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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
              /  ___   1\
            2*|\/ x  + -|
asin(2*x)     \        2/
--------- + -------------
     ___       __________
 2*\/ x       /        2 
            \/  1 - 4*x
2(x+12)1−4x2+asin⁡(2x)2x\frac{2 \left(\sqrt{x} + \frac{1}{2}\right)}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}} 
asin(2*x)/((2*sqrt(x))) + (2*(sqrt(x) + 1/2))/sqrt(1 - 4*x^2)
Simplificación general [src] 
                 __________          
                /        2           
  ___         \/  1 - 4*x  *asin(2*x)
\/ x  + 2*x + -----------------------
                         2           
-------------------------------------
                  __________         
           ___   /        2          
         \/ x *\/  1 - 4*x
x+2x+1−4x2asin⁡(2x)2x1−4x2\frac{\sqrt{x} + 2 x + \frac{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2}}{\sqrt{x} \sqrt{1 - 4 x^{2}}} 
(sqrt(x) + 2*x + sqrt(1 - 4*x^2)*asin(2*x)/2)/(sqrt(x)*sqrt(1 - 4*x^2))
Respuesta numérica [src] 
0.5*x^(-0.5)*asin(2*x) + 0.5*(0.25 - x^2)^(-0.5)*(1.0 + 2.0*x^0.5)
0.5*x^(-0.5)*asin(2*x) + 0.5*(0.25 - x^2)^(-0.5)*(1.0 + 2.0*x^0.5)
Combinatoria [src] 
                   __________          
    ___           /        2           
2*\/ x  + 4*x + \/  1 - 4*x  *asin(2*x)
---------------------------------------
       ___   _______________________   
   2*\/ x *\/ -(1 + 2*x)*(-1 + 2*x)
2x+4x+1−4x2asin⁡(2x)2x−(2x−1)(2x+1)\frac{2 \sqrt{x} + 4 x + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)}} 
(2*sqrt(x) + 4*x + sqrt(1 - 4*x^2)*asin(2*x))/(2*sqrt(x)*sqrt(-(1 + 2*x)*(-1 + 2*x)))
Parte trigonométrica [src] 
         ___             
 1 + 2*\/ x     asin(2*x)
------------- + ---------
   __________        ___ 
  /        2     2*\/ x  
\/  1 - 4*x
2x+11−4x2+asin⁡(2x)2x\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}} 
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Potencias [src] 
         ___             
 1 + 2*\/ x     asin(2*x)
------------- + ---------
   __________        ___ 
  /        2     2*\/ x  
\/  1 - 4*x
2x+11−4x2+asin⁡(2x)2x\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}} 
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Denominador común [src] 
                   __________          
    ___           /        2           
2*\/ x  + 4*x + \/  1 - 4*x  *asin(2*x)
---------------------------------------
                    __________         
             ___   /        2          
         2*\/ x *\/  1 - 4*x
2x+4x+1−4x2asin⁡(2x)2x1−4x2\frac{2 \sqrt{x} + 4 x + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{1 - 4 x^{2}}} 
(2*sqrt(x) + 4*x + sqrt(1 - 4*x^2)*asin(2*x))/(2*sqrt(x)*sqrt(1 - 4*x^2))
Denominador racional [src] 
                      __________              __________                 
                     /        2        ___   /        2       2          
-2*asin(2*x) - 8*x*\/  1 - 4*x   - 4*\/ x *\/  1 - 4*x   + 8*x *asin(2*x)
-------------------------------------------------------------------------
                               ___ /        2\                           
                           4*\/ x *\-1 + 4*x /
−4x1−4x2+8x2asin⁡(2x)−8x1−4x2−2asin⁡(2x)4x(4x2−1)\frac{- 4 \sqrt{x} \sqrt{1 - 4 x^{2}} + 8 x^{2} \operatorname{asin}{\left(2 x \right)} - 8 x \sqrt{1 - 4 x^{2}} - 2 \operatorname{asin}{\left(2 x \right)}}{4 \sqrt{x} \left(4 x^{2} - 1\right)} 
(-2*asin(2*x) - 8*x*sqrt(1 - 4*x^2) - 4*sqrt(x)*sqrt(1 - 4*x^2) + 8*x^2*asin(2*x))/(4*sqrt(x)*(-1 + 4*x^2))
Compilar la expresión [src] 
         ___             
 1 + 2*\/ x     asin(2*x)
------------- + ---------
   __________        ___ 
  /        2     2*\/ x  
\/  1 - 4*x
2x+11−4x2+asin⁡(2x)2x\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}} 
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Unión de expresiones racionales [src] 
   __________                                  
  /        2                  ___ /        ___\
\/  1 - 4*x  *asin(2*x) + 2*\/ x *\1 + 2*\/ x /
-----------------------------------------------
                        __________             
                 ___   /        2              
             2*\/ x *\/  1 - 4*x
2x(2x+1)+1−4x2asin⁡(2x)2x1−4x2\frac{2 \sqrt{x} \left(2 \sqrt{x} + 1\right) + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{1 - 4 x^{2}}} 
(sqrt(1 - 4*x^2)*asin(2*x) + 2*sqrt(x)*(1 + 2*sqrt(x)))/(2*sqrt(x)*sqrt(1 - 4*x^2))
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