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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x)/(x*log(5))+log(x)/(sqrt(1-x^2)*log(5))

¿Cómo vas a descomponer esta asin(x)/(x*log(5))+log(x)/(sqrt(1-x^2)*log(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
asin(x)          log(x)      
-------- + ------------------
x*log(5)      ________       
             /      2        
           \/  1 - x  *log(5)
$$\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \log{\left(5 \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{x \log{\left(5 \right)}}$$ 
asin(x)/((x*log(5))) + log(x)/((sqrt(1 - x^2)*log(5)))
Respuesta numérica [src] 
0.621334934559612*asin(x)/x + 0.621334934559612*(1.0 - x^2)^(-0.5)*log(x)
0.621334934559612*asin(x)/x + 0.621334934559612*(1.0 - x^2)^(-0.5)*log(x)
Denominador racional [src] 
                                           ________              
                   2                      /      2               
-asin(x)*log(5) + x *asin(x)*log(5) - x*\/  1 - x  *log(5)*log(x)
-----------------------------------------------------------------
                         /      2\    2                          
                       x*\-1 + x /*log (5)
$$\frac{x^{2} \log{\left(5 \right)} \operatorname{asin}{\left(x \right)} - x \sqrt{1 - x^{2}} \log{\left(5 \right)} \log{\left(x \right)} - \log{\left(5 \right)} \operatorname{asin}{\left(x \right)}}{x \left(x^{2} - 1\right) \log{\left(5 \right)}^{2}}$$ 
(-asin(x)*log(5) + x^2*asin(x)*log(5) - x*sqrt(1 - x^2)*log(5)*log(x))/(x*(-1 + x^2)*log(5)^2)
Combinatoria [src] 
              ________        
             /      2         
x*log(x) + \/  1 - x  *asin(x)
------------------------------
    ___________________       
x*\/ -(1 + x)*(-1 + x) *log(5)
$$\frac{x \log{\left(x \right)} + \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x \sqrt{- \left(x - 1\right) \left(x + 1\right)} \log{\left(5 \right)}}$$ 
(x*log(x) + sqrt(1 - x^2)*asin(x))/(x*sqrt(-(1 + x)*(-1 + x))*log(5))
Unión de expresiones racionales [src] 
              ________        
             /      2         
x*log(x) + \/  1 - x  *asin(x)
------------------------------
          ________            
         /      2             
     x*\/  1 - x  *log(5)
$$\frac{x \log{\left(x \right)} + \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} \log{\left(5 \right)}}$$ 
(x*log(x) + sqrt(1 - x^2)*asin(x))/(x*sqrt(1 - x^2)*log(5))
Denominador común [src] 
              ________        
             /      2         
x*log(x) + \/  1 - x  *asin(x)
------------------------------
          ________            
         /      2             
     x*\/  1 - x  *log(5)
$$\frac{x \log{\left(x \right)} + \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} \log{\left(5 \right)}}$$ 
(x*log(x) + sqrt(1 - x^2)*asin(x))/(x*sqrt(1 - x^2)*log(5))
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