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Simplificación de expresiones/ Descomposición en fracciones simples/ log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2)

¿Cómo vas a descomponer esta log(z)*(-2)+2*c^i*2*z-1/(2*z^2)+cos(2*z)/((2*z^2))-sin(2*z)/z+log(z^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                 I        1     cos(2*z)   sin(2*z)      / 2\
log(z)*(-2) + 2*c *2*z - ---- + -------- - -------- + log\z /
                            2        2        z              
                         2*z      2*z
((((z2⋅2ci+(−2)log⁡(z))−12z2)+cos⁡(2z)2z2)−sin⁡(2z)z)+log⁡(z2)\left(\left(\left(\left(z 2 \cdot 2 c^{i} + \left(-2\right) \log{\left(z \right)}\right) - \frac{1}{2 z^{2}}\right) + \frac{\cos{\left(2 z \right)}}{2 z^{2}}\right) - \frac{\sin{\left(2 z \right)}}{z}\right) + \log{\left(z^{2} \right)} 
log(z)*(-2) + ((2*c^i)*2)*z - 1/(2*z^2) + cos(2*z)/((2*z^2)) - sin(2*z)/z + log(z^2)
Simplificación general [src] 
             1     cos(2*z)   sin(2*z)        I      / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c  + log\z /
               2        2        z                       
            2*z      2*z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
-2*log(z) - 1/(2*z^2) + cos(2*z)/(2*z^2) - sin(2*z)/z + 4*z*c^i + log(z^2)
Respuesta numérica [src] 
-0.5/z^2 - 2.0*log(z) - sin(2*z)/z + 0.5*cos(2*z)/z^2 + 4.0*z*c^i + log(z^2)
-0.5/z^2 - 2.0*log(z) - sin(2*z)/z + 0.5*cos(2*z)/z^2 + 4.0*z*c^i + log(z^2)
Denominador racional [src] 
  /        2 /                 I\           \      2               3    / 2\
z*\-1 + 2*z *\-2*log(z) + 4*z*c / + cos(2*z)/ - 2*z *sin(2*z) + 2*z *log\z /
----------------------------------------------------------------------------
                                       3                                    
                                    2*z
2z3log⁡(z2)−2z2sin⁡(2z)+z(2z2(4ciz−2log⁡(z))+cos⁡(2z)−1)2z3\frac{2 z^{3} \log{\left(z^{2} \right)} - 2 z^{2} \sin{\left(2 z \right)} + z \left(2 z^{2} \left(4 c^{i} z - 2 \log{\left(z \right)}\right) + \cos{\left(2 z \right)} - 1\right)}{2 z^{3}} 
(z*(-1 + 2*z^2*(-2*log(z) + 4*z*c^i) + cos(2*z)) - 2*z^2*sin(2*z) + 2*z^3*log(z^2))/(2*z^3)
Potencias [src] 
             1     cos(2*z)   sin(2*z)        I      / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c  + log\z /
               2        2        z                       
            2*z      2*z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
                    -2*I*z    2*I*z                                            
                   e         e                                                 
                   ------- + ------              /   -2*I*z    2*I*z\          
             1        2        2           I   I*\- e       + e     /      / 2\
-2*log(z) - ---- + ---------------- + 4*z*c  + ---------------------- + log\z /
               2            2                           2*z                    
            2*z          2*z
4ciz−2log⁡(z)+log⁡(z2)+i(e2iz−e−2iz)2z+e2iz2+e−2iz22z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} + \frac{i \left(e^{2 i z} - e^{- 2 i z}\right)}{2 z} + \frac{\frac{e^{2 i z}}{2} + \frac{e^{- 2 i z}}{2}}{2 z^{2}} - \frac{1}{2 z^{2}} 
-2*log(z) - 1/(2*z^2) + (exp(-2*i*z)/2 + exp(2*i*z)/2)/(2*z^2) + 4*z*c^i + i*(-exp(-2*i*z) + exp(2*i*z))/(2*z) + log(z^2)
Unión de expresiones racionales [src] 
                       2    / 2\      2 /               I\           
-1 - 2*z*sin(2*z) + 2*z *log\z / + 4*z *\-log(z) + 2*z*c / + cos(2*z)
---------------------------------------------------------------------
                                    2                                
                                 2*z
4z2(2ciz−log⁡(z))+2z2log⁡(z2)−2zsin⁡(2z)+cos⁡(2z)−12z2\frac{4 z^{2} \left(2 c^{i} z - \log{\left(z \right)}\right) + 2 z^{2} \log{\left(z^{2} \right)} - 2 z \sin{\left(2 z \right)} + \cos{\left(2 z \right)} - 1}{2 z^{2}} 
(-1 - 2*z*sin(2*z) + 2*z^2*log(z^2) + 4*z^2*(-log(z) + 2*z*c^i) + cos(2*z))/(2*z^2)
Denominador común [src] 
                 I   1 - cos(2*z) + 2*z*sin(2*z)      / 2\
-2*log(z) + 4*z*c  - --------------------------- + log\z /
                                    2                     
                                 2*z
4ciz−2log⁡(z)+log⁡(z2)−2zsin⁡(2z)−cos⁡(2z)+12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 z \sin{\left(2 z \right)} - \cos{\left(2 z \right)} + 1}{2 z^{2}} 
-2*log(z) + 4*z*c^i - (1 - cos(2*z) + 2*z*sin(2*z))/(2*z^2) + log(z^2)
Combinatoria [src] 
        2                            2    / 2\      I  3           
-1 - 4*z *log(z) - 2*z*sin(2*z) + 2*z *log\z / + 8*c *z  + cos(2*z)
-------------------------------------------------------------------
                                   2                               
                                2*z
8ciz3−4z2log⁡(z)+2z2log⁡(z2)−2zsin⁡(2z)+cos⁡(2z)−12z2\frac{8 c^{i} z^{3} - 4 z^{2} \log{\left(z \right)} + 2 z^{2} \log{\left(z^{2} \right)} - 2 z \sin{\left(2 z \right)} + \cos{\left(2 z \right)} - 1}{2 z^{2}} 
(-1 - 4*z^2*log(z) - 2*z*sin(2*z) + 2*z^2*log(z^2) + 8*c^i*z^3 + cos(2*z))/(2*z^2)
Compilar la expresión [src] 
              1   cos(2*z)                              
            - - + --------                              
              2      2       sin(2*z)        I      / 2\
-2*log(z) + -------------- - -------- + 4*z*c  + log\z /
                   2            z                       
                  z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\frac{\cos{\left(2 z \right)}}{2} - \frac{1}{2}}{z^{2}} 
             1     cos(2*z)   sin(2*z)        I      / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c  + log\z /
               2        2        z                       
            2*z      2*z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
-2*log(z) - 1/(2*z^2) + cos(2*z)/(2*z^2) - sin(2*z)/z + 4*z*c^i + log(z^2)
Abrimos la expresión [src] 
          2                                                        
  1    cos (z)      I                     2*cos(z)*sin(z)      / 2\
- -- + ------- + 2*c *2*z + log(z)*(-2) - --------------- + log\z /
   2       2                                     z                 
  z       z
z2⋅2ci+(−2)log⁡(z)+log⁡(z2)−2sin⁡(z)cos⁡(z)z+cos⁡2(z)z2−1z2z 2 \cdot 2 c^{i} + \left(-2\right) \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 \sin{\left(z \right)} \cos{\left(z \right)}}{z} + \frac{\cos^{2}{\left(z \right)}}{z^{2}} - \frac{1}{z^{2}} 
   1        I                     cos(2*z)   sin(2*z)      / 2\
- ---- + 2*c *2*z + log(z)*(-2) + -------- - -------- + log\z /
     2                                 2        z              
  2*z                               2*z
z2⋅2ci+(−2)log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2z2−12z2z 2 \cdot 2 c^{i} + \left(-2\right) \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
-1/(2*z^2) + ((2*c^i)*2)*z + log(z)*(-2) + cos(2*z)/(2*z^2) - sin(2*z)/z + log(z^2)
Parte trigonométrica [src] 
                      /pi      \                              
                   sin|-- + 2*z|                              
             1        \2       /   sin(2*z)        I      / 2\
-2*log(z) - ---- + ------------- - -------- + 4*z*c  + log\z /
               2           2          z                       
            2*z         2*z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+sin⁡(2z+π2)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\sin{\left(2 z + \frac{\pi}{2} \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
                          2                      
            sin(2*z)   sin (z)        I      / 2\
-2*log(z) - -------- - ------- + 4*z*c  + log\z /
               z           2                     
                          z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z−sin⁡2(z)z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} - \frac{\sin^{2}{\left(z \right)}}{z^{2}} 
             1           1                1               I      / 2\
-2*log(z) - ---- + ------------- - --------------- + 4*z*c  + log\z /
               2      2                 /      pi\                   
            2*z    2*z *sec(2*z)   z*sec|2*z - --|                   
                                        \      2 /
4ciz−2log⁡(z)+log⁡(z2)−1zsec⁡(2z−π2)−12z2+12z2sec⁡(2z)4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \sec{\left(2 z - \frac{\pi}{2} \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \sec{\left(2 z \right)}} 
                                 /      pi\                   
                              cos|2*z - --|                   
             1     cos(2*z)      \      2 /        I      / 2\
-2*log(z) - ---- + -------- - ------------- + 4*z*c  + log\z /
               2        2           z                         
            2*z      2*z
4ciz−2log⁡(z)+log⁡(z2)−cos⁡(2z−π2)z+cos⁡(2z)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\cos{\left(2 z - \frac{\pi}{2} \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
             1           1             1             I      / 2\
-2*log(z) - ---- + ------------- - ---------- + 4*z*c  + log\z /
               2      2            z*csc(2*z)                   
            2*z    2*z *sec(2*z)
4ciz−2log⁡(z)+log⁡(z2)−1zcsc⁡(2z)−12z2+12z2sec⁡(2z)4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \csc{\left(2 z \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \sec{\left(2 z \right)}} 
                                       2                                  
             1          I      -1 + cot (z)          2*cot(z)         / 2\
-2*log(z) - ---- + 4*z*c  + ------------------ - --------------- + log\z /
               2               2 /       2   \     /       2   \          
            2*z             2*z *\1 + cot (z)/   z*\1 + cot (z)/
4ciz−2log⁡(z)+log⁡(z2)−2cot⁡(z)z(cot⁡2(z)+1)+cot⁡2(z)−12z2(cot⁡2(z)+1)−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 \cot{\left(z \right)}}{z \left(\cot^{2}{\left(z \right)} + 1\right)} + \frac{\cot^{2}{\left(z \right)} - 1}{2 z^{2} \left(\cot^{2}{\left(z \right)} + 1\right)} - \frac{1}{2 z^{2}} 
                                      2                                   
             1          I      1 - tan (z)           2*tan(z)         / 2\
-2*log(z) - ---- + 4*z*c  + ------------------ - --------------- + log\z /
               2               2 /       2   \     /       2   \          
            2*z             2*z *\1 + tan (z)/   z*\1 + tan (z)/
4ciz−2log⁡(z)+log⁡(z2)−2tan⁡(z)z(tan⁡2(z)+1)+1−tan⁡2(z)2z2(tan⁡2(z)+1)−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{2 \tan{\left(z \right)}}{z \left(\tan^{2}{\left(z \right)} + 1\right)} + \frac{1 - \tan^{2}{\left(z \right)}}{2 z^{2} \left(\tan^{2}{\left(z \right)} + 1\right)} - \frac{1}{2 z^{2}} 
             1     cos(2*z)   sin(2*z)        I      / 2\
-2*log(z) - ---- + -------- - -------- + 4*z*c  + log\z /
               2        2        z                       
            2*z      2*z
4ciz−2log⁡(z)+log⁡(z2)−sin⁡(2z)z+cos⁡(2z)2z2−12z24 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{\sin{\left(2 z \right)}}{z} + \frac{\cos{\left(2 z \right)}}{2 z^{2}} - \frac{1}{2 z^{2}} 
             1             1                1             I      / 2\
-2*log(z) - ---- + ------------------ - ---------- + 4*z*c  + log\z /
               2      2    /pi      \   z*csc(2*z)                   
            2*z    2*z *csc|-- - 2*z|                                
                           \2       /
4ciz−2log⁡(z)+log⁡(z2)−1zcsc⁡(2z)−12z2+12z2csc⁡(−2z+π2)4 c^{i} z - 2 \log{\left(z \right)} + \log{\left(z^{2} \right)} - \frac{1}{z \csc{\left(2 z \right)}} - \frac{1}{2 z^{2}} + \frac{1}{2 z^{2} \csc{\left(- 2 z + \frac{\pi}{2} \right)}} 
-2*log(z) - 1/(2*z^2) + 1/(2*z^2*csc(pi/2 - 2*z)) - 1/(z*csc(2*z)) + 4*z*c^i + log(z^2)
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