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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    x               x         
   e               e          
------- + --------------------
acos(x)      ________         
            /      2      2   
          \/  1 - x  *acos (x)
exacos⁡(x)+ex1−x2acos⁡2(x)\frac{e^{x}}{\operatorname{acos}{\left(x \right)}} + \frac{e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}} 
exp(x)/acos(x) + exp(x)/((sqrt(1 - x^2)*acos(x)^2))
Denominador racional [src] 
                                    ________           
      2     x    2     2     x     /      2           x
- acos (x)*e  + x *acos (x)*e  - \/  1 - x  *acos(x)*e 
-------------------------------------------------------
                   /      2\     3                     
                   \-1 + x /*acos (x)
x2exacos⁡2(x)−1−x2exacos⁡(x)−exacos⁡2(x)(x2−1)acos⁡3(x)\frac{x^{2} e^{x} \operatorname{acos}^{2}{\left(x \right)} - \sqrt{1 - x^{2}} e^{x} \operatorname{acos}{\left(x \right)} - e^{x} \operatorname{acos}^{2}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{3}{\left(x \right)}} 
(-acos(x)^2*exp(x) + x^2*acos(x)^2*exp(x) - sqrt(1 - x^2)*acos(x)*exp(x))/((-1 + x^2)*acos(x)^3)
Combinatoria [src] 
 /       ________        \    
 |      /      2         |  x 
 \1 + \/  1 - x  *acos(x)/*e  
------------------------------
  ___________________     2   
\/ -(1 + x)*(-1 + x) *acos (x)
(1−x2acos⁡(x)+1)ex−(x−1)(x+1)acos⁡2(x)\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 1\right) e^{x}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{acos}^{2}{\left(x \right)}} 
(1 + sqrt(1 - x^2)*acos(x))*exp(x)/(sqrt(-(1 + x)*(-1 + x))*acos(x)^2)
Respuesta numérica [src] 
exp(x)/acos(x) + (1.0 - x^2)^(-0.5)*exp(x)/acos(x)^2
exp(x)/acos(x) + (1.0 - x^2)^(-0.5)*exp(x)/acos(x)^2
Denominador común [src] 
   ________                
  /      2           x    x
\/  1 - x  *acos(x)*e  + e 
---------------------------
       ________            
      /      2      2      
    \/  1 - x  *acos (x)
1−x2exacos⁡(x)+ex1−x2acos⁡2(x)\frac{\sqrt{1 - x^{2}} e^{x} \operatorname{acos}{\left(x \right)} + e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}} 
(sqrt(1 - x^2)*acos(x)*exp(x) + exp(x))/(sqrt(1 - x^2)*acos(x)^2)
Unión de expresiones racionales [src] 
/       ________        \   
|      /      2         |  x
\1 + \/  1 - x  *acos(x)/*e 
----------------------------
       ________             
      /      2      2       
    \/  1 - x  *acos (x)
(1−x2acos⁡(x)+1)ex1−x2acos⁡2(x)\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 1\right) e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}} 
(1 + sqrt(1 - x^2)*acos(x))*exp(x)/(sqrt(1 - x^2)*acos(x)^2)
Parte trigonométrica [src] 
cosh(x) + sinh(x)    cosh(x) + sinh(x)  
----------------- + --------------------
     acos(x)           ________         
                      /      2      2   
                    \/  1 - x  *acos (x)
sinh⁡(x)+cosh⁡(x)acos⁡(x)+sinh⁡(x)+cosh⁡(x)1−x2acos⁡2(x)\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}} 
(cosh(x) + sinh(x))/acos(x) + (cosh(x) + sinh(x))/(sqrt(1 - x^2)*acos(x)^2)
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