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Simplificación de expresiones/ Descomposición en fracciones simples/ asinh(x/(sqrt(2)*|2*x+1|)-2^(3/2)/|2*x+1|)/3

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

Expresión a simplificar:

Solución

Ha introducido [src] 
     /                      3/2  \
     |       x             2     |
asinh|--------------- - ---------|
     |  ___             |2*x + 1||
     \\/ 2 *|2*x + 1|            /
----------------------------------
                3
$$\frac{\operatorname{asinh}{\left(\frac{x}{\sqrt{2} \left|{2 x + 1}\right|} - \frac{2^{\frac{3}{2}}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(x/((sqrt(2)*|2*x + 1|)) - 2^(3/2)/|2*x + 1|)/3
Simplificación general [src] 
     /  ___         \
     |\/ 2 *(-4 + x)|
asinh|--------------|
     \ 2*|1 + 2*x|  /
---------------------
          3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 4\right)}{2 \left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(sqrt(2)*(-4 + x)/(2*|1 + 2*x|))/3
Descomposición de una fracción [src] 
asinh(-2*sqrt(2)/|2*x + 1| + x*sqrt(2)/(2*|2*x + 1|))/3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2 \sqrt{2}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
     /       ___          ___  \
     |   2*\/ 2       x*\/ 2   |
asinh|- --------- + -----------|
     \  |2*x + 1|   2*|2*x + 1|/
--------------------------------
               3
Respuesta numérica [src] 
0.333333333333333*asinh(x/((sqrt(2)*|2*x + 1|)) - 2^(3/2)/|2*x + 1|)
0.333333333333333*asinh(x/((sqrt(2)*|2*x + 1|)) - 2^(3/2)/|2*x + 1|)
Parte trigonométrica [src] 
     /       ___          ___  \
     |   2*\/ 2       x*\/ 2   |
asinh|- --------- + -----------|
     \  |1 + 2*x|   2*|1 + 2*x|/
--------------------------------
               3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2 \sqrt{2}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(-2*sqrt(2)/|1 + 2*x| + x*sqrt(2)/(2*|1 + 2*x|))/3
Abrimos la expresión [src] 
     /      3/2           ___  \
     |     2          x*\/ 2   |
asinh|- --------- + -----------|
     \  |2*x + 1|   2*|2*x + 1|/
--------------------------------
               3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2^{\frac{3}{2}}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(-2^(3/2)/|2*x + 1| + x*sqrt(2)/(2*|2*x + 1|))/3
Denominador racional [src] 
     /  ___         \
     |\/ 2 *(-4 + x)|
asinh|--------------|
     \ 2*|1 + 2*x|  /
---------------------
          3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 4\right)}{2 \left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(sqrt(2)*(-4 + x)/(2*|1 + 2*x|))/3
Denominador común [src] 
     /       ___          ___  \
     |   2*\/ 2       x*\/ 2   |
asinh|- --------- + -----------|
     \  |1 + 2*x|   2*|1 + 2*x|/
--------------------------------
               3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2 \sqrt{2}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(-2*sqrt(2)/|1 + 2*x| + x*sqrt(2)/(2*|1 + 2*x|))/3
Combinatoria [src] 
     /       ___          ___  \
     |   2*\/ 2       x*\/ 2   |
asinh|- --------- + -----------|
     \  |1 + 2*x|   2*|1 + 2*x|/
--------------------------------
               3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2 \sqrt{2}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(-2*sqrt(2)/|1 + 2*x| + x*sqrt(2)/(2*|1 + 2*x|))/3
Unión de expresiones racionales [src] 
     /  ___         \
     |\/ 2 *(-4 + x)|
asinh|--------------|
     \ 2*|1 + 2*x|  /
---------------------
          3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} \left(x - 4\right)}{2 \left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(sqrt(2)*(-4 + x)/(2*|1 + 2*x|))/3
Potencias [src] 
     /       ___          ___  \
     |   2*\/ 2       x*\/ 2   |
asinh|- --------- + -----------|
     \  |1 + 2*x|   2*|1 + 2*x|/
--------------------------------
               3
$$\frac{\operatorname{asinh}{\left(\frac{\sqrt{2} x}{2 \left|{2 x + 1}\right|} - \frac{2 \sqrt{2}}{\left|{2 x + 1}\right|} \right)}}{3}$$ 
asinh(-2*sqrt(2)/|1 + 2*x| + x*sqrt(2)/(2*|1 + 2*x|))/3
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