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¿cómo vas a descomponer esta expresión en fracciones?:
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
(x^2-5*x+6)/(x-3)
a^5*b^4/(a*b^3)^2
(2x+3)/(x^2-9)
Factorizar el polinomio:
z^2-36
z^3-2*z^2+z-2
z^2-20*z+104
z^3/4-2*z^3/9+7*z^3/12
Descomponer al cuadrado:
-y^4+y^2+15
-y^4+y^2+11
y^4-9*y^2+7
y^4+9*y^2+8
Integral de d{x}:
1/(sin^2x*cos^2x)
Expresiones idénticas
uno /(sin^2x*cos^2x)
1 dividir por ( seno de al cuadrado x multiplicar por coseno de al cuadrado x)
uno dividir por ( seno de al cuadrado x multiplicar por coseno de al cuadrado x)
1/(sin2x*cos2x)
1/sin2x*cos2x
1/(sin²x*cos²x)
1/(sin en el grado 2x*cos en el grado 2x)
1/(sin^2xcos^2x)
1/(sin2xcos2x)
1/sin2xcos2x
1/sin^2xcos^2x
1 dividir por (sin^2x*cos^2x)
Expresiones con funciones
Seno sin
sin(2*x)/((9*sin(x)))
sin(2*x)/((5*sin(x)))
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(2*x)/((19*sin(x)))
sin10/(2*cos5)
Coseno cos
cos(4*x)/(cos(2*x)-sin(2*x))
cos(x)^2/(1-sin(x))^2-sin(x)/(1-sin(x))
cos(x)^5+cos(x)^7/(6*sin(x)^2)
cos(x)*sin(x)/(cos(x)+sin(x))/(1-cos(x)*sin(x))
cos(sqrt(x))/(2*sqrt(x)*sin(sqrt(x)))

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

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

Solución

Ha introducido [src]

       1       
---------------
   2       2   
sin (x)*cos (x)

\frac{1}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}

1/(sin(x)^2*cos(x)^2)

Simplificación general [src]

     8      
------------
1 - cos(4*x)

\frac{8}{1 - \cos{\left(4 x \right)}}

8/(1 - cos(4*x))

Potencias [src]

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

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

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

Respuesta numérica [src]

1/(cos(x)^2*sin(x)^2)

1/(cos(x)^2*sin(x)^2)

Parte trigonométrica [src]

    4    
---------
   2     
sin (2*x)

\frac{4}{\sin^{2}{\left(2 x \right)}}

                8           
   /       2/x\\     2/x\   
   |1 + tan |-|| *tan |-|   
   \        \4//      \2/   
----------------------------
                   2        
     /        1   \     8/x\
1024*|-1 + -------| *tan |-|
     |        2/x\|      \4/
     |     tan |-||         
     \         \2//

\frac{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{8} \tan^{2}{\left(\frac{x}{2} \right)}}{1024 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \tan^{8}{\left(\frac{x}{4} \right)}}

        8         
------------------
            2     
    -1 + cot (2*x)
1 - --------------
           2      
    1 + cot (2*x)

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

              6/x\           
           sec |-|           
               \2/           
-----------------------------
               2             
  /       2/x\\              
2*|1 - tan |-|| *(1 - cos(x))
  \        \2//

\frac{\sec^{6}{\left(\frac{x}{2} \right)}}{2 \left(1 - \cos{\left(x \right)}\right) \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}

                   4     
      /       2/x\\      
      |1 + cot |-||      
      \        \2//      
-------------------------
                2        
  /        2/x\\     2/x\
4*|-1 + cot |-|| *cot |-|
  \         \2//      \2/

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

                  4     
     /       2/x\\      
     |1 + tan |-||      
     \        \2//      
------------------------
               2        
  /       2/x\\     2/x\
4*|1 - tan |-|| *tan |-|
  \        \2//      \2/

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

        8        
-----------------
           2     
    1 - tan (2*x)
1 - -------------
           2     
    1 + tan (2*x)

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

     8      
------------
       1    
1 - --------
    sec(4*x)

\frac{8}{1 - \frac{1}{\sec{\left(4 x \right)}}}

    2/x\    6/pi   x\
 csc |-|*csc |-- - -|
     \2/     \2    2/
---------------------
                    2
  /       2/pi   x\\ 
  |    csc |-- - -|| 
  |        \2    2/| 
4*|1 - ------------| 
  |         2/x\   | 
  |      csc |-|   | 
  \          \2/   /

\frac{\csc^{2}{\left(\frac{x}{2} \right)} \csc^{6}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{4 \left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{2}}

                   2                    
                sin (x)                 
----------------------------------------
                  2                     
   /         4/x\\                      
   |    4*sin |-||                      
   |          \2/|     4/x\    8/pi   x\
16*|1 - ---------| *sin |-|*sin |-- + -|
   |        2    |      \2/     \2    2/
   \     sin (x) /

\frac{\sin^{2}{\left(x \right)}}{16 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)} \sin^{8}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}

                    2/x\                 
                 cot |-|                 
                     \2/                 
-----------------------------------------
               2               8         
  /       2/x\\  /        2/x\\     16/x\
4*|1 - tan |-|| *|-1 + cot |-|| *sin  |-|
  \        \2//  \         \4//       \4/

\frac{\cot^{2}{\left(\frac{x}{2} \right)}}{4 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{8} \sin^{16}{\left(\frac{x}{4} \right)}}

         1          
--------------------
   2       2/    pi\
cos (x)*cos |x - --|
            \    2 /

\frac{1}{\cos^{2}{\left(x \right)} \cos^{2}{\left(x - \frac{\pi}{2} \right)}}

   2       2/pi    \
csc (x)*csc |-- - x|
            \2     /

\csc^{2}{\left(x \right)} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}

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

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

   2       2/    pi\
sec (x)*sec |x - --|
            \    2 /

\sec^{2}{\left(x \right)} \sec^{2}{\left(x - \frac{\pi}{2} \right)}

   2       2   
csc (x)*sec (x)

\csc^{2}{\left(x \right)} \sec^{2}{\left(x \right)}

                          8            
             /       2/x\\             
             |1 + tan |-||             
             \        \4//             
---------------------------------------
               2              8        
  /       2/x\\  /       2/x\\     2/x\
4*|1 - tan |-|| *|1 - tan |-|| *tan |-|
  \        \2//  \        \4//      \2/

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

    6/x\    2/pi   x\ 
 csc |-|*csc |-- - -| 
     \2/     \2    2/ 
----------------------
                     2
  /          2/x\   \ 
  |       csc |-|   | 
  |           \2/   | 
4*|-1 + ------------| 
  |        2/pi   x\| 
  |     csc |-- - -|| 
  \         \2    2//

\frac{\csc^{6}{\left(\frac{x}{2} \right)} \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{4 \left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}

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

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

            2/x\         
         tan |-|         
             \2/         
-------------------------
                2        
  /        2/x\\     8/x\
4*|-1 + cot |-|| *sin |-|
  \         \2//      \2/

\frac{\tan^{2}{\left(\frac{x}{2} \right)}}{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{x}{2} \right)}}

                     1                     
-------------------------------------------
                     2                     
  /          2/x\   \                      
  |       cos |-|   |                      
  |           \2/   |     2/x\    6/x   pi\
4*|-1 + ------------| *cos |-|*cos |- - --|
  |        2/x   pi\|      \2/     \2   2 /
  |     cos |- - --||                      
  \         \2   2 //

\frac{1}{4 \left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2} \cos^{2}{\left(\frac{x}{2} \right)} \cos^{6}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}

         1          
--------------------
   2       2/    pi\
sin (x)*sin |x + --|
            \    2 /

\frac{1}{\sin^{2}{\left(x \right)} \sin^{2}{\left(x + \frac{\pi}{2} \right)}}

     8      
------------
1 - cos(4*x)

\frac{8}{1 - \cos{\left(4 x \right)}}

                     2        
        (-1 + cos(x))         
------------------------------
                  2       6/x\
8*(1 + cos(x))*cos (x)*sin |-|
                           \2/

\frac{\left(\cos{\left(x \right)} - 1\right)^{2}}{8 \left(\cos{\left(x \right)} + 1\right) \sin^{6}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)}}

                    2         
        (1 + cos(x))          
------------------------------
                  2       6/x\
8*(1 - cos(x))*cos (x)*cos |-|
                           \2/

\frac{\left(\cos{\left(x \right)} + 1\right)^{2}}{8 \left(1 - \cos{\left(x \right)}\right) \cos^{6}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)}}

                       1                        
------------------------------------------------
               2              8                 
  /       2/x\\  /       2/x\\     16/x\    2/x\
4*|1 - tan |-|| *|1 - tan |-|| *cos  |-|*tan |-|
  \        \2//  \        \4//       \4/     \2/

\frac{1}{4 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{8} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \cos^{16}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}

                1                
---------------------------------
                2                
/         2    \                 
|      sin (x) |     2       4/x\
|-1 + ---------| *sin (x)*sin |-|
|          4/x\|              \2/
|     4*sin |-||                 
\           \2//

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

                        8           
           /       2/x\\            
           |1 + cot |-||            
           \        \4//            
------------------------------------
                   2                
     /        2/x\\     2/x\    8/x\
1024*|-1 + cot |-|| *cot |-|*cot |-|
     \         \2//      \2/     \4/

\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{8}}{1024 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \cot^{8}{\left(\frac{x}{4} \right)} \cot^{2}{\left(\frac{x}{2} \right)}}

                  2/x\               
               tan |-|               
                   \2/               
-------------------------------------
                   2                 
     /        1   \     16/x\    8/x\
1024*|-1 + -------| *cos  |-|*tan |-|
     |        2/x\|       \4/     \4/
     |     tan |-||                  
     \         \2//

\frac{\tan^{2}{\left(\frac{x}{2} \right)}}{1024 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cos^{16}{\left(\frac{x}{4} \right)} \tan^{8}{\left(\frac{x}{4} \right)}}

    6/x\    2/x   pi\
 sec |-|*sec |- - --|
     \2/     \2   2 /
---------------------
                    2
  /         2/x\   \ 
  |      sec |-|   | 
  |          \2/   | 
4*|1 - ------------| 
  |       2/x   pi\| 
  |    sec |- - --|| 
  \        \2   2 //

\frac{\sec^{6}{\left(\frac{x}{2} \right)} \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{4 \left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}

             2  
 (1 + cos(x))   
----------------
   /x\    2     
cos|-|*sin (2*x)
   \2/

\frac{\left(\cos{\left(x \right)} + 1\right)^{2}}{\sin^{2}{\left(2 x \right)} \cos{\left(\frac{x}{2} \right)}}

              6/x\            
           csc |-|            
               \2/            
------------------------------
                             2
               /        1   \ 
2*(1 + cos(x))*|-1 + -------| 
               |        2/x\| 
               |     tan |-|| 
               \         \2//

\frac{\csc^{6}{\left(\frac{x}{2} \right)}}{2 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \left(\cos{\left(x \right)} + 1\right)}

               2 
  (-1 + cos(x))  
-----------------
   4/x\    2     
sin |-|*sin (2*x)
    \2/

\frac{\left(\cos{\left(x \right)} - 1\right)^{2}}{\sin^{4}{\left(\frac{x}{2} \right)} \sin^{2}{\left(2 x \right)}}

               1                
--------------------------------
               2                
  /       2/x\\     8/x\    2/x\
4*|1 - tan |-|| *cos |-|*tan |-|
  \        \2//      \2/     \2/

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

                    1                     
------------------------------------------
                    2                     
  /       2/x   pi\\                      
  |    cos |- - --||                      
  |        \2   2 /|     6/x\    2/x   pi\
4*|1 - ------------| *cos |-|*cos |- - --|
  |         2/x\   |      \2/     \2   2 /
  |      cos |-|   |                      
  \          \2/   /

\frac{1}{4 \left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cos^{6}{\left(\frac{x}{2} \right)} \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}

                  8             
     /       2/x\\     2/x\     
     |1 + cot |-|| *cot |-|     
     \        \4//      \2/     
--------------------------------
               2               8
  /       1   \  /        2/x\\ 
4*|1 - -------| *|-1 + cot |-|| 
  |       2/x\|  \         \4// 
  |    cot |-||                 
  \        \2//

\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{8} \cot^{2}{\left(\frac{x}{2} \right)}}{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{8}}

          2/x\    8/x\       
       tan |-|*tan |-|       
           \2/     \4/       
-----------------------------
                   2         
     /        2/x\\     16/x\
1024*|-1 + cot |-|| *sin  |-|
     \         \2//       \4/

\frac{\tan^{8}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{1024 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{16}{\left(\frac{x}{4} \right)}}

    2/x\    6/x   pi\ 
 sec |-|*sec |- - --| 
     \2/     \2   2 / 
----------------------
                     2
  /        2/x   pi\\ 
  |     sec |- - --|| 
  |         \2   2 /| 
4*|-1 + ------------| 
  |          2/x\   | 
  |       sec |-|   | 
  \           \2/   /

\frac{\sec^{2}{\left(\frac{x}{2} \right)} \sec^{6}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{4 \left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{2}}

sec(x/2)^2*sec(x/2 - pi/2)^6/(4*(-1 + sec(x/2 - pi/2)^2/sec(x/2)^2)^2)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

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

Solución