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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                      __________
     /  ___  \       /    2     
asinh\\/ 3 *x/   x*\/  3*x  + 1 
-------------- + ---------------
       ___              2       
   2*\/ 3
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(\sqrt{3} x \right)}}{2 \sqrt{3}}$$ 
asinh(sqrt(3)*x)/((2*sqrt(3))) + (x*sqrt(3*x^2 + 1))/2
Simplificación general [src] 
     __________                       
    /        2      ___      /    ___\
x*\/  1 + 3*x     \/ 3 *asinh\x*\/ 3 /
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(x*sqrt(3))/6
Respuesta numérica [src] 
0.288675134594813*asinh(sqrt(3)*x) + 0.866025403784439*x*(0.333333333333333 + x^2)^0.5
0.288675134594813*asinh(sqrt(3)*x) + 0.866025403784439*x*(0.333333333333333 + x^2)^0.5
Denominador racional [src] 
                              __________
  ___      /    ___\         /        2 
\/ 3 *asinh\x*\/ 3 / + 3*x*\/  1 + 3*x  
----------------------------------------
                   6
$$\frac{3 x \sqrt{3 x^{2} + 1} + \sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
(sqrt(3)*asinh(x*sqrt(3)) + 3*x*sqrt(1 + 3*x^2))/6
Denominador común [src] 
     __________                       
    /        2      ___      /    ___\
x*\/  1 + 3*x     \/ 3 *asinh\x*\/ 3 /
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(x*sqrt(3))/6
Potencias [src] 
     __________                       
    /        2      ___      /    ___\
x*\/  1 + 3*x     \/ 3 *asinh\x*\/ 3 /
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(x*sqrt(3))/6
Parte trigonométrica [src] 
     __________                       
    /        2      ___      /    ___\
x*\/  1 + 3*x     \/ 3 *asinh\x*\/ 3 /
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(x*sqrt(3))/6
Unión de expresiones racionales [src] 
                              __________
  ___      /    ___\         /        2 
\/ 3 *asinh\x*\/ 3 / + 3*x*\/  1 + 3*x  
----------------------------------------
                   6
$$\frac{3 x \sqrt{3 x^{2} + 1} + \sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
(sqrt(3)*asinh(x*sqrt(3)) + 3*x*sqrt(1 + 3*x^2))/6
Compilar la expresión [src] 
     __________                       
    /        2      ___      /  ___  \
x*\/  1 + 3*x     \/ 3 *asinh\\/ 3 *x/
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(sqrt(3)*x)/6
Combinatoria [src] 
     __________                       
    /        2      ___      /    ___\
x*\/  1 + 3*x     \/ 3 *asinh\x*\/ 3 /
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
x*sqrt(1 + 3*x^2)/2 + sqrt(3)*asinh(x*sqrt(3))/6
Abrimos la expresión [src] 
     __________                       
    /    2          ___      /  ___  \
x*\/  3*x  + 1    \/ 3 *asinh\\/ 3 *x/
--------------- + --------------------
       2                   6
$$\frac{x \sqrt{3 x^{2} + 1}}{2} + \frac{\sqrt{3} \operatorname{asinh}{\left(\sqrt{3} x \right)}}{6}$$ 
(x*sqrt(3*x^2 + 1))/2 + sqrt(3)*asinh(sqrt(3)*x)/6
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