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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)^(1/(x^2))*(-2*log(sin(x))/x^3+cos(x)/(x^2*sin(x)))

¿Cómo vas a descomponer esta sin(x)^(1/(x^2))(-2log(sin(x))/x^3+cos(x)/(x^2*sin(x))) expresión en fracciones?

Solución

Ha introducido [src]

        1                              
        --                             
         2                             
        x  /-2*log(sin(x))     cos(x) \
(sin(x))  *|-------------- + ---------|
           |       3          2       |
           \      x          x *sin(x)/

\left(\frac{\cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{\left(-1\right) 2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

sin(x)^(1/(x^2))*((-2*log(sin(x)))/x^3 + cos(x)/((x^2*sin(x))))

Simplificación general [src]

             1                                   
        -1 + --                                  
              2                                  
             x                                   
(sin(x))       *(x*cos(x) - 2*log(sin(x))*sin(x))
-------------------------------------------------
                         3                       
                        x

\frac{\left(x \cos{\left(x \right)} - 2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{-1 + \frac{1}{x^{2}}}{\left(x \right)}}{x^{3}}

sin(x)^(-1 + x^(-2))*(x*cos(x) - 2*log(sin(x))*sin(x))/x^3

Respuesta numérica [src]

sin(x)^(x^(-2))*(-2.0*log(sin(x))/x^3 + cos(x)/(x^2*sin(x)))

sin(x)^(x^(-2))*(-2.0*log(sin(x))/x^3 + cos(x)/(x^2*sin(x)))

Combinatoria [src]

        1                                   
        --                                  
         2                                  
        x                                   
(sin(x))  *(x*cos(x) - 2*log(sin(x))*sin(x))
--------------------------------------------
                  3                         
                 x *sin(x)

\frac{\left(x \cos{\left(x \right)} - 2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{3} \sin{\left(x \right)}}

sin(x)^(x^(-2))*(x*cos(x) - 2*log(sin(x))*sin(x))/(x^3*sin(x))

Potencias [src]

                      1                                                       
                      --                                                      
                       2 /       /   /   -I*x    I*x\ \        / I*x    -I*x\\
                      x  |       |-I*\- e     + e   / |        |e      e    ||
/   /   -I*x    I*x\ \   |  2*log|--------------------|    2*I*|---- + -----||
|-I*\- e     + e   / |   |       \         2          /        \ 2       2  /|
|--------------------|  *|- --------------------------- + -------------------|
\         2          /   |                3                2 /   -I*x    I*x\|
                         \               x                x *\- e     + e   //

\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)^{\frac{1}{x^{2}}} \left(\frac{2 i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{x^{2} \left(e^{i x} - e^{- i x}\right)} - \frac{2 \log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{x^{3}}\right)

        1                               
        --                              
         2                              
        x  /  2*log(sin(x))     cos(x) \
(sin(x))  *|- ------------- + ---------|
           |         3         2       |
           \        x         x *sin(x)/

\left(\frac{\cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

sin(x)^(x^(-2))*(-2*log(sin(x))/x^3 + cos(x)/(x^2*sin(x)))

Unión de expresiones racionales [src]

        1                                   
        --                                  
         2                                  
        x                                   
(sin(x))  *(x*cos(x) - 2*log(sin(x))*sin(x))
--------------------------------------------
                  3                         
                 x *sin(x)

\frac{\left(x \cos{\left(x \right)} - 2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{3} \sin{\left(x \right)}}

sin(x)^(x^(-2))*(x*cos(x) - 2*log(sin(x))*sin(x))/(x^3*sin(x))

Denominador común [src]

          1                     1                    
          --                    --                   
           2                     2                   
          x                     x                    
x*(sin(x))  *cos(x) - 2*(sin(x))  *log(sin(x))*sin(x)
-----------------------------------------------------
                       3                             
                      x *sin(x)

\frac{x \sin^{\frac{1}{x^{2}}}{\left(x \right)} \cos{\left(x \right)} - 2 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{3} \sin{\left(x \right)}}

(x*sin(x)^(x^(-2))*cos(x) - 2*sin(x)^(x^(-2))*log(sin(x))*sin(x))/(x^3*sin(x))

Denominador racional [src]

                1                             1                    
           -1 + --                       -1 + --                   
                 2                             2                   
 3              x              2              x                    
x *(sin(x))       *cos(x) - 2*x *(sin(x))       *log(sin(x))*sin(x)
-------------------------------------------------------------------
                                  5                                
                                 x

\frac{x^{3} \sin^{-1 + \frac{1}{x^{2}}}{\left(x \right)} \cos{\left(x \right)} - 2 x^{2} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{-1 + \frac{1}{x^{2}}}{\left(x \right)}}{x^{5}}

(x^3*sin(x)^(-1 + x^(-2))*cos(x) - 2*x^2*sin(x)^(-1 + x^(-2))*log(sin(x))*sin(x))/x^5

Abrimos la expresión [src]

            1                        1        
            --                       --       
             2                        2       
            x                        x        
  2*(sin(x))  *log(sin(x))   (sin(x))  *cos(x)
- ------------------------ + -----------------
              3                   2           
             x                   x *sin(x)

\frac{\sin^{\frac{1}{x^{2}}}{\left(x \right)} \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)} \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{3}}

        1                              
        --                             
         2                             
        x  /-2*log(sin(x))     cos(x) \
(sin(x))  *|-------------- + ---------|
           |       3          2       |
           \      x          x *sin(x)/

\left(\frac{\left(-1\right) 2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}} + \frac{\cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

sin(x)^(1/(x^2))*((-2*log(sin(x)))/x^3 + cos(x)/(x^2*sin(x)))

Parte trigonométrica [src]

        1                                   
        -- /   /x\      /x\                \
         2 |cot|-|   tan|-|                |
        x  |   \2/      \2/   2*log(sin(x))|
(sin(x))  *|------ - ------ - -------------|
           \  2        2            x      /
--------------------------------------------
                      2                     
                     x

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

        1                                     
        -- /              /x\                \
         2 |           tan|-|                |
        x  |   1          \2/   2*log(sin(x))|
(sin(x))  *|-------- - ------ - -------------|
           |     /x\     2            x      |
           |2*tan|-|                         |
           \     \2/                         /
----------------------------------------------
                       2                      
                      x

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

        1                               
        --                              
         2                              
        x  /  2*log(sin(x))     cos(x) \
(sin(x))  *|- ------------- + ---------|
           |         3         2       |
           \        x         x *sin(x)/

\left(\frac{\cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

             1  /       /       /x\ \               \
             -- |       |  2*cot|-| |               |
              2 |       |       \2/ |               |
             x  |  2*log|-----------|               |
/       /x\ \   |       |       2/x\|           2/x\|
|  2*cot|-| |   |       |1 + cot |-||   -1 + cot |-||
|       \2/ |   |       \        \2//            \2/|
|-----------|  *|- ------------------ + ------------|
|       2/x\|   |           3              2    /x\ |
|1 + cot |-||   |          x            2*x *cot|-| |
\        \2//   \                               \2/ /

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

             1  /                   /     1     \                \
             -- |              2*log|-----------|                |
              2 |   /x   pi\        |   /    pi\|          /x\   |
             x  |sec|- - --|        |sec|x - --||       sec|-|   |
/     1     \   |   \2   2 /        \   \    2 //          \2/   |
|-----------|  *|----------- - ------------------ - -------------|
|   /    pi\|   |       /x\            x                 /x   pi\|
|sec|x - --||   |  2*sec|-|                         2*sec|- - --||
\   \    2 //   \       \2/                              \2   2 //
------------------------------------------------------------------
                                 2                                
                                x

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

             1                                         
             --                                        
              2 /       /   /    pi\\                 \
             x  |  2*log|cos|x - --||                 |
/   /    pi\\   |       \   \    2 //       cos(x)    |
|cos|x - --||  *|- ------------------ + --------------|
\   \    2 //   |           3            2    /    pi\|
                |          x            x *cos|x - --||
                \                             \    2 //

\left(\frac{\cos{\left(x \right)}}{x^{2} \cos{\left(x - \frac{\pi}{2} \right)}} - \frac{2 \log{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}}{x^{3}}\right) \cos^{\frac{1}{x^{2}}}{\left(x - \frac{\pi}{2} \right)}

        1                                    
        --                                   
         2 /       /  1   \                 \
        x  |  2*log|------|                 |
/  1   \   |       \csc(x)/       csc(x)    |
|------|  *|- ------------- + --------------|
\csc(x)/   |         3         2    /pi    \|
           |        x         x *csc|-- - x||
           \                        \2     //

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

        1                               
        --                              
         2 /       /  1   \            \
        x  |  2*log|------|            |
/  1   \   |       \csc(x)/     csc(x) |
|------|  *|- ------------- + ---------|
\csc(x)/   |         3         2       |
           \        x         x *sec(x)/

\left(\frac{\csc{\left(x \right)}}{x^{2} \sec{\left(x \right)}} - \frac{2 \log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{x^{3}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\frac{1}{x^{2}}}

             1  /       /     1     \              \
             -- |  2*log|-----------|              |
              2 |       |   /    pi\|      /    pi\|
             x  |       |sec|x - --||   sec|x - --||
/     1     \   |       \   \    2 //      \    2 /|
|-----------|  *|- ------------------ + -----------|
|   /    pi\|   |           3             2        |
|sec|x - --||   \          x             x *sec(x) /
\   \    2 //

\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{x^{2} \sec{\left(x \right)}} - \frac{2 \log{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{x^{3}}\right) \left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\frac{1}{x^{2}}}

        1                          
        --                         
         2                         
        x  /  1      2*log(sin(x))\
(sin(x))  *|------ - -------------|
           \tan(x)         x      /
-----------------------------------
                  2                
                 x

\frac{\left(\frac{1}{\tan{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{2}}

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

\frac{\left(\cot{\left(x \right)} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}}{x^{2}}

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

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

             1                                                    
             --                                                   
              2 /       /x\           /   /    pi\\      /x   pi\\
             x  |    cos|-|      2*log|cos|x - --||   cos|- - --||
/   /    pi\\   |       \2/           \   \    2 //      \2   2 /|
|cos|x - --||  *|------------- - ------------------ - -----------|
\   \    2 //   |     /x   pi\           x                   /x\ |
                |2*cos|- - --|                          2*cos|-| |
                \     \2   2 /                               \2/ /
------------------------------------------------------------------
                                 2                                
                                x

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

        1                             
        --                            
         2                            
        x  / sin(2*x)   2*log(sin(x))\
(sin(x))  *|--------- - -------------|
           |     2            x      |
           \2*sin (x)                /
--------------------------------------
                   2                  
                  x

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

             1  /       /       /x\ \              \
             -- |       |  2*tan|-| |              |
              2 |       |       \2/ |              |
             x  |  2*log|-----------|              |
/       /x\ \   |       |       2/x\|          2/x\|
|  2*tan|-| |   |       |1 + tan |-||   1 - tan |-||
|       \2/ |   |       \        \2//           \2/|
|-----------|  *|- ------------------ + -----------|
|       2/x\|   |           3              2    /x\|
|1 + tan |-||   |          x            2*x *tan|-||
\        \2//   \                               \2//

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

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

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

             1  /                   /     1     \\
             -- |              2*log|-----------||
              2 |   /    pi\        |   /    pi\||
             x  |sec|x - --|        |sec|x - --|||
/     1     \   |   \    2 /        \   \    2 //|
|-----------|  *|----------- - ------------------|
|   /    pi\|   \   sec(x)             x         /
|sec|x - --||                                     
\   \    2 //                                     
--------------------------------------------------
                         2                        
                        x

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

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

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

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

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

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

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

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

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

        1                                 
        -- /                     /    pi\\
         2 |                  sin|x + --||
        x  |  2*log(sin(x))      \    2 /|
(sin(x))  *|- ------------- + -----------|
           |         3          2        |
           \        x          x *sin(x) /

\left(\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

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

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

        1                               
        --                              
         2 /                   /  1   \\
        x  |              2*log|------||
/  1   \   |   csc(x)          \csc(x)/|
|------|  *|----------- - -------------|
\csc(x)/   |   /pi    \         x      |
           |csc|-- - x|                |
           \   \2     /                /
----------------------------------------
                    2                   
                   x

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

        1                                               
        --                                              
         2 /       /x\           /  1   \      /pi   x\\
        x  |    csc|-|      2*log|------|   csc|-- - -||
/  1   \   |       \2/           \csc(x)/      \2    2/|
|------|  *|------------- - ------------- - -----------|
\csc(x)/   |     /pi   x\         x                /x\ |
           |2*csc|-- - -|                     2*csc|-| |
           \     \2    2/                          \2/ /
--------------------------------------------------------
                            2                           
                           x

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

(1/csc(x))^(x^(-2))*(csc(x/2)/(2*csc(pi/2 - x/2)) - 2*log(1/csc(x))/x - csc(pi/2 - x/2)/(2*csc(x/2)))/x^2

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        1                               
        --                              
         2                              
        x  /  2*log(sin(x))     cos(x) \
(sin(x))  *|- ------------- + ---------|
           |         3         2       |
           \        x         x *sin(x)/

\left(\frac{\cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(\sin{\left(x \right)} \right)}}{x^{3}}\right) \sin^{\frac{1}{x^{2}}}{\left(x \right)}

sin(x)^(1/(x^2))*(-2*log(sin(x))/x^3 + cos(x)/(x^2*sin(x)))

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¿Cómo vas a descomponer esta sin(x)^(1/(x^2))(-2log(sin(x))/x^3+cos(x)/(x^2*sin(x))) expresión en fracciones?

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

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Expresiones con funciones

¿Cómo vas a descomponer esta sin(x)^(1/(x^2))*(-2*log(sin(x))/x^3+cos(x)/(x^2*sin(x))) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta sin(x)^(1/(x^2))(-2log(sin(x))/x^3+cos(x)/(x^2*sin(x))) expresión en fracciones?