Descomposición de una fracción asin(5*x)²/(x-3)+10*asin(5*x)*log(x-3)/sqrt(1-25*x²) (ar coseno de eno de (5 multiplicar por x) al cuadrado dividir por (x menos 3) más 10 multiplicar por ar coseno de eno de (5 multiplicar por x) multiplicar por logaritmo de (x menos 3) dividir por raíz cuadrada de (1 menos 25 multiplicar por x al cuadrado))

Ha introducido [src]

    2                               
asin (5*x)   10*asin(5*x)*log(x - 3)
---------- + -----------------------
  x - 3              ___________    
                    /         2     
                  \/  1 - 25*x

\frac{\log{\left(x - 3 \right)} 10 \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{\operatorname{asin}^{2}{\left(5 x \right)}}{x - 3}

asin(5*x)^2/(x - 3) + ((10*asin(5*x))*log(x - 3))/sqrt(1 - 25*x^2)

Simplificación general [src]

/   ___________                                    \          
|  /         2                                     |          
\\/  1 - 25*x  *asin(5*x) + 10*(-3 + x)*log(-3 + x)/*asin(5*x)
--------------------------------------------------------------
                      ___________                             
                     /         2                              
                   \/  1 - 25*x  *(-3 + x)

\frac{\left(\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} + 10 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \left(x - 3\right)}

(sqrt(1 - 25*x^2)*asin(5*x) + 10*(-3 + x)*log(-3 + x))*asin(5*x)/(sqrt(1 - 25*x^2)*(-3 + x))

Respuesta numérica [src]

asin(5*x)^2/(-3.0 + x) + 2.0*(0.04 - x^2)^(-0.5)*asin(5*x)*log(x - 3)

asin(5*x)^2/(-3.0 + x) + 2.0*(0.04 - x^2)^(-0.5)*asin(5*x)*log(x - 3)

Combinatoria [src]

/                     ___________                             \          
|                    /         2                              |          
\-30*log(-3 + x) + \/  1 - 25*x  *asin(5*x) + 10*x*log(-3 + x)/*asin(5*x)
-------------------------------------------------------------------------
                      _______________________                            
                    \/ -(1 + 5*x)*(-1 + 5*x) *(-3 + x)

\frac{\left(10 x \log{\left(x - 3 \right)} + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 30 \log{\left(x - 3 \right)}\right) \operatorname{asin}{\left(5 x \right)}}{\sqrt{- \left(5 x - 1\right) \left(5 x + 1\right)} \left(x - 3\right)}

(-30*log(-3 + x) + sqrt(1 - 25*x^2)*asin(5*x) + 10*x*log(-3 + x))*asin(5*x)/(sqrt(-(1 + 5*x)*(-1 + 5*x))*(-3 + x))

Parte trigonométrica [src]

    2                                
asin (5*x)   10*asin(5*x)*log(-3 + x)
---------- + ------------------------
  -3 + x             ___________     
                    /         2      
                  \/  1 - 25*x

\frac{\operatorname{asin}^{2}{\left(5 x \right)}}{x - 3} + \frac{10 \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}

asin(5*x)^2/(-3 + x) + 10*asin(5*x)*log(-3 + x)/sqrt(1 - 25*x^2)

Unión de expresiones racionales [src]

/   ___________                                    \          
|  /         2                                     |          
\\/  1 - 25*x  *asin(5*x) + 10*(-3 + x)*log(-3 + x)/*asin(5*x)
--------------------------------------------------------------
                      ___________                             
                     /         2                              
                   \/  1 - 25*x  *(-3 + x)

\frac{\left(\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} + 10 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}} \left(x - 3\right)}

(sqrt(1 - 25*x^2)*asin(5*x) + 10*(-3 + x)*log(-3 + x))*asin(5*x)/(sqrt(1 - 25*x^2)*(-3 + x))

Denominador racional [src]

                                        ___________                                 ___________                      
      2            2     2             /         2                                 /         2                       
- asin (5*x) + 25*x *asin (5*x) + 30*\/  1 - 25*x  *asin(5*x)*log(-3 + x) - 10*x*\/  1 - 25*x  *asin(5*x)*log(-3 + x)
---------------------------------------------------------------------------------------------------------------------
                                                /         2\                                                         
                                                \-1 + 25*x /*(-3 + x)

\frac{25 x^{2} \operatorname{asin}^{2}{\left(5 x \right)} - 10 x \sqrt{1 - 25 x^{2}} \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)} + 30 \sqrt{1 - 25 x^{2}} \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)} - \operatorname{asin}^{2}{\left(5 x \right)}}{\left(x - 3\right) \left(25 x^{2} - 1\right)}

(-asin(5*x)^2 + 25*x^2*asin(5*x)^2 + 30*sqrt(1 - 25*x^2)*asin(5*x)*log(-3 + x) - 10*x*sqrt(1 - 25*x^2)*asin(5*x)*log(-3 + x))/((-1 + 25*x^2)*(-3 + x))

Potencias [src]

    2                                
asin (5*x)   10*asin(5*x)*log(-3 + x)
---------- + ------------------------
  -3 + x             ___________     
                    /         2      
                  \/  1 - 25*x

\frac{\operatorname{asin}^{2}{\left(5 x \right)}}{x - 3} + \frac{10 \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}

asin(5*x)^2/(-3 + x) + 10*asin(5*x)*log(-3 + x)/sqrt(1 - 25*x^2)

Denominador común [src]

   ___________                                                                   
  /         2      2                                                             
\/  1 - 25*x  *asin (5*x) - 30*asin(5*x)*log(-3 + x) + 10*x*asin(5*x)*log(-3 + x)
---------------------------------------------------------------------------------
                             ___________        ___________                      
                            /         2        /         2                       
                      - 3*\/  1 - 25*x   + x*\/  1 - 25*x

\frac{10 x \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)} + \sqrt{1 - 25 x^{2}} \operatorname{asin}^{2}{\left(5 x \right)} - 30 \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)}}{x \sqrt{1 - 25 x^{2}} - 3 \sqrt{1 - 25 x^{2}}}

(sqrt(1 - 25*x^2)*asin(5*x)^2 - 30*asin(5*x)*log(-3 + x) + 10*x*asin(5*x)*log(-3 + x))/(-3*sqrt(1 - 25*x^2) + x*sqrt(1 - 25*x^2))

Compilar la expresión [src]

    2                               
asin (5*x)   10*asin(5*x)*log(x - 3)
---------- + -----------------------
  -3 + x             ___________    
                    /         2     
                  \/  1 - 25*x

\frac{\operatorname{asin}^{2}{\left(5 x \right)}}{x - 3} + \frac{10 \log{\left(x - 3 \right)} \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}

asin(5*x)^2/(-3 + x) + 10*asin(5*x)*log(x - 3)/sqrt(1 - 25*x^2)

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