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Simplificación de expresiones/ Descomposición en fracciones simples/ acos(3*x)^4/(x-3)-12*acos(3*x)^3*log(x-3)/sqrt(1-9*x^2)

¿Cómo vas a descomponer esta acos(3*x)^4/(x-3)-12*acos(3*x)^3*log(x-3)/sqrt(1-9*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    4               3                
acos (3*x)   12*acos (3*x)*log(x - 3)
---------- - ------------------------
  x - 3              __________      
                    /        2       
                  \/  1 - 9*x
−log⁡(x−3)12acos⁡3(3x)1−9x2+acos⁡4(3x)x−3- \frac{\log{\left(x - 3 \right)} 12 \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} + \frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} 
acos(3*x)^4/(x - 3) - (12*acos(3*x)^3)*log(x - 3)/sqrt(1 - 9*x^2)
Simplificación general [src] 
           /   __________                                    \
    3      |  /        2                                     |
acos (3*x)*\\/  1 - 9*x  *acos(3*x) - 12*(-3 + x)*log(-3 + x)/
--------------------------------------------------------------
                       __________                             
                      /        2                              
                    \/  1 - 9*x  *(-3 + x)
(1−9x2acos⁡(3x)−12(x−3)log⁡(x−3))acos⁡3(3x)1−9x2(x−3)\frac{\left(\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 12 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \left(x - 3\right)} 
acos(3*x)^3*(sqrt(1 - 9*x^2)*acos(3*x) - 12*(-3 + x)*log(-3 + x))/(sqrt(1 - 9*x^2)*(-3 + x))
Respuesta numérica [src] 
acos(3*x)^4/(-3.0 + x) - 4.0*(0.111111111111111 - x^2)^(-0.5)*acos(3*x)^3*log(x - 3)
acos(3*x)^4/(-3.0 + x) - 4.0*(0.111111111111111 - x^2)^(-0.5)*acos(3*x)^3*log(x - 3)
Parte trigonométrica [src] 
    4               3                 
acos (3*x)   12*acos (3*x)*log(-3 + x)
---------- - -------------------------
  -3 + x              __________      
                     /        2       
                   \/  1 - 9*x
acos⁡4(3x)x−3−12log⁡(x−3)acos⁡3(3x)1−9x2\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} 
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(-3 + x)/sqrt(1 - 9*x^2)
Combinatoria [src] 
            /                     __________                             \ 
     3      |                    /        2                              | 
-acos (3*x)*\-36*log(-3 + x) - \/  1 - 9*x  *acos(3*x) + 12*x*log(-3 + x)/ 
---------------------------------------------------------------------------
                       _______________________                             
                     \/ -(1 + 3*x)*(-1 + 3*x) *(-3 + x)
−(12xlog⁡(x−3)−1−9x2acos⁡(3x)−36log⁡(x−3))acos⁡3(3x)−(3x−1)(3x+1)(x−3)- \frac{\left(12 x \log{\left(x - 3 \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 36 \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{- \left(3 x - 1\right) \left(3 x + 1\right)} \left(x - 3\right)} 
-acos(3*x)^3*(-36*log(-3 + x) - sqrt(1 - 9*x^2)*acos(3*x) + 12*x*log(-3 + x))/(sqrt(-(1 + 3*x)*(-1 + 3*x))*(-3 + x))
Potencias [src] 
    4               3                 
acos (3*x)   12*acos (3*x)*log(-3 + x)
---------- - -------------------------
  -3 + x              __________      
                     /        2       
                   \/  1 - 9*x
acos⁡4(3x)x−3−12log⁡(x−3)acos⁡3(3x)1−9x2\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} 
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(-3 + x)/sqrt(1 - 9*x^2)
Denominador racional [src] 
                                       __________                                  __________                       
      4           2     4             /        2      3                           /        2      3                 
- acos (3*x) + 9*x *acos (3*x) - 36*\/  1 - 9*x  *acos (3*x)*log(-3 + x) + 12*x*\/  1 - 9*x  *acos (3*x)*log(-3 + x)
--------------------------------------------------------------------------------------------------------------------
                                                /        2\                                                         
                                                \-1 + 9*x /*(-3 + x)
9x2acos⁡4(3x)+12x1−9x2log⁡(x−3)acos⁡3(3x)−361−9x2log⁡(x−3)acos⁡3(3x)−acos⁡4(3x)(x−3)(9x2−1)\frac{9 x^{2} \operatorname{acos}^{4}{\left(3 x \right)} + 12 x \sqrt{1 - 9 x^{2}} \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - 36 \sqrt{1 - 9 x^{2}} \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - \operatorname{acos}^{4}{\left(3 x \right)}}{\left(x - 3\right) \left(9 x^{2} - 1\right)} 
(-acos(3*x)^4 + 9*x^2*acos(3*x)^4 - 36*sqrt(1 - 9*x^2)*acos(3*x)^3*log(-3 + x) + 12*x*sqrt(1 - 9*x^2)*acos(3*x)^3*log(-3 + x))/((-1 + 9*x^2)*(-3 + x))
Unión de expresiones racionales [src] 
           /   __________                                    \
    3      |  /        2                                     |
acos (3*x)*\\/  1 - 9*x  *acos(3*x) - 12*(-3 + x)*log(-3 + x)/
--------------------------------------------------------------
                       __________                             
                      /        2                              
                    \/  1 - 9*x  *(-3 + x)
(1−9x2acos⁡(3x)−12(x−3)log⁡(x−3))acos⁡3(3x)1−9x2(x−3)\frac{\left(\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)} - 12 \left(x - 3\right) \log{\left(x - 3 \right)}\right) \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \left(x - 3\right)} 
acos(3*x)^3*(sqrt(1 - 9*x^2)*acos(3*x) - 12*(-3 + x)*log(-3 + x))/(sqrt(1 - 9*x^2)*(-3 + x))
Denominador común [src] 
 /     __________                                                                     \ 
 |    /        2      4               3                             3                 | 
-\- \/  1 - 9*x  *acos (3*x) - 36*acos (3*x)*log(-3 + x) + 12*x*acos (3*x)*log(-3 + x)/ 
----------------------------------------------------------------------------------------
                                 __________        __________                           
                                /        2        /        2                            
                          - 3*\/  1 - 9*x   + x*\/  1 - 9*x
−12xlog⁡(x−3)acos⁡3(3x)−1−9x2acos⁡4(3x)−36log⁡(x−3)acos⁡3(3x)x1−9x2−31−9x2- \frac{12 x \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)} - \sqrt{1 - 9 x^{2}} \operatorname{acos}^{4}{\left(3 x \right)} - 36 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{x \sqrt{1 - 9 x^{2}} - 3 \sqrt{1 - 9 x^{2}}} 
-(-sqrt(1 - 9*x^2)*acos(3*x)^4 - 36*acos(3*x)^3*log(-3 + x) + 12*x*acos(3*x)^3*log(-3 + x))/(-3*sqrt(1 - 9*x^2) + x*sqrt(1 - 9*x^2))
Compilar la expresión [src] 
    4               3                
acos (3*x)   12*acos (3*x)*log(x - 3)
---------- - ------------------------
  -3 + x             __________      
                    /        2       
                  \/  1 - 9*x
acos⁡4(3x)x−3−12log⁡(x−3)acos⁡3(3x)1−9x2\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{x - 3} - \frac{12 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}} 
acos(3*x)^4/(-3 + x) - 12*acos(3*x)^3*log(x - 3)/sqrt(1 - 9*x^2)
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