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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(E^asin(x))^3/(2*sqrt(x))+3*sqrt(x)*tan(E^asin(x))^2*(1+tan(E^asin(x))^2)*exp(asin(x))/sqrt(1-x^2)

¿Cómo vas a descomponer esta tan(E^asin(x))^3/(2*sqrt(x))+3*sqrt(x)*tan(E^asin(x))^2*(1+tan(E^asin(x))^2)*exp(asin(x))/sqrt(1-x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   3/ asin(x)\       ___    2/ asin(x)\ /       2/ asin(x)\\  asin(x)
tan \E       /   3*\/ x *tan \E       /*\1 + tan \E       //*e       
-------------- + ----------------------------------------------------
       ___                              ________                     
   2*\/ x                              /      2                      
                                     \/  1 - x
$$\frac{3 \sqrt{x} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
tan(E^asin(x))^3/((2*sqrt(x))) + ((((3*sqrt(x))*tan(E^asin(x))^2)*(1 + tan(E^asin(x))^2))*exp(asin(x)))/sqrt(1 - x^2)
Simplificación general [src] 
   3/ asin(x)\       ___    2/ asin(x)\  asin(x)
tan \e       /   3*\/ x *tan \e       /*e       
-------------- + -------------------------------
       ___             ________                 
   2*\/ x             /      2     2/ asin(x)\  
                    \/  1 - x  *cos \e       /
$$\frac{3 \sqrt{x} e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
tan(exp(asin(x)))^3/(2*sqrt(x)) + 3*sqrt(x)*tan(exp(asin(x)))^2*exp(asin(x))/(sqrt(1 - x^2)*cos(exp(asin(x)))^2)
Respuesta numérica [src] 
0.5*x^(-0.5)*tan(E^asin(x))^3 + 3.0*x^0.5*(1.0 - x^2)^(-0.5)*tan(E^asin(x))^2*(1.0 + tan(E^asin(x))^2)*exp(asin(x))
0.5*x^(-0.5)*tan(E^asin(x))^3 + 3.0*x^0.5*(1.0 - x^2)^(-0.5)*tan(E^asin(x))^2*(1.0 + tan(E^asin(x))^2)*exp(asin(x))
Potencias [src] 
                                                                                  /                                  2\         
                                                                                2 |    /      asin(x)        asin(x)\ |         
                                                  /      asin(x)        asin(x)\  |    |   I*e           -I*e       | |         
                                              ___ |   I*e           -I*e       |  |    \- e           + e           / |  asin(x)
                                          3*\/ x *\- e           + e           / *|1 - -------------------------------|*e       
                                    3                                             |                                 2 |         
      /      asin(x)        asin(x)\                                              |     /    asin(x)        asin(x)\  |         
      |   I*e           -I*e       |                                              |     | I*e           -I*e       |  |         
    I*\- e           + e           /                                              \     \e           + e           /  /         
- ------------------------------------- - --------------------------------------------------------------------------------------
                                      3                                                                 2                       
          /    asin(x)        asin(x)\                             ________ /    asin(x)        asin(x)\                        
      ___ | I*e           -I*e       |                            /      2  | I*e           -I*e       |                        
  2*\/ x *\e           + e           /                          \/  1 - x  *\e           + e           /
$$- \frac{3 \sqrt{x} \left(- \frac{\left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}}{\left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}} + 1\right) \left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2} e^{\operatorname{asin}{\left(x \right)}}}{\sqrt{1 - x^{2}} \left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{2}} - \frac{i \left(- e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{3}}{2 \sqrt{x} \left(e^{i e^{\operatorname{asin}{\left(x \right)}}} + e^{- i e^{\operatorname{asin}{\left(x \right)}}}\right)^{3}}$$ 
   3/ asin(x)\       ___    2/ asin(x)\ /       2/ asin(x)\\  asin(x)
tan \e       /   3*\/ x *tan \e       /*\1 + tan \e       //*e       
-------------- + ----------------------------------------------------
       ___                              ________                     
   2*\/ x                              /      2                      
                                     \/  1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
   3/ asin(x)\     ___    2/ asin(x)\ /         2/ asin(x)\\  asin(x)
tan \e       /   \/ x *tan \e       /*\3 + 3*tan \e       //*e       
-------------- + ----------------------------------------------------
       ___                              ________                     
   2*\/ x                              /      2                      
                                     \/  1 - x
$$\frac{\sqrt{x} \left(3 \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 3\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
tan(exp(asin(x)))^3/(2*sqrt(x)) + sqrt(x)*tan(exp(asin(x)))^2*(3 + 3*tan(exp(asin(x)))^2)*exp(asin(x))/sqrt(1 - x^2)
Combinatoria [src] 
               /   ________                                                           \
   2/ asin(x)\ |  /      2     / asin(x)\        asin(x)          2/ asin(x)\  asin(x)|
tan \e       /*\\/  1 - x  *tan\e       / + 6*x*e        + 6*x*tan \e       /*e       /
---------------------------------------------------------------------------------------
                                 ___   ___________________                             
                             2*\/ x *\/ -(1 + x)*(-1 + x)
$$\frac{\left(6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 6 x e^{\operatorname{asin}{\left(x \right)}} + \sqrt{1 - x^{2}} \tan{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}\right) \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{- \left(x - 1\right) \left(x + 1\right)}}$$ 
tan(exp(asin(x)))^2*(sqrt(1 - x^2)*tan(exp(asin(x))) + 6*x*exp(asin(x)) + 6*x*tan(exp(asin(x)))^2*exp(asin(x)))/(2*sqrt(x)*sqrt(-(1 + x)*(-1 + x)))
Denominador común [src] 
   ________                                                                           
  /      2     3/ asin(x)\          2/ asin(x)\  asin(x)          4/ asin(x)\  asin(x)
\/  1 - x  *tan \e       / + 6*x*tan \e       /*e        + 6*x*tan \e       /*e       
--------------------------------------------------------------------------------------
                                            ________                                  
                                     ___   /      2                                   
                                 2*\/ x *\/  1 - x
$$\frac{6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{4}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 6 x e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + \sqrt{1 - x^{2}} \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{1 - x^{2}}}$$ 
(sqrt(1 - x^2)*tan(exp(asin(x)))^3 + 6*x*tan(exp(asin(x)))^2*exp(asin(x)) + 6*x*tan(exp(asin(x)))^4*exp(asin(x)))/(2*sqrt(x)*sqrt(1 - x^2))
Denominador racional [src] 
                                              ________                                  ________                        
     3/ asin(x)\    2    3/ asin(x)\         /      2     2/ asin(x)\  asin(x)         /      2     4/ asin(x)\  asin(x)
- tan \e       / + x *tan \e       / - 6*x*\/  1 - x  *tan \e       /*e        - 6*x*\/  1 - x  *tan \e       /*e       
------------------------------------------------------------------------------------------------------------------------
                                                       ___ /      2\                                                    
                                                   2*\/ x *\-1 + x /
$$\frac{x^{2} \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - 6 x \sqrt{1 - x^{2}} e^{\operatorname{asin}{\left(x \right)}} \tan^{4}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - 6 x \sqrt{1 - x^{2}} e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} - \tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \left(x^{2} - 1\right)}$$ 
(-tan(exp(asin(x)))^3 + x^2*tan(exp(asin(x)))^3 - 6*x*sqrt(1 - x^2)*tan(exp(asin(x)))^2*exp(asin(x)) - 6*x*sqrt(1 - x^2)*tan(exp(asin(x)))^4*exp(asin(x)))/(2*sqrt(x)*(-1 + x^2))
Unión de expresiones racionales [src] 
               /   ________                                                  \
   2/ asin(x)\ |  /      2     / asin(x)\       /       2/ asin(x)\\  asin(x)|
tan \e       /*\\/  1 - x  *tan\e       / + 6*x*\1 + tan \e       //*e       /
------------------------------------------------------------------------------
                                        ________                              
                                 ___   /      2                               
                             2*\/ x *\/  1 - x
$$\frac{\left(6 x \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} + \sqrt{1 - x^{2}} \tan{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}\right) \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x} \sqrt{1 - x^{2}}}$$ 
tan(exp(asin(x)))^2*(sqrt(1 - x^2)*tan(exp(asin(x))) + 6*x*(1 + tan(exp(asin(x)))^2)*exp(asin(x)))/(2*sqrt(x)*sqrt(1 - x^2))
Compilar la expresión [src] 
   3/ asin(x)\       ___    2/ asin(x)\ /       2/ asin(x)\\  asin(x)
tan \e       /   3*\/ x *tan \e       /*\1 + tan \e       //*e       
-------------- + ----------------------------------------------------
       ___                              ________                     
   2*\/ x                              /      2                      
                                     \/  1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
   3/ asin(x)\       ___    2/ asin(x)\ /       2/ asin(x)\\  asin(x)
tan \E       /   3*\/ x *tan \E       /*\1 + tan \E       //*e       
-------------- + ----------------------------------------------------
       ___                              ________                     
   2*\/ x                              /      2                      
                                     \/  1 - x
$$\frac{3 \sqrt{x} \left(\tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)} + 1\right) e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
tan(E^asin(x))^3/(2*sqrt(x)) + 3*sqrt(x)*tan(E^asin(x))^2*(1 + tan(E^asin(x))^2)*exp(asin(x))/sqrt(1 - x^2)
Abrimos la expresión [src] 
   3/ asin(x)\       ___    2/ asin(x)\  asin(x)       ___    4/ asin(x)\  asin(x)
tan \e       /   3*\/ x *tan \e       /*e          3*\/ x *tan \e       /*e       
-------------- + ------------------------------- + -------------------------------
       ___                    ________                          ________          
   2*\/ x                    /      2                          /      2           
                           \/  1 - x                         \/  1 - x
$$\frac{3 \sqrt{x} e^{\operatorname{asin}{\left(x \right)}} \tan^{4}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{3 \sqrt{x} e^{\operatorname{asin}{\left(x \right)}} \tan^{2}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}}} + \frac{\tan^{3}{\left(e^{\operatorname{asin}{\left(x \right)}} \right)}}{2 \sqrt{x}}$$ 
tan(exp(asin(x)))^3/(2*sqrt(x)) + 3*sqrt(x)*tan(exp(asin(x)))^2*exp(asin(x))/sqrt(1 - x^2) + 3*sqrt(x)*tan(exp(asin(x)))^4*exp(asin(x))/sqrt(1 - x^2)
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