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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)*exp(sqrt(sin(x)))/(2*sqrt(sin(x)))

¿Cómo vas a descomponer esta cos(x)*exp(sqrt(sin(x)))/(2*sqrt(sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
          ________
        \/ sin(x) 
cos(x)*e          
------------------
       ________   
   2*\/ sin(x)
esin⁡(x)cos⁡(x)2sin⁡(x)\frac{e^{\sqrt{\sin{\left(x \right)}}} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}} 
(cos(x)*exp(sqrt(sin(x))))/((2*sqrt(sin(x))))
Respuesta numérica [src] 
0.5*sin(x)^(-0.5)*cos(x)*exp(sqrt(sin(x)))
0.5*sin(x)^(-0.5)*cos(x)*exp(sqrt(sin(x)))
Potencias [src] 
                               _____________________
                        ___   /    /   -I*x    I*x\ 
                      \/ 2 *\/  -I*\- e     + e   / 
      / I*x    -I*x\  ------------------------------
  ___ |e      e    |                2               
\/ 2 *|---- + -----|*e                              
      \ 2       2  /                                
----------------------------------------------------
                  _____________________             
                 /    /   -I*x    I*x\              
             2*\/  -I*\- e     + e   /
2(eix2+e−ix2)e2−i(eix−e−ix)22−i(eix−e−ix)\frac{\sqrt{2} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) e^{\frac{\sqrt{2} \sqrt{- i \left(e^{i x} - e^{- i x}\right)}}{2}}}{2 \sqrt{- i \left(e^{i x} - e^{- i x}\right)}} 
sqrt(2)*(exp(i*x)/2 + exp(-i*x)/2)*exp(sqrt(2)*sqrt(-i*(-exp(-i*x) + exp(i*x)))/2)/(2*sqrt(-i*(-exp(-i*x) + exp(i*x))))
Denominador racional [src] 
                     ________
  ________         \/ sin(x) 
\/ sin(x) *cos(x)*e          
-----------------------------
           2*sin(x)
esin⁡(x)sin⁡(x)cos⁡(x)2sin⁡(x)\frac{e^{\sqrt{\sin{\left(x \right)}}} \sqrt{\sin{\left(x \right)}} \cos{\left(x \right)}}{2 \sin{\left(x \right)}} 
sqrt(sin(x))*cos(x)*exp(sqrt(sin(x)))/(2*sin(x))
Parte trigonométrica [src] 
                     /    /              _____________\       /              _____________\\
                     |    |             /       /x\   |       |             /       /x\   ||
                     |    |            /     cot|-|   |       |            /     cot|-|   ||
  ___ /        2/x\\ |    |  ___      /         \2/   |       |  ___      /         \2/   ||
\/ 2 *|-1 + cot |-||*|cosh|\/ 2 *    /    ----------- | + sinh|\/ 2 *    /    ----------- ||
      \         \2// |    |         /            2/x\ |       |         /            2/x\ ||
                     |    |        /      1 + cot |-| |       |        /      1 + cot |-| ||
                     \    \      \/               \2/ /       \      \/               \2/ //
--------------------------------------------------------------------------------------------
                                     _____________                                          
                                    /       /x\                                             
                                   /     cot|-|                                             
                                  /         \2/    /       2/x\\                            
                           4*    /    ----------- *|1 + cot |-||                            
                                /            2/x\  \        \2//                            
                               /      1 + cot |-|                                           
                             \/               \2/
2(cot⁡2(x2)−1)(sinh⁡(2cot⁡(x2)cot⁡2(x2)+1)+cosh⁡(2cot⁡(x2)cot⁡2(x2)+1))4cot⁡(x2)cot⁡2(x2)+1(cot⁡2(x2)+1)\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} + \cosh{\left(\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}\right)}{4 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
           ________       
          /   1           
         /  ------        
       \/   csc(x)        
      e                   
--------------------------
      ________            
     /   1        /pi    \
2*  /  ------ *csc|-- - x|
  \/   csc(x)     \2     /
e1csc⁡(x)21csc⁡(x)csc⁡(−x+π2)\frac{e^{\sqrt{\frac{1}{\csc{\left(x \right)}}}}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}} 
                    /    /              _____________\       /              _____________\\
                    |    |             /       /x\   |       |             /       /x\   ||
                    |    |            /     tan|-|   |       |            /     tan|-|   ||
  ___ /       2/x\\ |    |  ___      /         \2/   |       |  ___      /         \2/   ||
\/ 2 *|1 - tan |-||*|cosh|\/ 2 *    /    ----------- | + sinh|\/ 2 *    /    ----------- ||
      \        \2// |    |         /            2/x\ |       |         /            2/x\ ||
                    |    |        /      1 + tan |-| |       |        /      1 + tan |-| ||
                    \    \      \/               \2/ /       \      \/               \2/ //
-------------------------------------------------------------------------------------------
                                     _____________                                         
                                    /       /x\                                            
                                   /     tan|-|                                            
                                  /         \2/    /       2/x\\                           
                           4*    /    ----------- *|1 + tan |-||                           
                                /            2/x\  \        \2//                           
                               /      1 + tan |-|                                          
                             \/               \2/
2(1−tan⁡2(x2))(sinh⁡(2tan⁡(x2)tan⁡2(x2)+1)+cosh⁡(2tan⁡(x2)tan⁡2(x2)+1))4tan⁡(x2)tan⁡2(x2)+1(tan⁡2(x2)+1)\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\sinh{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)} + \cosh{\left(\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \right)}\right)}{4 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
    2/x\ /        2/x\\ /    /  ________\       /  ________\\ 
-cos |-|*|-1 + tan |-||*\cosh\\/ sin(x) / + sinh\\/ sin(x) // 
     \2/ \         \2//                                       
--------------------------------------------------------------
                             ________                         
                         2*\/ sin(x)
−(tan⁡2(x2)−1)(sinh⁡(sin⁡(x))+cosh⁡(sin⁡(x)))cos⁡2(x2)2sin⁡(x)- \frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \cos^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}} 
                                    _____________
                                   /       /x\   
                                  /     cot|-|   
                        ___      /         \2/   
                      \/ 2 *    /    ----------- 
                               /            2/x\ 
                              /      1 + cot |-| 
  ___ /        2/x\\        \/               \2/ 
\/ 2 *|-1 + cot |-||*e                           
      \         \2//                             
-------------------------------------------------
                _____________                    
               /       /x\                       
              /     cot|-|                       
             /         \2/    /       2/x\\      
      4*    /    ----------- *|1 + cot |-||      
           /            2/x\  \        \2//      
          /      1 + cot |-|                     
        \/               \2/
2(cot⁡2(x2)−1)e2cot⁡(x2)cot⁡2(x2)+14cot⁡(x2)cot⁡2(x2)+1(cot⁡2(x2)+1)\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) e^{\sqrt{2} \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}}}{4 \sqrt{\frac{\cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
/    /  ________\       /  ________\\    /    pi\
\cosh\\/ sin(x) / + sinh\\/ sin(x) //*sin|x + --|
                                         \    2 /
-------------------------------------------------
                       ________                  
                   2*\/ sin(x)
(sinh⁡(sin⁡(x))+cosh⁡(sin⁡(x)))sin⁡(x+π2)2sin⁡(x)\frac{\left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \sin{\left(x + \frac{\pi}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}} 
                                   _____________
                                  /       /x\   
                                 /     tan|-|   
                       ___      /         \2/   
                     \/ 2 *    /    ----------- 
                              /            2/x\ 
                             /      1 + tan |-| 
  ___ /       2/x\\        \/               \2/ 
\/ 2 *|1 - tan |-||*e                           
      \        \2//                             
------------------------------------------------
               _____________                    
              /       /x\                       
             /     tan|-|                       
            /         \2/    /       2/x\\      
     4*    /    ----------- *|1 + tan |-||      
          /            2/x\  \        \2//      
         /      1 + tan |-|                     
       \/               \2/
2(1−tan⁡2(x2))e2tan⁡(x2)tan⁡2(x2)+14tan⁡(x2)tan⁡2(x2)+1(tan⁡2(x2)+1)\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) e^{\sqrt{2} \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}}}{4 \sqrt{\frac{\tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
    /    ________\       /    ________\
    |   /   1    |       |   /   1    |
cosh|  /  ------ | + sinh|  /  ------ |
    \\/   csc(x) /       \\/   csc(x) /
---------------------------------------
             ________                  
            /   1        /pi    \      
       2*  /  ------ *csc|-- - x|      
         \/   csc(x)     \2     /
sinh⁡(1csc⁡(x))+cosh⁡(1csc⁡(x))21csc⁡(x)csc⁡(−x+π2)\frac{\sinh{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)} + \cosh{\left(\sqrt{\frac{1}{\csc{\left(x \right)}}} \right)}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}} 
/    /  ________\       /  ________\\       
\cosh\\/ sin(x) / + sinh\\/ sin(x) //*cos(x)
--------------------------------------------
                    ________                
                2*\/ sin(x)
(sinh⁡(sin⁡(x))+cosh⁡(sin⁡(x)))cos⁡(x)2sin⁡(x)\frac{\left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}} 
           _____________    
          /      1          
         /  -----------     
        /      /    pi\     
       /    sec|x - --|     
     \/        \    2 /     
    e                       
----------------------------
        _____________       
       /      1             
2*    /  ----------- *sec(x)
     /      /    pi\        
    /    sec|x - --|        
  \/        \    2 /
e1sec⁡(x−π2)21sec⁡(x−π2)sec⁡(x)\frac{e^{\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}}}}{2 \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}} 
    /      _____________\       /      _____________\
    |     /      1      |       |     /      1      |
cosh|    /  ----------- | + sinh|    /  ----------- |
    |   /      /    pi\ |       |   /      /    pi\ |
    |  /    sec|x - --| |       |  /    sec|x - --| |
    \\/        \    2 / /       \\/        \    2 / /
-----------------------------------------------------
                     _____________                   
                    /      1                         
             2*    /  ----------- *sec(x)            
                  /      /    pi\                    
                 /    sec|x - --|                    
               \/        \    2 /
sinh⁡(1sec⁡(x−π2))+cosh⁡(1sec⁡(x−π2))21sec⁡(x−π2)sec⁡(x)\frac{\sinh{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)} + \cosh{\left(\sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \right)}}{2 \sqrt{\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}} 
         ________    
        /   1        
       /  ------     
     \/   csc(x)     
    e                
---------------------
      ________       
     /   1           
2*  /  ------ *sec(x)
  \/   csc(x)
e1csc⁡(x)21csc⁡(x)sec⁡(x)\frac{e^{\sqrt{\frac{1}{\csc{\left(x \right)}}}}}{2 \sqrt{\frac{1}{\csc{\left(x \right)}}} \sec{\left(x \right)}} 
   2/x\ /        2/x\\ /    /  ________\       /  ________\\
sin |-|*|-1 + cot |-||*\cosh\\/ sin(x) / + sinh\\/ sin(x) //
    \2/ \         \2//                                      
------------------------------------------------------------
                            ________                        
                        2*\/ sin(x)
(cot⁡2(x2)−1)(sinh⁡(sin⁡(x))+cosh⁡(sin⁡(x)))sin⁡2(x2)2sin⁡(x)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\sinh{\left(\sqrt{\sin{\left(x \right)}} \right)} + \cosh{\left(\sqrt{\sin{\left(x \right)}} \right)}\right) \sin^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)}}} 
/    /    _____________\       /    _____________\\       
|    |   /    /    pi\ |       |   /    /    pi\ ||       
|cosh|  /  cos|x - --| | + sinh|  /  cos|x - --| ||*cos(x)
\    \\/      \    2 / /       \\/      \    2 / //       
----------------------------------------------------------
                         _____________                    
                        /    /    pi\                     
                   2*  /  cos|x - --|                     
                     \/      \    2 /
(sinh⁡(cos⁡(x−π2))+cosh⁡(cos⁡(x−π2)))cos⁡(x)2cos⁡(x−π2)\frac{\left(\sinh{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)} + \cosh{\left(\sqrt{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}\right) \cos{\left(x \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)}}} 
(cosh(sqrt(cos(x - pi/2))) + sinh(sqrt(cos(x - pi/2))))*cos(x)/(2*sqrt(cos(x - pi/2)))
    © Sr Examen – Калькулятор