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

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

Expresión a simplificar:

Solución

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