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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+3)/8-(3*log(x+1))/8+atan(x/sqrt(3))/(2*sqrt(3))+log(x-1)/8

¿Cómo vas a descomponer esta log(x^2+3)/8-(3*log(x+1))/8+atan(x/sqrt(3))/(2*sqrt(3))+log(x-1)/8 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                                 /  x  \             
                             atan|-----|             
   / 2    \                      |  ___|             
log\x  + 3/   3*log(x + 1)       \\/ 3 /   log(x - 1)
----------- - ------------ + ----------- + ----------
     8             8               ___         8     
                               2*\/ 3
$$\left(\left(- \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8}\right) + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{3}} \right)}}{2 \sqrt{3}}\right) + \frac{\log{\left(x - 1 \right)}}{8}$$ 
log(x^2 + 3)/8 - 3*log(x + 1)/8 + atan(x/sqrt(3))/((2*sqrt(3))) + log(x - 1)/8
Simplificación general [src] 
                                                       /    ___\
                                               ___     |x*\/ 3 |
                                  /     2\   \/ 3 *atan|-------|
  3*log(1 + x)   log(-1 + x)   log\3 + x /             \   3   /
- ------------ + ----------- + ----------- + -------------------
       8              8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}$$ 
-3*log(1 + x)/8 + log(-1 + x)/8 + log(3 + x^2)/8 + sqrt(3)*atan(x*sqrt(3)/3)/6
Respuesta numérica [src] 
0.125*log(x - 1) + 0.125*log(x^2 + 3) + 0.288675134594813*atan(x/sqrt(3)) - 0.375*log(x + 1)
0.125*log(x - 1) + 0.125*log(x^2 + 3) + 0.288675134594813*atan(x/sqrt(3)) - 0.375*log(x + 1)
Parte trigonométrica [src] 
                                                       /    ___\
                                               ___     |x*\/ 3 |
                                  /     2\   \/ 3 *atan|-------|
  3*log(1 + x)   log(-1 + x)   log\3 + x /             \   3   /
- ------------ + ----------- + ----------- + -------------------
       8              8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}$$ 
-3*log(1 + x)/8 + log(-1 + x)/8 + log(3 + x^2)/8 + sqrt(3)*atan(x*sqrt(3)/3)/6
Denominador común [src] 
                                                       /    ___\
                                               ___     |x*\/ 3 |
                                  /     2\   \/ 3 *atan|-------|
  3*log(1 + x)   log(-1 + x)   log\3 + x /             \   3   /
- ------------ + ----------- + ----------- + -------------------
       8              8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}$$ 
-3*log(1 + x)/8 + log(-1 + x)/8 + log(3 + x^2)/8 + sqrt(3)*atan(x*sqrt(3)/3)/6
Denominador racional [src] 
                                                            /    ___\
                                     /     2\       ___     |x*\/ 3 |
-9*log(1 + x) + 3*log(-1 + x) + 3*log\3 + x / + 4*\/ 3 *atan|-------|
                                                            \   3   /
---------------------------------------------------------------------
                                  24
$$\frac{3 \log{\left(x - 1 \right)} - 9 \log{\left(x + 1 \right)} + 3 \log{\left(x^{2} + 3 \right)} + 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{24}$$ 
(-9*log(1 + x) + 3*log(-1 + x) + 3*log(3 + x^2) + 4*sqrt(3)*atan(x*sqrt(3)/3))/24
Potencias [src] 
                                                       /    ___\
                                               ___     |x*\/ 3 |
                                  /     2\   \/ 3 *atan|-------|
  3*log(1 + x)   log(-1 + x)   log\3 + x /             \   3   /
- ------------ + ----------- + ----------- + -------------------
       8              8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}$$ 
-3*log(1 + x)/8 + log(-1 + x)/8 + log(3 + x^2)/8 + sqrt(3)*atan(x*sqrt(3)/3)/6
Combinatoria [src] 
                                                       /    ___\
                                               ___     |x*\/ 3 |
                                  /     2\   \/ 3 *atan|-------|
  3*log(1 + x)   log(-1 + x)   log\3 + x /             \   3   /
- ------------ + ----------- + ----------- + -------------------
       8              8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{6}$$ 
-3*log(1 + x)/8 + log(-1 + x)/8 + log(3 + x^2)/8 + sqrt(3)*atan(x*sqrt(3)/3)/6
Unión de expresiones racionales [src] 
                                                            /    ___\
                                     /     2\       ___     |x*\/ 3 |
-9*log(1 + x) + 3*log(-1 + x) + 3*log\3 + x / + 4*\/ 3 *atan|-------|
                                                            \   3   /
---------------------------------------------------------------------
                                  24
$$\frac{3 \log{\left(x - 1 \right)} - 9 \log{\left(x + 1 \right)} + 3 \log{\left(x^{2} + 3 \right)} + 4 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}}{24}$$ 
(-9*log(1 + x) + 3*log(-1 + x) + 3*log(3 + x^2) + 4*sqrt(3)*atan(x*sqrt(3)/3))/24
Abrimos la expresión [src] 
                                            ___     /  x  \
                                          \/ 3 *atan|-----|
                / 2    \                            |  ___|
log(x - 1)   log\x  + 3/   3*log(x + 1)             \\/ 3 /
---------- + ----------- - ------------ + -----------------
    8             8             8                 6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{x}{\sqrt{3}} \right)}}{6}$$ 
log(x - 1)/8 + log(x^2 + 3)/8 - 3*log(x + 1)/8 + sqrt(3)*atan(x/sqrt(3))/6
Compilar la expresión [src] 
                                              ___     /  x  \
                                            \/ 3 *atan|-----|
                                 / 2    \             |  ___|
  3*log(x + 1)   log(x - 1)   log\x  + 3/             \\/ 3 /
- ------------ + ---------- + ----------- + -----------------
       8             8             8                6
$$\frac{\log{\left(x - 1 \right)}}{8} - \frac{3 \log{\left(x + 1 \right)}}{8} + \frac{\log{\left(x^{2} + 3 \right)}}{8} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{x}{\sqrt{3}} \right)}}{6}$$ 
-3*log(x + 1)/8 + log(x - 1)/8 + log(x^2 + 3)/8 + sqrt(3)*atan(x/sqrt(3))/6
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