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¿cómo vas a descomponer esta expresión en fracciones?:
((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z))
x^3*y^12/(x*y^4)^3
(((z/(1+z*v))/(1+(z/(1+z*v)))))*y*((1/(1-1*u*x)))*(x-t)
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Factorizar el polinomio:
y^5-y^3-y+1
y^5+y+1
-y^3+y^2-1
y^3+y^2*x-3*y*x+9*x+27
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4+8*y^2+4
-y^4+8*y^2+8
Expresiones idénticas
cos(cuatro *x)/(ocho *(cos(cuatro *x)^ dos)^(tres / dos))
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coseno de (cuatro multiplicar por x) dividir por (ocho multiplicar por ( coseno de (cuatro multiplicar por x) en el grado dos) en el grado (tres dividir por dos))
cos(4*x)/(8*(cos(4*x)2)(3/2))
cos4*x/8*cos4*x23/2
cos(4*x)/(8*(cos(4*x)²)^(3/2))
cos(4*x)/(8*(cos(4*x) en el grado 2) en el grado (3/2))
cos(4x)/(8(cos(4x)^2)^(3/2))
cos(4x)/(8(cos(4x)2)(3/2))
cos4x/8cos4x23/2
cos4x/8cos4x^2^3/2
cos(4*x) dividir por (8*(cos(4*x)^2)^(3 dividir por 2))
Expresiones con funciones
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cos(2*x)*x/(sin(x)+cos(x))
cos(106)/(sin(8)*cos(8))
cos(a+b)/((cos(a)*sin(b)))
cos(6*a)/(cos(3*a)+sin(3*a))
Coseno cos
cos(2*x)*x/(cos(x)+sin(x))-cos(x)
cos(2*x)*x/(sin(x)+cos(x))
cos(106)/(sin(8)*cos(8))
cos(a+b)/((cos(a)*sin(b)))
cos(6*a)/(cos(3*a)+sin(3*a))

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(4*x)/(8*(cos(4*x)^2)^(3/2))

¿Cómo vas a descomponer esta cos(4x)/(8(cos(4*x)^2)^(3/2)) expresión en fracciones?

Solución

Ha introducido [src]

   cos(4*x)   
--------------
           3/2
     2        
8*cos (4*x)

$$\frac{\cos{\left(4 x \right)}}{8 \left(\cos^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}}$$

cos(4*x)/((8*(cos(4*x)^2)^(3/2)))

Respuesta numérica [src]

0.125*(cos(4*x)^2)^(-1.5)*cos(4*x)

0.125*(cos(4*x)^2)^(-1.5)*cos(4*x)

Potencias [src]

      -4*I*x    4*I*x     
     e         e          
     ------- + ------     
        2        2        
--------------------------
                       3/2
  /                  2\   
  |/ -4*I*x    4*I*x\ |   
  ||e         e     | |   
8*||------- + ------| |   
  \\   2        2   / /

$$\frac{\frac{e^{4 i x}}{2} + \frac{e^{- 4 i x}}{2}}{8 \left(\left(\frac{e^{4 i x}}{2} + \frac{e^{- 4 i x}}{2}\right)^{2}\right)^{\frac{3}{2}}}$$

(exp(-4*i*x)/2 + exp(4*i*x)/2)/(8*((exp(-4*i*x)/2 + exp(4*i*x)/2)^2)^(3/2))

Denominador racional [src]

   ___________
  /    6      
\/  cos (4*x) 
--------------
      5       
 8*cos (4*x)

$$\frac{\sqrt{\cos^{6}{\left(4 x \right)}}}{8 \cos^{5}{\left(4 x \right)}}$$

sqrt(cos(4*x)^6)/(8*cos(4*x)^5)

Abrimos la expresión [src]

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      4                                                                                                                                                                                                                                                                                                                                                                  2                                                                                                                                                                                
                                                                                                                                                                                 1                                                                                                                                                                                                                                                                                                                                                                 cos (x)                                                                                                                                                                                                                                                                                                                                                            cos (x)                                                                                                                                                                             
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  /   ________________________________________________________          ________________________________________________________                 ________________________________________________________                 ________________________________________________________                 ________________________________________________________        \      ________________________________________________________          ________________________________________________________                 ________________________________________________________                 ________________________________________________________                 ________________________________________________________              ________________________________________________________          ________________________________________________________                 ________________________________________________________                 ________________________________________________________                 ________________________________________________________        
  |  /            6            2            8            4             /            6            2            8            4        6           /            6            2            8            4        2           /            6            2            8            4        8           /            6            2            8            4        4   |     /            6            2            8            4             /            6            2            8            4        6           /            6            2            8            4        2           /            6            2            8            4        8           /            6            2            8            4        4        /            6            2            8            4             /            6            2            8            4        6           /            6            2            8            4        2           /            6            2            8            4        8           /            6            2            8            4        4   
8*\\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x)  - 128*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) - 16*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 64*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 80*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x)/   \/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x)  - 128*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) - 16*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 64*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 80*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x)   \/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x)  - 128*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) - 16*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 64*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x) + 80*\/  1 - 128*cos (x) - 16*cos (x) + 64*cos (x) + 80*cos (x) *cos (x)

$$\frac{\cos^{4}{\left(x \right)}}{64 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{8}{\left(x \right)} - 128 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{6}{\left(x \right)} + 80 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{4}{\left(x \right)} - 16 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{2}{\left(x \right)} + \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1}} - \frac{\cos^{2}{\left(x \right)}}{64 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{8}{\left(x \right)} - 128 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{6}{\left(x \right)} + 80 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{4}{\left(x \right)} - 16 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{2}{\left(x \right)} + \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1}} + \frac{1}{8 \left(64 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{8}{\left(x \right)} - 128 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{6}{\left(x \right)} + 80 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{4}{\left(x \right)} - 16 \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1} \cos^{2}{\left(x \right)} + \sqrt{64 \cos^{8}{\left(x \right)} - 128 \cos^{6}{\left(x \right)} + 80 \cos^{4}{\left(x \right)} - 16 \cos^{2}{\left(x \right)} + 1}\right)}$$

1/(8*(sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4) - 128*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^6 - 16*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^2 + 64*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^8 + 80*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^4)) + cos(x)^4/(sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4) - 128*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^6 - 16*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^2 + 64*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^8 + 80*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^4) - cos(x)^2/(sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4) - 128*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^6 - 16*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^2 + 64*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^8 + 80*sqrt(1 - 128*cos(x)^6 - 16*cos(x)^2 + 64*cos(x)^8 + 80*cos(x)^4)*cos(x)^4)

Parte trigonométrica [src]

            1            
-------------------------
             3/2         
  /    1    \            
8*|---------|   *sec(4*x)
  |   2     |            
  \sec (4*x)/

$$\frac{1}{8 \left(\frac{1}{\sec^{2}{\left(4 x \right)}}\right)^{\frac{3}{2}} \sec{\left(4 x \right)}}$$

                     /          2        \
  ___    2/      pi\ |       cos (2*x)   |
\/ 2 *cos |2*x - --|*|-1 + --------------|
          \      2 / |        2/      pi\|
                     |     cos |2*x - --||
                     \         \      2 //
------------------------------------------
                           3/2            
           4*(1 + cos(8*x))

$$\frac{\sqrt{2} \left(\frac{\cos^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$

                    2                        
  ___ /        2   \     4    /       2     \
\/ 2 *\-1 + cot (x)/ *sin (x)*\1 - tan (2*x)/
---------------------------------------------
                                      3/2    
      /       2      /        2     \\       
    4*\1 + sin (4*x)*\-1 + cot (4*x)//

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\cot^{2}{\left(x \right)} - 1\right)^{2} \sin^{4}{\left(x \right)}}{4 \left(\left(\cot^{2}{\left(4 x \right)} - 1\right) \sin^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$

         /          2        \    
     ___ |       csc (2*x)   |    
   \/ 2 *|-1 + --------------|    
         |        2/pi      \|    
         |     csc |-- - 2*x||    
         \         \2       //    
----------------------------------
                     3/2          
  /          1      \       2     
4*|1 + -------------|   *csc (2*x)
  |       /pi      \|             
  |    csc|-- - 8*x||             
  \       \2       //

$$\frac{\sqrt{2} \left(\frac{\csc^{2}{\left(2 x \right)}}{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}} - 1\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(2 x \right)}}$$

  ___    2       4    /        2     \
\/ 2 *cot (x)*sin (x)*\-1 + cot (2*x)/
--------------------------------------
                                 3/2  
 /       2      /        2     \\     
 \1 + sin (4*x)*\-1 + cot (4*x)//

$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \sin^{4}{\left(x \right)} \cot^{2}{\left(x \right)}}{\left(\left(\cot^{2}{\left(4 x \right)} - 1\right) \sin^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$

                     2                  
   ___ /        2   \  /        1    \  
 \/ 2 *\-1 + cot (x)/ *|1 - ---------|  
                       |       2     |  
                       \    cot (2*x)/  
----------------------------------------
                                     3/2
               2 /            2     \   
  /       2   \  |    -1 + cot (4*x)|   
4*\1 + cot (x)/ *|1 + --------------|   
                 |           2      |   
                 \    1 + cot (4*x) /

$$\frac{\sqrt{2} \left(1 - \frac{1}{\cot^{2}{\left(2 x \right)}}\right) \left(\cot^{2}{\left(x \right)} - 1\right)^{2}}{4 \left(\frac{\cot^{2}{\left(4 x \right)} - 1}{\cot^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}$$

                /       2/      pi\\
                |    cos |2*x - --||
  ___    2      |        \      2 /|
\/ 2 *cos (2*x)*|1 - --------------|
                |         2        |
                \      cos (2*x)   /
------------------------------------
                        3/2         
        4*(1 + cos(8*x))

$$\frac{\sqrt{2} \left(1 - \frac{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$

        2/      pi\    /      pi\    
     sin |2*x + --|*cot|2*x + --|    
         \      4 /    \      4 /    
-------------------------------------
                                  3/2
   /   2/      pi\    4/      pi\\   
32*|cot |2*x + --|*sin |2*x + --||   
   \    \      4 /     \      4 //

$$\frac{\sin^{2}{\left(2 x + \frac{\pi}{4} \right)} \cot{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\sin^{4}{\left(2 x + \frac{\pi}{4} \right)} \cot^{2}{\left(2 x + \frac{\pi}{4} \right)}\right)^{\frac{3}{2}}}$$

  ___    2      /       2     \
\/ 2 *cos (2*x)*\1 - tan (2*x)/
-------------------------------
                         3/2   
      /          1      \      
    4*|1 + -------------|      
      |       /pi      \|      
      |    csc|-- - 8*x||      
      \       \2       //

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{2}{\left(2 x \right)}}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}}}$$

  ___    2      /       2     \
\/ 2 *cos (2*x)*\1 - tan (2*x)/
-------------------------------
                      3/2      
      4*(1 + cos(8*x))

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$

             /       2/pi      \\      
             |    csc |-- - 2*x||      
         ___ |        \2       /|      
       \/ 2 *|1 - --------------|      
             |         2        |      
             \      csc (2*x)   /      
---------------------------------------
                     3/2               
  /          1      \       2/pi      \
4*|1 + -------------|   *csc |-- - 2*x|
  |       /pi      \|        \2       /
  |    csc|-- - 8*x||                  
  \       \2       //

$$\frac{\sqrt{2} \left(1 - \frac{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}$$

                   2                        
  ___ /       2   \     4    /       2     \
\/ 2 *\1 - tan (x)/ *cos (x)*\1 - tan (2*x)/
--------------------------------------------
                                     3/2    
      /       2      /       2     \\       
    4*\1 + cos (4*x)*\1 - tan (4*x)//

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 x \right)}\right) \cos^{4}{\left(x \right)}}{4 \left(\left(1 - \tan^{2}{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$

                /         4     \
  ___    2      |    4*sin (2*x)|
\/ 2 *cos (2*x)*|1 - -----------|
                |        2      |
                \     sin (4*x) /
---------------------------------
                          3/2    
       /       /pi      \\       
     4*|1 + sin|-- + 8*x||       
       \       \2       //

$$\frac{\sqrt{2} \left(- \frac{4 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 1\right) \cos^{2}{\left(2 x \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$

      /pi      \   
   sin|-- + 4*x|   
      \2       /   
-------------------
                3/2
     2/pi      \   
8*sin |-- + 4*x|   
      \2       /

$$\frac{\sin{\left(4 x + \frac{\pi}{2} \right)}}{8 \left(\sin^{2}{\left(4 x + \frac{\pi}{2} \right)}\right)^{\frac{3}{2}}}$$

                     /      pi\                   
                  tan|2*x + --|                   
                     \      4 /                   
--------------------------------------------------
                          3/2                     
   /       2/      pi\   \                        
   |    tan |2*x + --|   |                        
   |        \      4 /   |    /       2/      pi\\
32*|---------------------|   *|1 + tan |2*x + --||
   |                    2|    \        \      4 //
   |/       2/      pi\\ |                        
   ||1 + tan |2*x + --|| |                        
   \\        \      4 // /

$$\frac{\tan{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\frac{\tan^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\tan^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$

                /         2      \
  ___    2      |      sin (4*x) |
\/ 2 *sin (2*x)*|-1 + -----------|
                |          4     |
                \     4*sin (2*x)/
----------------------------------
                          3/2     
       /       /pi      \\        
     4*|1 + sin|-- + 8*x||        
       \       \2       //

$$\frac{\sqrt{2} \left(-1 + \frac{\sin^{2}{\left(4 x \right)}}{4 \sin^{4}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$

                 1                 
-----------------------------------
                  3/2              
  /      1       \       /pi      \
8*|--------------|   *csc|-- - 4*x|
  |   2/pi      \|       \2       /
  |csc |-- - 4*x||                 
  \    \2       //

$$\frac{1}{8 \left(\frac{1}{\csc^{2}{\left(- 4 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc{\left(- 4 x + \frac{\pi}{2} \right)}}$$

        /         2        \ 
    ___ |      sec (2*x)   | 
  \/ 2 *|1 - --------------| 
        |       2/      pi\| 
        |    sec |2*x - --|| 
        \        \      2 // 
-----------------------------
                3/2          
  /       1    \       2     
4*|1 + --------|   *sec (2*x)
  \    sec(8*x)/

$$\frac{\sqrt{2} \left(- \frac{\sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} + 1\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x \right)}}$$

        ___ /         1    \      
      \/ 2 *|-1 + ---------|      
            |        2     |      
            \     tan (2*x)/      
----------------------------------
                     3/2          
  /          1      \       2     
4*|1 + -------------|   *csc (2*x)
  |       /pi      \|             
  |    csc|-- - 8*x||             
  \       \2       //

$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\csc{\left(- 8 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{2}} \csc^{2}{\left(2 x \right)}}$$

         /        2/      pi\\    
         |     sec |2*x - --||    
     ___ |         \      2 /|    
   \/ 2 *|-1 + --------------|    
         |          2        |    
         \       sec (2*x)   /    
----------------------------------
                3/2               
  /       1    \       2/      pi\
4*|1 + --------|   *sec |2*x - --|
  \    sec(8*x)/        \      2 /

$$\frac{\sqrt{2} \left(-1 + \frac{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 x \right)}}\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}$$

  ___    2      /        2     \
\/ 2 *sin (2*x)*\-1 + cot (2*x)/
--------------------------------
                      3/2       
      4*(1 + cos(8*x))

$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \sin^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$

      ___    2    /         1    \   
    \/ 2 *tan (x)*|-1 + ---------|   
                  |        2     |   
                  \     tan (2*x)/   
-------------------------------------
                                  3/2
             2 /           2     \   
/       2   \  |    1 - tan (4*x)|   
\1 + tan (x)/ *|1 + -------------|   
               |           2     |   
               \    1 + tan (4*x)/

$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \tan^{2}{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(4 x \right)}}{\tan^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}$$

      ___ /       2     \    
    \/ 2 *\1 - tan (2*x)/    
-----------------------------
                3/2          
  /       1    \       2     
4*|1 + --------|   *sec (2*x)
  \    sec(8*x)/

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(2 x \right)}\right)}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}} \sec^{2}{\left(2 x \right)}}$$

                     /         4     \
  ___    2/pi      \ |    4*sin (2*x)|
\/ 2 *sin |-- + 2*x|*|1 - -----------|
          \2       / |        2      |
                     \     sin (4*x) /
--------------------------------------
                            3/2       
         /       /pi      \\          
       4*|1 + sin|-- + 8*x||          
         \       \2       //

$$\frac{\sqrt{2} \left(- \frac{4 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 1\right) \sin^{2}{\left(2 x + \frac{\pi}{2} \right)}}{4 \left(\sin{\left(8 x + \frac{\pi}{2} \right)} + 1\right)^{\frac{3}{2}}}$$

                     2                 
    ___ /       2   \  /       2     \ 
  \/ 2 *\1 - tan (x)/ *\1 - tan (2*x)/ 
---------------------------------------
                                    3/2
               2 /           2     \   
  /       2   \  |    1 - tan (4*x)|   
4*\1 + tan (x)/ *|1 + -------------|   
                 |           2     |   
                 \    1 + tan (4*x)/

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 x \right)}\right)}{4 \left(\frac{1 - \tan^{2}{\left(4 x \right)}}{\tan^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}$$

  ___    2      /         1    \
\/ 2 *sin (2*x)*|-1 + ---------|
                |        2     |
                \     tan (2*x)/
--------------------------------
                      3/2       
        /       1    \          
      4*|1 + --------|          
        \    sec(8*x)/

$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(1 + \frac{1}{\sec{\left(8 x \right)}}\right)^{\frac{3}{2}}}$$

  ___    2      /         1    \
\/ 2 *sin (2*x)*|-1 + ---------|
                |        2     |
                \     tan (2*x)/
--------------------------------
                      3/2       
      4*(1 + cos(8*x))

$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \sin^{2}{\left(2 x \right)}}{4 \left(\cos{\left(8 x \right)} + 1\right)^{\frac{3}{2}}}$$

  ___    4       2    /         1    \
\/ 2 *cos (x)*tan (x)*|-1 + ---------|
                      |        2     |
                      \     tan (2*x)/
--------------------------------------
                                 3/2  
  /       2      /       2     \\     
  \1 + cos (4*x)*\1 - tan (4*x)//

$$\frac{\sqrt{2} \left(-1 + \frac{1}{\tan^{2}{\left(2 x \right)}}\right) \cos^{4}{\left(x \right)} \tan^{2}{\left(x \right)}}{\left(\left(1 - \tan^{2}{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)} + 1\right)^{\frac{3}{2}}}$$

                    2                  
             1 - tan (2*x)             
---------------------------------------
                    3/2                
  /               2\                   
  |/       2     \ |                   
  |\1 - tan (2*x)/ |    /       2     \
8*|----------------|   *\1 + tan (2*x)/
  |               2|                   
  |/       2     \ |                   
  \\1 + tan (2*x)/ /

$$\frac{1 - \tan^{2}{\left(2 x \right)}}{8 \left(\frac{\left(1 - \tan^{2}{\left(2 x \right)}\right)^{2}}{\left(\tan^{2}{\left(2 x \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$

                     2                  
             -1 + cot (2*x)             
----------------------------------------
                     3/2                
  /                2\                   
  |/        2     \ |                   
  |\-1 + cot (2*x)/ |    /       2     \
8*|-----------------|   *\1 + cot (2*x)/
  |                2|                   
  | /       2     \ |                   
  \ \1 + cot (2*x)/ /

$$\frac{\cot^{2}{\left(2 x \right)} - 1}{8 \left(\frac{\left(\cot^{2}{\left(2 x \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(2 x \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$

      ___    2    /        2     \    
    \/ 2 *cot (x)*\-1 + cot (2*x)/    
--------------------------------------
                                   3/2
             2 /            2     \   
/       2   \  |    -1 + cot (4*x)|   
\1 + cot (x)/ *|1 + --------------|   
               |           2      |   
               \    1 + cot (4*x) /

$$\frac{\sqrt{2} \left(\cot^{2}{\left(2 x \right)} - 1\right) \cot^{2}{\left(x \right)}}{\left(\frac{\cot^{2}{\left(4 x \right)} - 1}{\cot^{2}{\left(4 x \right)} + 1} + 1\right)^{\frac{3}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}$$

                     /      pi\                   
                  cot|2*x + --|                   
                     \      4 /                   
--------------------------------------------------
                          3/2                     
   /       2/      pi\   \                        
   |    cot |2*x + --|   |                        
   |        \      4 /   |    /       2/      pi\\
32*|---------------------|   *|1 + cot |2*x + --||
   |                    2|    \        \      4 //
   |/       2/      pi\\ |                        
   ||1 + cot |2*x + --|| |                        
   \\        \      4 // /

$$\frac{\cot{\left(2 x + \frac{\pi}{4} \right)}}{32 \left(\frac{\cot^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)^{2}}\right)^{\frac{3}{2}} \left(\cot^{2}{\left(2 x + \frac{\pi}{4} \right)} + 1\right)}$$

cot(2*x + pi/4)/(32*(cot(2*x + pi/4)^2/(1 + cot(2*x + pi/4)^2)^2)^(3/2)*(1 + cot(2*x + pi/4)^2))

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¿Cómo vas a descomponer esta cos(4*x)/(8*(cos(4*x)^2)^(3/2)) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta cos(4x)/(8(cos(4*x)^2)^(3/2)) expresión en fracciones?