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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(5*x)^4/(3*(x-4)^(2/3))+20*(x-4)^(1/3)*asin(5*x)^3/sqrt(1-25*x^2)

¿Cómo vas a descomponer esta asin(5*x)^4/(3*(x-4)^(2/3))+20*(x-4)^(1/3)*asin(5*x)^3/sqrt(1-25*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
     4            3 _______     3     
 asin (5*x)    20*\/ x - 4 *asin (5*x)
------------ + -----------------------
         2/3           ___________    
3*(x - 4)             /         2     
                    \/  1 - 25*x
20x−43asin⁡3(5x)1−25x2+asin⁡4(5x)3(x−4)23\frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} 
asin(5*x)^4/((3*(x - 4)^(2/3))) + ((20*(x - 4)^(1/3))*asin(5*x)^3)/sqrt(1 - 25*x^2)
Simplificación general [src] 
           /                 ___________          \
    3      |                /         2           |
asin (5*x)*\-240 + 60*x + \/  1 - 25*x  *asin(5*x)/
---------------------------------------------------
                 ___________                       
                /         2          2/3           
            3*\/  1 - 25*x  *(-4 + x)
(60x+1−25x2asin⁡(5x)−240)asin⁡3(5x)31−25x2(x−4)23\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}} 
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Respuesta numérica [src] 
0.13228342099735*(-1 + 0.25*x)^(-0.666666666666667)*asin(5*x)^4 + 6.3496042078728*(-1 + 0.25*x)^0.333333333333333*(0.04 - x^2)^(-0.5)*asin(5*x)^3
0.13228342099735*(-1 + 0.25*x)^(-0.666666666666667)*asin(5*x)^4 + 6.3496042078728*(-1 + 0.25*x)^0.333333333333333*(0.04 - x^2)^(-0.5)*asin(5*x)^3
Denominador racional [src] 
                                         ___________                      ___________           
      4            2     4              /         2      3               /         2      3     
- asin (5*x) + 25*x *asin (5*x) + 240*\/  1 - 25*x  *asin (5*x) - 60*x*\/  1 - 25*x  *asin (5*x)
------------------------------------------------------------------------------------------------
                                     /         2\         2/3                                   
                                   3*\-1 + 25*x /*(-4 + x)
25x2asin⁡4(5x)−60x1−25x2asin⁡3(5x)+2401−25x2asin⁡3(5x)−asin⁡4(5x)3(x−4)23(25x2−1)\frac{25 x^{2} \operatorname{asin}^{4}{\left(5 x \right)} - 60 x \sqrt{1 - 25 x^{2}} \operatorname{asin}^{3}{\left(5 x \right)} + 240 \sqrt{1 - 25 x^{2}} \operatorname{asin}^{3}{\left(5 x \right)} - \operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}} \left(25 x^{2} - 1\right)} 
(-asin(5*x)^4 + 25*x^2*asin(5*x)^4 + 240*sqrt(1 - 25*x^2)*asin(5*x)^3 - 60*x*sqrt(1 - 25*x^2)*asin(5*x)^3)/(3*(-1 + 25*x^2)*(-4 + x)^(2/3))
Potencias [src] 
      4            3 ________     3     
  asin (5*x)    20*\/ -4 + x *asin (5*x)
------------- + ------------------------
          2/3           ___________     
3*(-4 + x)             /         2      
                     \/  1 - 25*x
asin⁡4(5x)3(x−4)23+20x−43asin⁡3(5x)1−25x2\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)
Compilar la expresión [src] 
      4            3 ________     3     
  asin (5*x)    20*\/ -4 + x *asin (5*x)
------------- + ------------------------
          2/3           ___________     
3*(-4 + x)             /         2      
                     \/  1 - 25*x
asin⁡4(5x)3(x−4)23+20x−43asin⁡3(5x)1−25x2\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)
Denominador común [src] 
                      ___________                             
          3          /         2      4                 3     
- 240*asin (5*x) + \/  1 - 25*x  *asin (5*x) + 60*x*asin (5*x)
--------------------------------------------------------------
                      ___________                             
                     /         2          2/3                 
                 3*\/  1 - 25*x  *(-4 + x)
60xasin⁡3(5x)+1−25x2asin⁡4(5x)−240asin⁡3(5x)31−25x2(x−4)23\frac{60 x \operatorname{asin}^{3}{\left(5 x \right)} + \sqrt{1 - 25 x^{2}} \operatorname{asin}^{4}{\left(5 x \right)} - 240 \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}} 
(-240*asin(5*x)^3 + sqrt(1 - 25*x^2)*asin(5*x)^4 + 60*x*asin(5*x)^3)/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Unión de expresiones racionales [src] 
           /                 ___________          \
    3      |                /         2           |
asin (5*x)*\-240 + 60*x + \/  1 - 25*x  *asin(5*x)/
---------------------------------------------------
                 ___________                       
                /         2          2/3           
            3*\/  1 - 25*x  *(-4 + x)
(60x+1−25x2asin⁡(5x)−240)asin⁡3(5x)31−25x2(x−4)23\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}} 
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Combinatoria [src] 
           /                 ___________          \
    3      |                /         2           |
asin (5*x)*\-240 + 60*x + \/  1 - 25*x  *asin(5*x)/
---------------------------------------------------
          _______________________         2/3      
      3*\/ -(1 + 5*x)*(-1 + 5*x) *(-4 + x)
(60x+1−25x2asin⁡(5x)−240)asin⁡3(5x)3−(5x−1)(5x+1)(x−4)23\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{- \left(5 x - 1\right) \left(5 x + 1\right)} \left(x - 4\right)^{\frac{2}{3}}} 
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(-(1 + 5*x)*(-1 + 5*x))*(-4 + x)^(2/3))
Parte trigonométrica [src] 
      4            3 ________     3     
  asin (5*x)    20*\/ -4 + x *asin (5*x)
------------- + ------------------------
          2/3           ___________     
3*(-4 + x)             /         2      
                     \/  1 - 25*x
asin⁡4(5x)3(x−4)23+20x−43asin⁡3(5x)1−25x2\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} 
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)
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