 
log(x^2 + 4*x + 7)/2 - 2*sqrt(3)*atan((2*x + 4)/((2*sqrt(3))))/3
Abrimos la expresión [src] 
   / 2          \       ___     /  ___          \
log\x  + 4*x + 7/     \/ 3      |\/ 3 *(2*x + 4)|
----------------- - 2*-----*atan|---------------|
        2               3       \       6       /
$$\frac{\log{\left(\left(x^{2} + 4 x\right) + 7 \right)}}{2} - 2 \frac{\sqrt{3}}{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 x + 4\right)}{6} \right)}$$ 
log(x^2 + 4*x + 7)/2 - 2*sqrt(3)/3*atan(sqrt(3)*(2*x + 4)/6)
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