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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2)

¿Cómo vas a descomponer esta cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           x       x          
cos(pi*x)*e    pi*e *sin(pi*x)
------------ + ---------------
        2                2    
  1 + pi           1 + pi
excos⁡(πx)1+π2+πexsin⁡(πx)1+π2\frac{e^{x} \cos{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{\pi e^{x} \sin{\left(\pi x \right)}}{1 + \pi^{2}} 
(cos(pi*x)*exp(x))/(1 + pi^2) + ((pi*exp(x))*sin(pi*x))/(1 + pi^2)
Simplificación general [src] 
                            x
(pi*sin(pi*x) + cos(pi*x))*e 
-----------------------------
                 2           
           1 + pi
(πsin⁡(πx)+cos⁡(πx))ex1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \cos{\left(\pi x \right)}\right) e^{x}}{1 + \pi^{2}} 
(pi*sin(pi*x) + cos(pi*x))*exp(x)/(1 + pi^2)
Denominador racional [src] 
           x       x          
cos(pi*x)*e  + pi*e *sin(pi*x)
------------------------------
                 2            
           1 + pi
πexsin⁡(πx)+excos⁡(πx)1+π2\frac{\pi e^{x} \sin{\left(\pi x \right)} + e^{x} \cos{\left(\pi x \right)}}{1 + \pi^{2}} 
(cos(pi*x)*exp(x) + pi*exp(x)*sin(pi*x))/(1 + pi^2)
Unión de expresiones racionales [src] 
                            x
(pi*sin(pi*x) + cos(pi*x))*e 
-----------------------------
                 2           
           1 + pi
(πsin⁡(πx)+cos⁡(πx))ex1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \cos{\left(\pi x \right)}\right) e^{x}}{1 + \pi^{2}} 
(pi*sin(pi*x) + cos(pi*x))*exp(x)/(1 + pi^2)
Compilar la expresión [src] 
           x       x          
cos(pi*x)*e    pi*e *sin(pi*x)
------------ + ---------------
        2                2    
  1 + pi           1 + pi
πexsin⁡(πx)1+π2+excos⁡(πx)1+π2\frac{\pi e^{x} \sin{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{e^{x} \cos{\left(\pi x \right)}}{1 + \pi^{2}} 
cos(pi*x)*exp(x)/(1 + pi^2) + pi*exp(x)*sin(pi*x)/(1 + pi^2)
Parte trigonométrica [src] 
            x                         x       
           e                      pi*e        
------------------------ + -------------------
/      2\    /pi       \   /      2\          
\1 + pi /*csc|-- - pi*x|   \1 + pi /*csc(pi*x)
             \2        /
ex(1+π2)csc⁡(−πx+π2)+πex(1+π2)csc⁡(πx)\frac{e^{x}}{\left(1 + \pi^{2}\right) \csc{\left(- \pi x + \frac{\pi}{2} \right)}} + \frac{\pi e^{x}}{\left(1 + \pi^{2}\right) \csc{\left(\pi x \right)}} 
                       /pi       \                                   
(cosh(x) + sinh(x))*sin|-- + pi*x|                                   
                       \2        /   pi*(cosh(x) + sinh(x))*sin(pi*x)
---------------------------------- + --------------------------------
                   2                                   2             
             1 + pi                              1 + pi
π(sinh⁡(x)+cosh⁡(x))sin⁡(πx)1+π2+(sinh⁡(x)+cosh⁡(x))sin⁡(πx+π2)1+π2\frac{\pi \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sin{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sin{\left(\pi x + \frac{\pi}{2} \right)}}{1 + \pi^{2}} 
/      /  pi       \            \                    
|pi*cos|- -- + pi*x| + cos(pi*x)|*(cosh(x) + sinh(x))
\      \  2        /            /                    
-----------------------------------------------------
                             2                       
                       1 + pi
(cos⁡(πx)+πcos⁡(πx−π2))(sinh⁡(x)+cosh⁡(x))1+π2\frac{\left(\cos{\left(\pi x \right)} + \pi \cos{\left(\pi x - \frac{\pi}{2} \right)}\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{1 + \pi^{2}} 
                                                          /  pi       \
                                pi*(cosh(x) + sinh(x))*cos|- -- + pi*x|
(cosh(x) + sinh(x))*cos(pi*x)                             \  2        /
----------------------------- + ---------------------------------------
                 2                                    2                
           1 + pi                               1 + pi
(sinh⁡(x)+cosh⁡(x))cos⁡(πx)1+π2+π(sinh⁡(x)+cosh⁡(x))cos⁡(πx−π2)1+π2\frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cos{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{\pi \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cos{\left(\pi x - \frac{\pi}{2} \right)}}{1 + \pi^{2}} 
(pi*sin(pi*x) + cos(pi*x))*(cosh(x) + sinh(x))
----------------------------------------------
                         2                    
                   1 + pi
(πsin⁡(πx)+cos⁡(πx))(sinh⁡(x)+cosh⁡(x))1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \cos{\left(\pi x \right)}\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{1 + \pi^{2}} 
           /pi       \      /pi       \                                                      
cosh(x)*sin|-- + pi*x| + sin|-- + pi*x|*sinh(x) + pi*cosh(x)*sin(pi*x) + pi*sin(pi*x)*sinh(x)
           \2        /      \2        /                                                      
---------------------------------------------------------------------------------------------
                                                 2                                           
                                           1 + pi
πsin⁡(πx)sinh⁡(x)+πsin⁡(πx)cosh⁡(x)+sin⁡(πx+π2)sinh⁡(x)+sin⁡(πx+π2)cosh⁡(x)1+π2\frac{\pi \sin{\left(\pi x \right)} \sinh{\left(x \right)} + \pi \sin{\left(\pi x \right)} \cosh{\left(x \right)} + \sin{\left(\pi x + \frac{\pi}{2} \right)} \sinh{\left(x \right)} + \sin{\left(\pi x + \frac{\pi}{2} \right)} \cosh{\left(x \right)}}{1 + \pi^{2}} 
/        2/pi*x\\           /        2/pi*x\\                           /pi*x\           /pi*x\        
|-1 + cot |----||*cosh(x)   |-1 + cot |----||*sinh(x)   2*pi*cosh(x)*cot|----|   2*pi*cot|----|*sinh(x)
\         \ 2  //           \         \ 2  //                           \ 2  /           \ 2  /        
------------------------- + ------------------------- + ---------------------- + ----------------------
             2/pi*x\                     2/pi*x\                   2/pi*x\                  2/pi*x\    
      1 + cot |----|              1 + cot |----|            1 + cot |----|           1 + cot |----|    
              \ 2  /                      \ 2  /                    \ 2  /                   \ 2  /    
-------------------------------------------------------------------------------------------------------
                                                      2                                                
                                                1 + pi
(cot⁡2(πx2)−1)sinh⁡(x)cot⁡2(πx2)+1+(cot⁡2(πx2)−1)cosh⁡(x)cot⁡2(πx2)+1+2πcot⁡(πx2)sinh⁡(x)cot⁡2(πx2)+1+2πcot⁡(πx2)cosh⁡(x)cot⁡2(πx2)+11+π2\frac{\frac{\left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right) \sinh{\left(x \right)}}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{\left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right) \cosh{\left(x \right)}}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \cot{\left(\frac{\pi x}{2} \right)} \sinh{\left(x \right)}}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \cot{\left(\frac{\pi x}{2} \right)} \cosh{\left(x \right)}}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1}}{1 + \pi^{2}} 
/      1              pi   \  x
|-------------- + ---------|*e 
|   /pi       \   csc(pi*x)|   
|csc|-- - pi*x|            |   
\   \2        /            /   
-------------------------------
                  2            
            1 + pi
(1csc⁡(−πx+π2)+πcsc⁡(πx))ex1+π2\frac{\left(\frac{1}{\csc{\left(- \pi x + \frac{\pi}{2} \right)}} + \frac{\pi}{\csc{\left(\pi x \right)}}\right) e^{x}}{1 + \pi^{2}} 
/    1              pi       \  x
|--------- + ----------------|*e 
|sec(pi*x)      /  pi       \|   
|            sec|- -- + pi*x||   
\               \  2        //   
---------------------------------
                   2             
             1 + pi
(πsec⁡(πx−π2)+1sec⁡(πx))ex1+π2\frac{\left(\frac{\pi}{\sec{\left(\pi x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\pi x \right)}}\right) e^{x}}{1 + \pi^{2}} 
                                              /  pi       \                 /  pi       \        
cos(pi*x)*cosh(x) + cos(pi*x)*sinh(x) + pi*cos|- -- + pi*x|*cosh(x) + pi*cos|- -- + pi*x|*sinh(x)
                                              \  2        /                 \  2        /        
-------------------------------------------------------------------------------------------------
                                                   2                                             
                                             1 + pi
cos⁡(πx)sinh⁡(x)+cos⁡(πx)cosh⁡(x)+πcos⁡(πx−π2)sinh⁡(x)+πcos⁡(πx−π2)cosh⁡(x)1+π2\frac{\cos{\left(\pi x \right)} \sinh{\left(x \right)} + \cos{\left(\pi x \right)} \cosh{\left(x \right)} + \pi \cos{\left(\pi x - \frac{\pi}{2} \right)} \sinh{\left(x \right)} + \pi \cos{\left(\pi x - \frac{\pi}{2} \right)} \cosh{\left(x \right)}}{1 + \pi^{2}} 
   /        2/pi*x\\  x                  /pi*x\  x     
   |-1 + cot |----||*e           2*pi*cot|----|*e      
   \         \ 2  //                     \ 2  /        
-------------------------- + --------------------------
/      2\ /       2/pi*x\\   /      2\ /       2/pi*x\\
\1 + pi /*|1 + cot |----||   \1 + pi /*|1 + cot |----||
          \        \ 2  //             \        \ 2  //
(cot⁡2(πx2)−1)ex(1+π2)(cot⁡2(πx2)+1)+2πexcot⁡(πx2)(1+π2)(cot⁡2(πx2)+1)\frac{\left(\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1\right) e^{x}}{\left(1 + \pi^{2}\right) \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)} + \frac{2 \pi e^{x} \cot{\left(\frac{\pi x}{2} \right)}}{\left(1 + \pi^{2}\right) \left(\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)} 
          x                         x           
         e                      pi*e            
------------------- + --------------------------
/      2\             /      2\    /  pi       \
\1 + pi /*sec(pi*x)   \1 + pi /*sec|- -- + pi*x|
                                   \  2        /
πex(1+π2)sec⁡(πx−π2)+ex(1+π2)sec⁡(πx)\frac{\pi e^{x}}{\left(1 + \pi^{2}\right) \sec{\left(\pi x - \frac{\pi}{2} \right)}} + \frac{e^{x}}{\left(1 + \pi^{2}\right) \sec{\left(\pi x \right)}} 
          x                      x       
         e                   pi*e        
------------------- + -------------------
/      2\             /      2\          
\1 + pi /*sec(pi*x)   \1 + pi /*csc(pi*x)
ex(1+π2)sec⁡(πx)+πex(1+π2)csc⁡(πx)\frac{e^{x}}{\left(1 + \pi^{2}\right) \sec{\left(\pi x \right)}} + \frac{\pi e^{x}}{\left(1 + \pi^{2}\right) \csc{\left(\pi x \right)}} 
                            x
(pi*sin(pi*x) + cos(pi*x))*e 
-----------------------------
                 2           
           1 + pi
(πsin⁡(πx)+cos⁡(πx))ex1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \cos{\left(\pi x \right)}\right) e^{x}}{1 + \pi^{2}} 
/                  /pi       \\                    
|pi*sin(pi*x) + sin|-- + pi*x||*(cosh(x) + sinh(x))
\                  \2        //                    
---------------------------------------------------
                            2                      
                      1 + pi
(πsin⁡(πx)+sin⁡(πx+π2))(sinh⁡(x)+cosh⁡(x))1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \sin{\left(\pi x + \frac{\pi}{2} \right)}\right) \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{1 + \pi^{2}} 
/       2/pi*x\           /pi*x\\   
|1 - tan |----|   2*pi*tan|----||   
|        \ 2  /           \ 2  /|  x
|-------------- + --------------|*e 
|       2/pi*x\          2/pi*x\|   
|1 + tan |----|   1 + tan |----||   
\        \ 2  /           \ 2  //   
------------------------------------
                    2               
              1 + pi
(1−tan⁡2(πx2)tan⁡2(πx2)+1+2πtan⁡(πx2)tan⁡2(πx2)+1)ex1+π2\frac{\left(\frac{1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \tan{\left(\frac{\pi x}{2} \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1}\right) e^{x}}{1 + \pi^{2}} 
   /       2/pi*x\\  x                 x    /pi*x\     
   |1 - tan |----||*e            2*pi*e *tan|----|     
   \        \ 2  //                         \ 2  /     
-------------------------- + --------------------------
/      2\ /       2/pi*x\\   /      2\ /       2/pi*x\\
\1 + pi /*|1 + tan |----||   \1 + pi /*|1 + tan |----||
          \        \ 2  //             \        \ 2  //
(1−tan⁡2(πx2))ex(1+π2)(tan⁡2(πx2)+1)+2πextan⁡(πx2)(1+π2)(tan⁡2(πx2)+1)\frac{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right) e^{x}}{\left(1 + \pi^{2}\right) \left(\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)} + \frac{2 \pi e^{x} \tan{\left(\frac{\pi x}{2} \right)}}{\left(1 + \pi^{2}\right) \left(\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1\right)} 
(cosh(x) + sinh(x))*cos(pi*x)   pi*(cosh(x) + sinh(x))*sin(pi*x)
----------------------------- + --------------------------------
                 2                                2             
           1 + pi                           1 + pi
π(sinh⁡(x)+cosh⁡(x))sin⁡(πx)1+π2+(sinh⁡(x)+cosh⁡(x))cos⁡(πx)1+π2\frac{\pi \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \sin{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \cos{\left(\pi x \right)}}{1 + \pi^{2}} 
/        2/pi*x\           /pi*x\\   
|-1 + cot |----|   2*pi*cot|----||   
|         \ 2  /           \ 2  /|  x
|--------------- + --------------|*e 
|        2/pi*x\          2/pi*x\|   
| 1 + cot |----|   1 + cot |----||   
\         \ 2  /           \ 2  //   
-------------------------------------
                     2               
               1 + pi
(cot⁡2(πx2)−1cot⁡2(πx2)+1+2πcot⁡(πx2)cot⁡2(πx2)+1)ex1+π2\frac{\left(\frac{\cot^{2}{\left(\frac{\pi x}{2} \right)} - 1}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \cot{\left(\frac{\pi x}{2} \right)}}{\cot^{2}{\left(\frac{\pi x}{2} \right)} + 1}\right) e^{x}}{1 + \pi^{2}} 
   cosh(x)          sinh(x)       pi*cosh(x)   pi*sinh(x)
-------------- + -------------- + ---------- + ----------
   /pi       \      /pi       \   csc(pi*x)    csc(pi*x) 
csc|-- - pi*x|   csc|-- - pi*x|                          
   \2        /      \2        /                          
---------------------------------------------------------
                               2                         
                         1 + pi
sinh⁡(x)csc⁡(−πx+π2)+πsinh⁡(x)csc⁡(πx)+cosh⁡(x)csc⁡(−πx+π2)+πcosh⁡(x)csc⁡(πx)1+π2\frac{\frac{\sinh{\left(x \right)}}{\csc{\left(- \pi x + \frac{\pi}{2} \right)}} + \frac{\pi \sinh{\left(x \right)}}{\csc{\left(\pi x \right)}} + \frac{\cosh{\left(x \right)}}{\csc{\left(- \pi x + \frac{\pi}{2} \right)}} + \frac{\pi \cosh{\left(x \right)}}{\csc{\left(\pi x \right)}}}{1 + \pi^{2}} 
 cosh(x)     sinh(x)       pi*cosh(x)         pi*sinh(x)   
--------- + --------- + ---------------- + ----------------
sec(pi*x)   sec(pi*x)      /  pi       \      /  pi       \
                        sec|- -- + pi*x|   sec|- -- + pi*x|
                           \  2        /      \  2        /
-----------------------------------------------------------
                                2                          
                          1 + pi
πsinh⁡(x)sec⁡(πx−π2)+sinh⁡(x)sec⁡(πx)+πcosh⁡(x)sec⁡(πx−π2)+cosh⁡(x)sec⁡(πx)1+π2\frac{\frac{\pi \sinh{\left(x \right)}}{\sec{\left(\pi x - \frac{\pi}{2} \right)}} + \frac{\sinh{\left(x \right)}}{\sec{\left(\pi x \right)}} + \frac{\pi \cosh{\left(x \right)}}{\sec{\left(\pi x - \frac{\pi}{2} \right)}} + \frac{\cosh{\left(x \right)}}{\sec{\left(\pi x \right)}}}{1 + \pi^{2}} 
cos(pi*x)*cosh(x) + cos(pi*x)*sinh(x) + pi*cosh(x)*sin(pi*x) + pi*sin(pi*x)*sinh(x)
-----------------------------------------------------------------------------------
                                            2                                      
                                      1 + pi
πsin⁡(πx)sinh⁡(x)+πsin⁡(πx)cosh⁡(x)+cos⁡(πx)sinh⁡(x)+cos⁡(πx)cosh⁡(x)1+π2\frac{\pi \sin{\left(\pi x \right)} \sinh{\left(x \right)} + \pi \sin{\left(\pi x \right)} \cosh{\left(x \right)} + \cos{\left(\pi x \right)} \sinh{\left(x \right)} + \cos{\left(\pi x \right)} \cosh{\left(x \right)}}{1 + \pi^{2}} 
/       2/pi*x\\           /       2/pi*x\\                           /pi*x\                   /pi*x\
|1 - tan |----||*cosh(x)   |1 - tan |----||*sinh(x)   2*pi*cosh(x)*tan|----|   2*pi*sinh(x)*tan|----|
\        \ 2  //           \        \ 2  //                           \ 2  /                   \ 2  /
------------------------ + ------------------------ + ---------------------- + ----------------------
            2/pi*x\                    2/pi*x\                   2/pi*x\                  2/pi*x\    
     1 + tan |----|             1 + tan |----|            1 + tan |----|           1 + tan |----|    
             \ 2  /                     \ 2  /                    \ 2  /                   \ 2  /    
-----------------------------------------------------------------------------------------------------
                                                     2                                               
                                               1 + pi
(1−tan⁡2(πx2))sinh⁡(x)tan⁡2(πx2)+1+(1−tan⁡2(πx2))cosh⁡(x)tan⁡2(πx2)+1+2πtan⁡(πx2)sinh⁡(x)tan⁡2(πx2)+1+2πtan⁡(πx2)cosh⁡(x)tan⁡2(πx2)+11+π2\frac{\frac{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right) \sinh{\left(x \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{\left(1 - \tan^{2}{\left(\frac{\pi x}{2} \right)}\right) \cosh{\left(x \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \tan{\left(\frac{\pi x}{2} \right)} \sinh{\left(x \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1} + \frac{2 \pi \tan{\left(\frac{\pi x}{2} \right)} \cosh{\left(x \right)}}{\tan^{2}{\left(\frac{\pi x}{2} \right)} + 1}}{1 + \pi^{2}} 
((1 - tan(pi*x/2)^2)*cosh(x)/(1 + tan(pi*x/2)^2) + (1 - tan(pi*x/2)^2)*sinh(x)/(1 + tan(pi*x/2)^2) + 2*pi*cosh(x)*tan(pi*x/2)/(1 + tan(pi*x/2)^2) + 2*pi*sinh(x)*tan(pi*x/2)/(1 + tan(pi*x/2)^2))/(1 + pi^2)
Combinatoria [src] 
                            x
(pi*sin(pi*x) + cos(pi*x))*e 
-----------------------------
                 2           
           1 + pi
(πsin⁡(πx)+cos⁡(πx))ex1+π2\frac{\left(\pi \sin{\left(\pi x \right)} + \cos{\left(\pi x \right)}\right) e^{x}}{1 + \pi^{2}} 
(pi*sin(pi*x) + cos(pi*x))*exp(x)/(1 + pi^2)
Respuesta numérica [src] 
0.289025482222236*exp(x)*sin(pi*x) + 0.0919996683503752*cos(pi*x)*exp(x)
0.289025482222236*exp(x)*sin(pi*x) + 0.0919996683503752*cos(pi*x)*exp(x)
Potencias [src] 
           x       x          
cos(pi*x)*e    pi*e *sin(pi*x)
------------ + ---------------
        2                2    
  1 + pi           1 + pi
πexsin⁡(πx)1+π2+excos⁡(πx)1+π2\frac{\pi e^{x} \sin{\left(\pi x \right)}}{1 + \pi^{2}} + \frac{e^{x} \cos{\left(\pi x \right)}}{1 + \pi^{2}} 
/ pi*I*x    -pi*I*x\                                    
|e         e       |  x                                 
|------- + --------|*e         /   -pi*I*x    pi*I*x\  x
\   2         2    /      pi*I*\- e        + e      /*e 
----------------------- - ------------------------------
              2                      /      2\          
        1 + pi                     2*\1 + pi /
(eiπx2+e−iπx2)ex1+π2−iπ(eiπx−e−iπx)ex2(1+π2)\frac{\left(\frac{e^{i \pi x}}{2} + \frac{e^{- i \pi x}}{2}\right) e^{x}}{1 + \pi^{2}} - \frac{i \pi \left(e^{i \pi x} - e^{- i \pi x}\right) e^{x}}{2 \left(1 + \pi^{2}\right)} 
(exp(pi*i*x)/2 + exp(-pi*i*x)/2)*exp(x)/(1 + pi^2) - pi*i*(-exp(-pi*i*x) + exp(pi*i*x))*exp(x)/(2*(1 + pi^2))
Denominador común [src] 
           x       x          
cos(pi*x)*e  + pi*e *sin(pi*x)
------------------------------
                 2            
           1 + pi
πexsin⁡(πx)+excos⁡(πx)1+π2\frac{\pi e^{x} \sin{\left(\pi x \right)} + e^{x} \cos{\left(\pi x \right)}}{1 + \pi^{2}} 
(cos(pi*x)*exp(x) + pi*exp(x)*sin(pi*x))/(1 + pi^2)
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