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Simplificación de expresiones/ Descomposición en fracciones simples/ acos(4*x)^2/(x-10)-8*acos(4*x)*log(x-10)/sqrt(1-16*x^2)

¿Cómo vas a descomponer esta acos(4*x)^2/(x-10)-8*acos(4*x)*log(x-10)/sqrt(1-16*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    2                               
acos (4*x)   8*acos(4*x)*log(x - 10)
---------- - -----------------------
  x - 10             ___________    
                    /         2     
                  \/  1 - 16*x
$$- \frac{\log{\left(x - 10 \right)} 8 \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}} + \frac{\operatorname{acos}^{2}{\left(4 x \right)}}{x - 10}$$ 
acos(4*x)^2/(x - 10) - (8*acos(4*x))*log(x - 10)/sqrt(1 - 16*x^2)
Simplificación general [src] 
/   ___________                                     \          
|  /         2                                      |          
\\/  1 - 16*x  *acos(4*x) - 8*(-10 + x)*log(-10 + x)/*acos(4*x)
---------------------------------------------------------------
                       ___________                             
                      /         2                              
                    \/  1 - 16*x  *(-10 + x)
$$\frac{\left(\sqrt{1 - 16 x^{2}} \operatorname{acos}{\left(4 x \right)} - 8 \left(x - 10\right) \log{\left(x - 10 \right)}\right) \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 10\right)}$$ 
(sqrt(1 - 16*x^2)*acos(4*x) - 8*(-10 + x)*log(-10 + x))*acos(4*x)/(sqrt(1 - 16*x^2)*(-10 + x))
Respuesta numérica [src] 
acos(4*x)^2/(-10.0 + x) - 2.0*(0.0625 - x^2)^(-0.5)*acos(4*x)*log(x - 10)
acos(4*x)^2/(-10.0 + x) - 2.0*(0.0625 - x^2)^(-0.5)*acos(4*x)*log(x - 10)
Parte trigonométrica [src] 
    2                                
acos (4*x)   8*acos(4*x)*log(-10 + x)
---------- - ------------------------
 -10 + x             ___________     
                    /         2      
                  \/  1 - 16*x
$$\frac{\operatorname{acos}^{2}{\left(4 x \right)}}{x - 10} - \frac{8 \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}}$$ 
acos(4*x)^2/(-10 + x) - 8*acos(4*x)*log(-10 + x)/sqrt(1 - 16*x^2)
Denominador racional [src] 
                                        ___________                                 ___________                       
      2            2     2             /         2                                 /         2                        
- acos (4*x) + 16*x *acos (4*x) - 80*\/  1 - 16*x  *acos(4*x)*log(-10 + x) + 8*x*\/  1 - 16*x  *acos(4*x)*log(-10 + x)
----------------------------------------------------------------------------------------------------------------------
                                                /         2\                                                          
                                                \-1 + 16*x /*(-10 + x)
$$\frac{16 x^{2} \operatorname{acos}^{2}{\left(4 x \right)} + 8 x \sqrt{1 - 16 x^{2}} \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)} - 80 \sqrt{1 - 16 x^{2}} \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)} - \operatorname{acos}^{2}{\left(4 x \right)}}{\left(x - 10\right) \left(16 x^{2} - 1\right)}$$ 
(-acos(4*x)^2 + 16*x^2*acos(4*x)^2 - 80*sqrt(1 - 16*x^2)*acos(4*x)*log(-10 + x) + 8*x*sqrt(1 - 16*x^2)*acos(4*x)*log(-10 + x))/((-1 + 16*x^2)*(-10 + x))
Potencias [src] 
    2                                
acos (4*x)   8*acos(4*x)*log(-10 + x)
---------- - ------------------------
 -10 + x             ___________     
                    /         2      
                  \/  1 - 16*x
$$\frac{\operatorname{acos}^{2}{\left(4 x \right)}}{x - 10} - \frac{8 \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}}$$ 
acos(4*x)^2/(-10 + x) - 8*acos(4*x)*log(-10 + x)/sqrt(1 - 16*x^2)
Unión de expresiones racionales [src] 
/   ___________                                     \          
|  /         2                                      |          
\\/  1 - 16*x  *acos(4*x) - 8*(-10 + x)*log(-10 + x)/*acos(4*x)
---------------------------------------------------------------
                       ___________                             
                      /         2                              
                    \/  1 - 16*x  *(-10 + x)
$$\frac{\left(\sqrt{1 - 16 x^{2}} \operatorname{acos}{\left(4 x \right)} - 8 \left(x - 10\right) \log{\left(x - 10 \right)}\right) \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 10\right)}$$ 
(sqrt(1 - 16*x^2)*acos(4*x) - 8*(-10 + x)*log(-10 + x))*acos(4*x)/(sqrt(1 - 16*x^2)*(-10 + x))
Compilar la expresión [src] 
    2                               
acos (4*x)   8*acos(4*x)*log(x - 10)
---------- - -----------------------
 -10 + x             ___________    
                    /         2     
                  \/  1 - 16*x
$$\frac{\operatorname{acos}^{2}{\left(4 x \right)}}{x - 10} - \frac{8 \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}}$$ 
acos(4*x)^2/(-10 + x) - 8*acos(4*x)*log(x - 10)/sqrt(1 - 16*x^2)
Denominador común [src] 
 /     ___________                                                                    \ 
 |    /         2      2                                                              | 
-\- \/  1 - 16*x  *acos (4*x) - 80*acos(4*x)*log(-10 + x) + 8*x*acos(4*x)*log(-10 + x)/ 
----------------------------------------------------------------------------------------
                                 ___________        ___________                         
                                /         2        /         2                          
                         - 10*\/  1 - 16*x   + x*\/  1 - 16*x
$$- \frac{8 x \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)} - \sqrt{1 - 16 x^{2}} \operatorname{acos}^{2}{\left(4 x \right)} - 80 \log{\left(x - 10 \right)} \operatorname{acos}{\left(4 x \right)}}{x \sqrt{1 - 16 x^{2}} - 10 \sqrt{1 - 16 x^{2}}}$$ 
-(-sqrt(1 - 16*x^2)*acos(4*x)^2 - 80*acos(4*x)*log(-10 + x) + 8*x*acos(4*x)*log(-10 + x))/(-10*sqrt(1 - 16*x^2) + x*sqrt(1 - 16*x^2))
Combinatoria [src] 
 /                      ___________                             \           
 |                     /         2                              |           
-\-80*log(-10 + x) - \/  1 - 16*x  *acos(4*x) + 8*x*log(-10 + x)/*acos(4*x) 
----------------------------------------------------------------------------
                      _______________________                               
                    \/ -(1 + 4*x)*(-1 + 4*x) *(-10 + x)
$$- \frac{\left(8 x \log{\left(x - 10 \right)} - \sqrt{1 - 16 x^{2}} \operatorname{acos}{\left(4 x \right)} - 80 \log{\left(x - 10 \right)}\right) \operatorname{acos}{\left(4 x \right)}}{\sqrt{- \left(4 x - 1\right) \left(4 x + 1\right)} \left(x - 10\right)}$$ 
-(-80*log(-10 + x) - sqrt(1 - 16*x^2)*acos(4*x) + 8*x*log(-10 + x))*acos(4*x)/(sqrt(-(1 + 4*x)*(-1 + 4*x))*(-10 + x))
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