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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x)^2*(10-2*x)/(5-x)^4+2*asin(x)/(sqrt(1-x^2)*(5-x)^2)

¿Cómo vas a descomponer esta asin(x)^2*(10-2*x)/(5-x)^4+2*asin(x)/(sqrt(1-x^2)*(5-x)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    2                                     
asin (x)*(10 - 2*x)        2*asin(x)      
------------------- + --------------------
             4           ________         
      (5 - x)           /      2         2
                      \/  1 - x  *(5 - x)
(10−2x)asin⁡2(x)(5−x)4+2asin⁡(x)1−x2(5−x)2\frac{\left(10 - 2 x\right) \operatorname{asin}^{2}{\left(x \right)}}{\left(5 - x\right)^{4}} + \frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 - x\right)^{2}} 
(asin(x)^2*(10 - 2*x))/(5 - x)^4 + (2*asin(x))/((sqrt(1 - x^2)*(5 - x)^2))
Simplificación general [src] 
  /               ________                \        
  |        2     /      2                 |        
2*\(-5 + x)  + \/  1 - x  *(5 - x)*asin(x)/*asin(x)
---------------------------------------------------
                  ________                         
                 /      2          4               
               \/  1 - x  *(-5 + x)
2(1−x2(5−x)asin⁡(x)+(x−5)2)asin⁡(x)1−x2(x−5)4\frac{2 \left(\sqrt{1 - x^{2}} \left(5 - x\right) \operatorname{asin}{\left(x \right)} + \left(x - 5\right)^{2}\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 5\right)^{4}} 
2*((-5 + x)^2 + sqrt(1 - x^2)*(5 - x)*asin(x))*asin(x)/(sqrt(1 - x^2)*(-5 + x)^4)
Respuesta numérica [src] 
0.08*(1.0 - x^2)^(-0.5)*asin(x)/(1 - 0.2*x)^2 + 0.0016*asin(x)^2*(10.0 - 2.0*x)/(1 - 0.2*x)^4
0.08*(1.0 - x^2)^(-0.5)*asin(x)/(1 - 0.2*x)^2 + 0.0016*asin(x)^2*(10.0 - 2.0*x)/(1 - 0.2*x)^4
Denominador común [src] 
                               ________                                  
                              /      2      2                            
            -10*asin(x) - 2*\/  1 - x  *asin (x) + 2*x*asin(x)           
-------------------------------------------------------------------------
         ________         ________            ________           ________
        /      2     3   /      2        2   /      2           /      2 
- 125*\/  1 - x   + x *\/  1 - x   - 15*x *\/  1 - x   + 75*x*\/  1 - x
2xasin⁡(x)−21−x2asin⁡2(x)−10asin⁡(x)x31−x2−15x21−x2+75x1−x2−1251−x2\frac{2 x \operatorname{asin}{\left(x \right)} - 2 \sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} - 10 \operatorname{asin}{\left(x \right)}}{x^{3} \sqrt{1 - x^{2}} - 15 x^{2} \sqrt{1 - x^{2}} + 75 x \sqrt{1 - x^{2}} - 125 \sqrt{1 - x^{2}}} 
(-10*asin(x) - 2*sqrt(1 - x^2)*asin(x)^2 + 2*x*asin(x))/(-125*sqrt(1 - x^2) + x^3*sqrt(1 - x^2) - 15*x^2*sqrt(1 - x^2) + 75*x*sqrt(1 - x^2))
Denominador racional [src] 
                                                         ________                                                                      
             2     2         3         2     2          /      2          4                       2     2          2         2     2   
- 10*(-5 + x) *asin (x) - 2*x *(-5 + x) *asin (x) - 2*\/  1 - x  *(-5 + x) *asin(x) + 2*x*(-5 + x) *asin (x) + 10*x *(-5 + x) *asin (x)
---------------------------------------------------------------------------------------------------------------------------------------
                                                          /      2\         6                                                          
                                                          \-1 + x /*(-5 + x)
−2x3(x−5)2asin⁡2(x)+10x2(x−5)2asin⁡2(x)+2x(x−5)2asin⁡2(x)−21−x2(x−5)4asin⁡(x)−10(x−5)2asin⁡2(x)(x−5)6(x2−1)\frac{- 2 x^{3} \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} + 10 x^{2} \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} + 2 x \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} - 2 \sqrt{1 - x^{2}} \left(x - 5\right)^{4} \operatorname{asin}{\left(x \right)} - 10 \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(x - 5\right)^{6} \left(x^{2} - 1\right)} 
(-10*(-5 + x)^2*asin(x)^2 - 2*x^3*(-5 + x)^2*asin(x)^2 - 2*sqrt(1 - x^2)*(-5 + x)^4*asin(x) + 2*x*(-5 + x)^2*asin(x)^2 + 10*x^2*(-5 + x)^2*asin(x)^2)/((-1 + x^2)*(-5 + x)^6)
Unión de expresiones racionales [src] 
  /           ________        \        
  |          /      2         |        
2*\5 - x + \/  1 - x  *asin(x)/*asin(x)
---------------------------------------
             ________                  
            /      2         3         
          \/  1 - x  *(5 - x)
2(−x+1−x2asin⁡(x)+5)asin⁡(x)1−x2(5−x)3\frac{2 \left(- x + \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} + 5\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 - x\right)^{3}} 
2*(5 - x + sqrt(1 - x^2)*asin(x))*asin(x)/(sqrt(1 - x^2)*(5 - x)^3)
Combinatoria [src] 
  /            ________        \        
  |           /      2         |        
2*\-5 + x - \/  1 - x  *asin(x)/*asin(x)
----------------------------------------
      ___________________         3     
    \/ -(1 + x)*(-1 + x) *(-5 + x)
2(x−1−x2asin⁡(x)−5)asin⁡(x)−(x−1)(x+1)(x−5)3\frac{2 \left(x - \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - 5\right) \operatorname{asin}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x - 5\right)^{3}} 
2*(-5 + x - sqrt(1 - x^2)*asin(x))*asin(x)/(sqrt(-(1 + x)*(-1 + x))*(-5 + x)^3)
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