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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)^4/(2*sqrt(x)*sqrt(1-x))+4*log(x)^3*asin(sqrt(x))/x

¿Cómo vas a descomponer esta log(x)^4/(2*sqrt(x)*sqrt(1-x))+4*log(x)^3*asin(sqrt(x))/x expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
        4                3        /  ___\
     log (x)        4*log (x)*asin\\/ x /
----------------- + ---------------------
    ___   _______             x          
2*\/ x *\/ 1 - x
$$\frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}} + \frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x}$$ 
log(x)^4/(((2*sqrt(x))*sqrt(1 - x))) + ((4*log(x)^3)*asin(sqrt(x)))/x
Simplificación general [src] 
        4                3        /  ___\
     log (x)        4*log (x)*asin\\/ x /
----------------- + ---------------------
    ___   _______             x          
2*\/ x *\/ 1 - x
$$\frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}}$$ 
log(x)^4/(2*sqrt(x)*sqrt(1 - x)) + 4*log(x)^3*asin(sqrt(x))/x
Combinatoria [src] 
   3    /               ___   _______     /  ___\\
log (x)*\x*log(x) + 8*\/ x *\/ 1 - x *asin\\/ x //
--------------------------------------------------
                    3/2   _______                 
                 2*x   *\/ 1 - x
$$\frac{\left(8 \sqrt{x} \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} + x \log{\left(x \right)}\right) \log{\left(x \right)}^{3}}{2 x^{\frac{3}{2}} \sqrt{1 - x}}$$ 
log(x)^3*(x*log(x) + 8*sqrt(x)*sqrt(1 - x)*asin(sqrt(x)))/(2*x^(3/2)*sqrt(1 - x))
Potencias [src] 
       4               3        /  ___\
    log (x)       4*log (x)*asin\\/ x /
--------------- + ---------------------
    ___________             x          
2*\/ x*(1 - x)
$$\frac{\log{\left(x \right)}^{4}}{2 \sqrt{x \left(1 - x\right)}} + \frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x}$$ 
        4                3        /  ___\
     log (x)        4*log (x)*asin\\/ x /
----------------- + ---------------------
    ___   _______             x          
2*\/ x *\/ 1 - x
$$\frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}}$$ 
log(x)^4/(2*sqrt(x)*sqrt(1 - x)) + 4*log(x)^3*asin(sqrt(x))/x
Parte trigonométrica [src] 
        4                3        /  ___\
     log (x)        4*log (x)*asin\\/ x /
----------------- + ---------------------
    ___   _______             x          
2*\/ x *\/ 1 - x
$$\frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}}$$ 
log(x)^4/(2*sqrt(x)*sqrt(1 - x)) + 4*log(x)^3*asin(sqrt(x))/x
Denominador racional [src] 
       ____                                ____                                 ____                    
      /  3    _______    4          ___   /  3     3        /  ___\      3/2   /  3     3        /  ___\
- x*\/  x  *\/ 1 - x *log (x) - 8*\/ x *\/  x  *log (x)*asin\\/ x / + 8*x   *\/  x  *log (x)*asin\\/ x /
--------------------------------------------------------------------------------------------------------
                                                3                                                       
                                             2*x *(-1 + x)
$$\frac{8 x^{\frac{3}{2}} \sqrt{x^{3}} \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)} - 8 \sqrt{x} \sqrt{x^{3}} \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)} - x \sqrt{1 - x} \sqrt{x^{3}} \log{\left(x \right)}^{4}}{2 x^{3} \left(x - 1\right)}$$ 
(-x*sqrt(x^3)*sqrt(1 - x)*log(x)^4 - 8*sqrt(x)*sqrt(x^3)*log(x)^3*asin(sqrt(x)) + 8*x^(3/2)*sqrt(x^3)*log(x)^3*asin(sqrt(x)))/(2*x^3*(-1 + x))
Denominador común [src] 
     4          ___   _______    3        /  ___\
x*log (x) + 8*\/ x *\/ 1 - x *log (x)*asin\\/ x /
-------------------------------------------------
                    3/2   _______                
                 2*x   *\/ 1 - x
$$\frac{8 \sqrt{x} \sqrt{1 - x} \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)} + x \log{\left(x \right)}^{4}}{2 x^{\frac{3}{2}} \sqrt{1 - x}}$$ 
(x*log(x)^4 + 8*sqrt(x)*sqrt(1 - x)*log(x)^3*asin(sqrt(x)))/(2*x^(3/2)*sqrt(1 - x))
Unión de expresiones racionales [src] 
   3    /               ___   _______     /  ___\\
log (x)*\x*log(x) + 8*\/ x *\/ 1 - x *asin\\/ x //
--------------------------------------------------
                    3/2   _______                 
                 2*x   *\/ 1 - x
$$\frac{\left(8 \sqrt{x} \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} + x \log{\left(x \right)}\right) \log{\left(x \right)}^{3}}{2 x^{\frac{3}{2}} \sqrt{1 - x}}$$ 
log(x)^3*(x*log(x) + 8*sqrt(x)*sqrt(1 - x)*asin(sqrt(x)))/(2*x^(3/2)*sqrt(1 - x))
Respuesta numérica [src] 
0.5*x^(-0.5)*(1.0 - x)^(-0.5)*log(x)^4 + 4.0*log(x)^3*asin(sqrt(x))/x
0.5*x^(-0.5)*(1.0 - x)^(-0.5)*log(x)^4 + 4.0*log(x)^3*asin(sqrt(x))/x
Compilar la expresión [src] 
        4                3        /  ___\
     log (x)        4*log (x)*asin\\/ x /
----------------- + ---------------------
    ___   _______             x          
2*\/ x *\/ 1 - x
$$\frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}}$$ 
log(x)^4/(2*sqrt(x)*sqrt(1 - x)) + 4*log(x)^3*asin(sqrt(x))/x
Abrimos la expresión [src] 
     3        /  ___\           4        
4*log (x)*asin\\/ x /        log (x)     
--------------------- + -----------------
          x                 ___   _______
                        2*\/ x *\/ 1 - x
$$\frac{4 \log{\left(x \right)}^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}^{4}}{2 \sqrt{x} \sqrt{1 - x}}$$ 
((4*log(x)^3)*asin(sqrt(x)))/x + log(x)^4/(2*sqrt(x)*sqrt(1 - x))
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