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Simplificación de expresiones/ Descomposición en fracciones simples/ asinh((6*x-1)/sqrt(59))/(2*3^(3/2))+sqrt(3*x^2-x+5)/3

¿Cómo vas a descomponer esta asinh((6*x-1)/sqrt(59))/(2*3^(3/2))+sqrt(3*x^2-x+5)/3 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     /6*x - 1\                    
asinh|-------|      ______________
     |   ____|     /    2         
     \ \/ 59 /   \/  3*x  - x + 5 
-------------- + -----------------
       3/2               3        
    2*3
$$\frac{\sqrt{\left(3 x^{2} - x\right) + 5}}{3} + \frac{\operatorname{asinh}{\left(\frac{6 x - 1}{\sqrt{59}} \right)}}{2 \cdot 3^{\frac{3}{2}}}$$ 
asinh((6*x - 1)/sqrt(59))/((2*3^(3/2))) + sqrt(3*x^2 - x + 5)/3
Simplificación general [src] 
                               /  ____           \
   ______________     ___      |\/ 59 *(-1 + 6*x)|
  /            2    \/ 3 *asinh|-----------------|
\/  5 - x + 3*x                \        59       /
----------------- + ------------------------------
        3                         18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{59} \left(6 x - 1\right)}{59} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh(sqrt(59)*(-1 + 6*x)/59)/18
Respuesta numérica [src] 
0.0962250448649376*asinh((6*x - 1)/sqrt(59)) + 0.74535599249993*(1 + 0.6*x^2 - 0.2*x)^0.5
0.0962250448649376*asinh((6*x - 1)/sqrt(59)) + 0.74535599249993*(1 + 0.6*x^2 - 0.2*x)^0.5
Compilar la expresión [src] 
                      ___      /6*x - 1\
   ______________   \/ 3 *asinh|-------|
  /            2               |   ____|
\/  5 - x + 3*x                \ \/ 59 /
----------------- + --------------------
        3                    18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 x - 1}{\sqrt{59}} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh((6*x - 1)/sqrt(59))/18
Potencias [src] 
   ______________     ___      /  ____ /  1    6*x\\
  /            2    \/ 3 *asinh|\/ 59 *|- -- + ---||
\/  5 - x + 3*x                \       \  59    59//
----------------- + --------------------------------
        3                          18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{59} \left(\frac{6 x}{59} - \frac{1}{59}\right) \right)}}{18}$$ 
                               /  ____           \
   ______________     ___      |\/ 59 *(-1 + 6*x)|
  /            2    \/ 3 *asinh|-----------------|
\/  5 - x + 3*x                \        59       /
----------------- + ------------------------------
        3                         18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{59} \left(6 x - 1\right)}{59} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh(sqrt(59)*(-1 + 6*x)/59)/18
Parte trigonométrica [src] 
                               /  ____           \
   ______________     ___      |\/ 59 *(-1 + 6*x)|
  /            2    \/ 3 *asinh|-----------------|
\/  5 - x + 3*x                \        59       /
----------------- + ------------------------------
        3                         18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{59} \left(6 x - 1\right)}{59} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh(sqrt(59)*(-1 + 6*x)/59)/18
Denominador racional [src] 
     ______________              /    ____         ____\
    /            2      ___      |  \/ 59    6*x*\/ 59 |
6*\/  5 - x + 3*x   + \/ 3 *asinh|- ------ + ----------|
                                 \    59         59    /
--------------------------------------------------------
                           18
$$\frac{6 \sqrt{3 x^{2} - x + 5} + \sqrt{3} \operatorname{asinh}{\left(\frac{6 \sqrt{59} x}{59} - \frac{\sqrt{59}}{59} \right)}}{18}$$ 
(6*sqrt(5 - x + 3*x^2) + sqrt(3)*asinh(-sqrt(59)/59 + 6*x*sqrt(59)/59))/18
Denominador común [src] 
                               /    ____         ____\
   ______________     ___      |  \/ 59    6*x*\/ 59 |
  /            2    \/ 3 *asinh|- ------ + ----------|
\/  5 - x + 3*x                \    59         59    /
----------------- + ----------------------------------
        3                           18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 \sqrt{59} x}{59} - \frac{\sqrt{59}}{59} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh(-sqrt(59)/59 + 6*x*sqrt(59)/59)/18
Combinatoria [src] 
                               /    ____         ____\
   ______________     ___      |  \/ 59    6*x*\/ 59 |
  /            2    \/ 3 *asinh|- ------ + ----------|
\/  5 - x + 3*x                \    59         59    /
----------------- + ----------------------------------
        3                           18
$$\frac{\sqrt{3 x^{2} - x + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 \sqrt{59} x}{59} - \frac{\sqrt{59}}{59} \right)}}{18}$$ 
sqrt(5 - x + 3*x^2)/3 + sqrt(3)*asinh(-sqrt(59)/59 + 6*x*sqrt(59)/59)/18
Unión de expresiones racionales [src] 
                                    /  ____           \
    __________________     ___      |\/ 59 *(-1 + 6*x)|
6*\/ 5 + x*(-1 + 3*x)  + \/ 3 *asinh|-----------------|
                                    \        59       /
-------------------------------------------------------
                           18
$$\frac{6 \sqrt{x \left(3 x - 1\right) + 5} + \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{59} \left(6 x - 1\right)}{59} \right)}}{18}$$ 
(6*sqrt(5 + x*(-1 + 3*x)) + sqrt(3)*asinh(sqrt(59)*(-1 + 6*x)/59))/18
Abrimos la expresión [src] 
                      ___      /6*x - 1\
   ______________   \/ 3 *asinh|-------|
  /    2                       |   ____|
\/  3*x  - x + 5               \ \/ 59 /
----------------- + --------------------
        3                    18
$$\frac{\sqrt{\left(3 x^{2} - x\right) + 5}}{3} + \frac{\sqrt{3} \operatorname{asinh}{\left(\frac{6 x - 1}{\sqrt{59}} \right)}}{18}$$ 
sqrt(3*x^2 - x + 5)/3 + sqrt(3)*asinh((6*x - 1)/sqrt(59))/18
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