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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)^5+cos(x)^7/(6*sin(x)^2)

¿Cómo vas a descomponer esta cos(x)^5+cos(x)^7/(6*sin(x)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
              7    
   5       cos (x) 
cos (x) + ---------
               2   
          6*sin (x)
cos⁡5(x)+cos⁡7(x)6sin⁡2(x)\cos^{5}{\left(x \right)} + \frac{\cos^{7}{\left(x \right)}}{6 \sin^{2}{\left(x \right)}} 
cos(x)^5 + cos(x)^7/((6*sin(x)^2))
Simplificación general [src] 
   5    /       1   \
cos (x)*|5 + -------|
        |       2   |
        \    sin (x)/
---------------------
          6
(5+1sin⁡2(x))cos⁡5(x)6\frac{\left(5 + \frac{1}{\sin^{2}{\left(x \right)}}\right) \cos^{5}{\left(x \right)}}{6} 
cos(x)^5*(5 + sin(x)^(-2))/6
Combinatoria [src] 
   5    /   2           2   \
cos (x)*\cos (x) + 6*sin (x)/
-----------------------------
               2             
          6*sin (x)
(6sin⁡2(x)+cos⁡2(x))cos⁡5(x)6sin⁡2(x)\frac{\left(6 \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \cos^{5}{\left(x \right)}}{6 \sin^{2}{\left(x \right)}} 
cos(x)^5*(cos(x)^2 + 6*sin(x)^2)/(6*sin(x)^2)
Potencias [src] 
                                   7 
                     / I*x    -I*x\  
              5      |e      e    |  
/ I*x    -I*x\     2*|---- + -----|  
|e      e    |       \ 2       2  /  
|---- + -----|  - -------------------
\ 2       2  /                      2
                    /   -I*x    I*x\ 
                  3*\- e     + e   /
−2(eix2+e−ix2)73(eix−e−ix)2+(eix2+e−ix2)5- \frac{2 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{7}}{3 \left(e^{i x} - e^{- i x}\right)^{2}} + \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{5} 
(exp(i*x)/2 + exp(-i*x)/2)^5 - 2*(exp(i*x)/2 + exp(-i*x)/2)^7/(3*(-exp(-i*x) + exp(i*x))^2)
Respuesta numérica [src] 
cos(x)^5 + 0.166666666666667*cos(x)^7/sin(x)^2
cos(x)^5 + 0.166666666666667*cos(x)^7/sin(x)^2
Unión de expresiones racionales [src] 
   5    /   2           2   \
cos (x)*\cos (x) + 6*sin (x)/
-----------------------------
               2             
          6*sin (x)
(6sin⁡2(x)+cos⁡2(x))cos⁡5(x)6sin⁡2(x)\frac{\left(6 \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \cos^{5}{\left(x \right)}}{6 \sin^{2}{\left(x \right)}} 
cos(x)^5*(cos(x)^2 + 6*sin(x)^2)/(6*sin(x)^2)
Parte trigonométrica [src] 
                 5              5                                          
     /       /x\\  /        /x\\     10/x\    10/x\ /       1         22  \
-128*|1 + tan|-|| *|-1 + tan|-|| *cos  |-|*sin  |-|*|1 + ------- + -------|
     \       \2//  \        \2//       \4/      \4/ |       4/x\      2/x\|
                                                    |    tan |-|   tan |-||
                                                    \        \2/       \2//
---------------------------------------------------------------------------
                                      8/x\                                 
                                 3*tan |-|                                 
                                       \2/
−128(tan⁡(x2)−1)5(tan⁡(x2)+1)5(1+22tan⁡2(x2)+1tan⁡4(x2))sin⁡10(x4)cos⁡10(x4)3tan⁡8(x2)- \frac{128 \left(\tan{\left(\frac{x}{2} \right)} - 1\right)^{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)^{5} \left(1 + \frac{22}{\tan^{2}{\left(\frac{x}{2} \right)}} + \frac{1}{\tan^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{10}{\left(\frac{x}{4} \right)} \cos^{10}{\left(\frac{x}{4} \right)}}{3 \tan^{8}{\left(\frac{x}{2} \right)}} 
        5       10/x\         7       2/x\    12/x\
  32*cos (x)*sin  |-|   16*cos (x)*sec |-|*sin  |-|
                  \2/                  \2/      \2/
- ------------------- - ---------------------------
                  5                          7     
     (-1 + cos(x))            3*(-1 + cos(x))
−32sin⁡10(x2)cos⁡5(x)(cos⁡(x)−1)5−16sin⁡12(x2)cos⁡7(x)sec⁡2(x2)3(cos⁡(x)−1)7- \frac{32 \sin^{10}{\left(\frac{x}{2} \right)} \cos^{5}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{5}} - \frac{16 \sin^{12}{\left(\frac{x}{2} \right)} \cos^{7}{\left(x \right)} \sec^{2}{\left(\frac{x}{2} \right)}}{3 \left(\cos{\left(x \right)} - 1\right)^{7}} 
                                             7         
                             /         2    \          
                             |      sin (x) |     14/x\
                             |-1 + ---------| *sin  |-|
                5            |          4/x\|       \2/
/         2    \             |     4*sin |-||          
|      sin (x) |     10/x\   \           \2//          
|-1 + ---------| *sin  |-| + --------------------------
|          4/x\|       \2/                2            
|     4*sin |-||                     6*sin (x)         
\           \2//
(−1+sin⁡2(x)4sin⁡4(x2))7sin⁡14(x2)6sin⁡2(x)+(−1+sin⁡2(x)4sin⁡4(x2))5sin⁡10(x2)\frac{\left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{7} \sin^{14}{\left(\frac{x}{2} \right)}}{6 \sin^{2}{\left(x \right)}} + \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{5} \sin^{10}{\left(\frac{x}{2} \right)} 
                                                 7         
                               /       2/x   pi\\          
                               |    cos |- - --||          
                               |        \2   2 /|     12/x\
                  5            |1 - ------------| *cos  |-|
/       2/x   pi\\             |         2/x\   |       \2/
|    cos |- - --||             |      cos |-|   |          
|        \2   2 /|     10/x\   \          \2/   /          
|1 - ------------| *cos  |-| + ----------------------------
|         2/x\   |       \2/               2/x   pi\       
|      cos |-|   |                   24*cos |- - --|       
\          \2/   /                          \2   2 /
(1−cos⁡2(x2−π2)cos⁡2(x2))7cos⁡12(x2)24cos⁡2(x2−π2)+(1−cos⁡2(x2−π2)cos⁡2(x2))5cos⁡10(x2)\frac{\left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \cos^{12}{\left(\frac{x}{2} \right)}}{24 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{5} \cos^{10}{\left(\frac{x}{2} \right)} 
              5                      7     
/        2/x\\         /        2/x\\      
|-1 + cot |-||         |-1 + cot |-||      
\         \2//         \         \2//      
--------------- + -------------------------
              5                   5        
 /       2/x\\       /       2/x\\     2/x\
 |1 + cot |-||    24*|1 + cot |-|| *cot |-|
 \        \2//       \        \2//      \2/
(cot⁡2(x2)−1)724(cot⁡2(x2)+1)5cot⁡2(x2)+(cot⁡2(x2)−1)5(cot⁡2(x2)+1)5\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{7}}{24 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{5} \cot^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{5}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{5}} 
                                                           7                          
                                             /        2/x\\     10/x\    20/x\    2/x\
                   5                     128*|-1 + cot |-|| *cot  |-|*sin  |-|*tan |-|
     /        2/x\\     10/x\    20/x\       \         \2//       \4/      \4/     \2/
1024*|-1 + cot |-|| *cot  |-|*sin  |-| + ---------------------------------------------
     \         \2//       \4/      \4/                         3
128(cot⁡2(x2)−1)7sin⁡20(x4)tan⁡2(x2)cot⁡10(x4)3+1024(cot⁡2(x2)−1)5sin⁡20(x4)cot⁡10(x4)\frac{128 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{7} \sin^{20}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)} \cot^{10}{\left(\frac{x}{4} \right)}}{3} + 1024 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{5} \sin^{20}{\left(\frac{x}{4} \right)} \cot^{10}{\left(\frac{x}{4} \right)} 
                                         7         
                           /        1   \     12/x\
                           |-1 + -------| *sin  |-|
                           |        2/x\|       \2/
              5            |     tan |-||          
/        1   \     10/x\   \         \2//          
|-1 + -------| *sin  |-| + ------------------------
|        2/x\|       \2/       12*(1 + cos(x))     
|     tan |-||                                     
\         \2//
(−1+1tan⁡2(x2))7sin⁡12(x2)12(cos⁡(x)+1)+(−1+1tan⁡2(x2))5sin⁡10(x2)\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \sin^{12}{\left(\frac{x}{2} \right)}}{12 \left(\cos{\left(x \right)} + 1\right)} + \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{5} \sin^{10}{\left(\frac{x}{2} \right)} 
        5       10/x\                         
  32*cos (x)*sin  |-|                 3       
                  \2/   (1 + cos(2*x)) *cos(x)
- ------------------- + ----------------------
                  5       24*(1 - cos(2*x))   
     (-1 + cos(x))
−32sin⁡10(x2)cos⁡5(x)(cos⁡(x)−1)5+(cos⁡(2x)+1)3cos⁡(x)24(1−cos⁡(2x))- \frac{32 \sin^{10}{\left(\frac{x}{2} \right)} \cos^{5}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{5}} + \frac{\left(\cos{\left(2 x \right)} + 1\right)^{3} \cos{\left(x \right)}}{24 \left(1 - \cos{\left(2 x \right)}\right)} 
                   5                              7                 
     /        1   \     10/x\       /        1   \     2/x\    10/x\
1024*|-1 + -------| *tan  |-|   128*|-1 + -------| *tan |-|*tan  |-|
     |        2/x\|       \4/       |        2/x\|      \2/      \4/
     |     tan |-||                 |     tan |-||                  
     \         \2//                 \         \2//                  
----------------------------- + ------------------------------------
                    10                                  10          
       /       2/x\\                       /       2/x\\            
       |1 + tan |-||                     3*|1 + tan |-||            
       \        \4//                       \        \4//
128(−1+1tan⁡2(x2))7tan⁡10(x4)tan⁡2(x2)3(tan⁡2(x4)+1)10+1024(−1+1tan⁡2(x2))5tan⁡10(x4)(tan⁡2(x4)+1)10\frac{128 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \tan^{10}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} + \frac{1024 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{5} \tan^{10}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} 
                  5                     7             
/         2/x\   \    /         2/x\   \              
|      sec |-|   |    |      sec |-|   |              
|          \2/   |    |          \2/   |     2/x   pi\
|1 - ------------|    |1 - ------------| *sec |- - --|
|       2/x   pi\|    |       2/x   pi\|      \2   2 /
|    sec |- - --||    |    sec |- - --||              
\        \2   2 //    \        \2   2 //              
------------------- + --------------------------------
         10/x\                        12/x\           
      sec  |-|                  24*sec  |-|           
           \2/                          \2/
(−sec⁡2(x2)sec⁡2(x2−π2)+1)7sec⁡2(x2−π2)24sec⁡12(x2)+(−sec⁡2(x2)sec⁡2(x2−π2)+1)5sec⁡10(x2)\frac{\left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{7} \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{24 \sec^{12}{\left(\frac{x}{2} \right)}} + \frac{\left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{5}}{\sec^{10}{\left(\frac{x}{2} \right)}} 
             2/    pi\
          sec |x - --|
   1          \    2 /
------- + ------------
   5            7     
sec (x)    6*sec (x)
1sec⁡5(x)+sec⁡2(x−π2)6sec⁡7(x)\frac{1}{\sec^{5}{\left(x \right)}} + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{6 \sec^{7}{\left(x \right)}} 
             5             10              5              10                                   
 /       /x\\  /       /x\\   /        /x\\  /        /x\\      20/x\ /        1         2/x\\ 
-|1 + tan|-|| *|1 + tan|-||  *|-1 + tan|-|| *|-1 + tan|-||  *cos  |-|*|22 + ------- + tan |-|| 
 \       \2//  \       \4//   \        \2//  \        \4//        \4/ |        2/x\       \2/| 
                                                                      |     tan |-|          | 
                                                                      \         \2/          / 
-----------------------------------------------------------------------------------------------
                                               24
−(tan⁡(x4)−1)10(tan⁡(x4)+1)10(tan⁡(x2)−1)5(tan⁡(x2)+1)5(tan⁡2(x2)+22+1tan⁡2(x2))cos⁡20(x4)24- \frac{\left(\tan{\left(\frac{x}{4} \right)} - 1\right)^{10} \left(\tan{\left(\frac{x}{4} \right)} + 1\right)^{10} \left(\tan{\left(\frac{x}{2} \right)} - 1\right)^{5} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)^{5} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 22 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{20}{\left(\frac{x}{4} \right)}}{24} 
              2    
   1       csc (x) 
------- + ---------
   5           7   
sec (x)   6*sec (x)
csc⁡2(x)6sec⁡7(x)+1sec⁡5(x)\frac{\csc^{2}{\left(x \right)}}{6 \sec^{7}{\left(x \right)}} + \frac{1}{\sec^{5}{\left(x \right)}} 
                                         7                 
                           /        2/x\\     10/x\    2/x\
              5            |-1 + cot |-|| *sin  |-|*tan |-|
/        2/x\\     10/x\   \         \2//       \2/     \2/
|-1 + cot |-|| *sin  |-| + --------------------------------
\         \2//       \2/                  24
(cot⁡2(x2)−1)7sin⁡10(x2)tan⁡2(x2)24+(cot⁡2(x2)−1)5sin⁡10(x2)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{7} \sin^{10}{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{24} + \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{5} \sin^{10}{\left(\frac{x}{2} \right)} 
             7       2   
   5      cos (x)*csc (x)
cos (x) + ---------------
                 6
cos⁡7(x)csc⁡2(x)6+cos⁡5(x)\frac{\cos^{7}{\left(x \right)} \csc^{2}{\left(x \right)}}{6} + \cos^{5}{\left(x \right)} 
                7       
   5         cos (x)    
cos (x) + --------------
               2/    pi\
          6*cos |x - --|
                \    2 /
cos⁡7(x)6cos⁡2(x−π2)+cos⁡5(x)\frac{\cos^{7}{\left(x \right)}}{6 \cos^{2}{\left(x - \frac{\pi}{2} \right)}} + \cos^{5}{\left(x \right)} 
                                                        7              
                                     /          2/x\   \               
                                     |       cos |-|   |               
                                     |           \2/   |     12/x   pi\
                   5                 |-1 + ------------| *cos  |- - --|
/          2/x\   \                  |        2/x   pi\|       \2   2 /
|       cos |-|   |                  |     cos |- - --||               
|           \2/   |     10/x   pi\   \         \2   2 //               
|-1 + ------------| *cos  |- - --| + ----------------------------------
|        2/x   pi\|       \2   2 /                     2/x\            
|     cos |- - --||                              24*cos |-|            
\         \2   2 //                                     \2/
(cos⁡2(x2)cos⁡2(x2−π2)−1)7cos⁡12(x2−π2)24cos⁡2(x2)+(cos⁡2(x2)cos⁡2(x2−π2)−1)5cos⁡10(x2−π2)\frac{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{7} \cos^{12}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{24 \cos^{2}{\left(\frac{x}{2} \right)}} + \left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{5} \cos^{10}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} 
                   5                      7             
/          2/x\   \    /          2/x\   \              
|       csc |-|   |    |       csc |-|   |              
|           \2/   |    |           \2/   |     2/pi   x\
|-1 + ------------|    |-1 + ------------| *csc |-- - -|
|        2/pi   x\|    |        2/pi   x\|      \2    2/
|     csc |-- - -||    |     csc |-- - -||              
\         \2    2//    \         \2    2//              
-------------------- + ---------------------------------
         10/x\                          12/x\           
      csc  |-|                    24*csc  |-|           
           \2/                            \2/
(csc⁡2(x2)csc⁡2(−x2+π2)−1)7csc⁡2(−x2+π2)24csc⁡12(x2)+(csc⁡2(x2)csc⁡2(−x2+π2)−1)5csc⁡10(x2)\frac{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{7} \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{24 \csc^{12}{\left(\frac{x}{2} \right)}} + \frac{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{5}}{\csc^{10}{\left(\frac{x}{2} \right)}} 
                                       7         
                          /       2/x\\     10/x\
             5            |1 - tan |-|| *cos  |-|
/       2/x\\     10/x\   \        \2//       \2/
|1 - tan |-|| *cos  |-| + -----------------------
\        \2//       \2/                2/x\      
                                 24*tan |-|      
                                        \2/
(1−tan⁡2(x2))7cos⁡10(x2)24tan⁡2(x2)+(1−tan⁡2(x2))5cos⁡10(x2)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{7} \cos^{10}{\left(\frac{x}{2} \right)}}{24 \tan^{2}{\left(\frac{x}{2} \right)}} + \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{5} \cos^{10}{\left(\frac{x}{2} \right)} 
             5               10                7               10        
/       1   \  /        2/x\\     /       1   \  /        2/x\\      2/x\
|1 - -------| *|-1 + cot |-||     |1 - -------| *|-1 + cot |-||  *cot |-|
|       2/x\|  \         \4//     |       2/x\|  \         \4//       \2/
|    cot |-||                     |    cot |-||                          
\        \2//                     \        \2//                          
------------------------------- + ---------------------------------------
                     10                                      10          
        /       2/x\\                           /       2/x\\            
        |1 + cot |-||                        24*|1 + cot |-||            
        \        \4//                           \        \4//
(1−1cot⁡2(x2))7(cot⁡2(x4)−1)10cot⁡2(x2)24(cot⁡2(x4)+1)10+(1−1cot⁡2(x2))5(cot⁡2(x4)−1)10(cot⁡2(x4)+1)10\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{10} \cot^{2}{\left(\frac{x}{2} \right)}}{24 \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} + \frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{5} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{10}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} 
             2/pi    \
          sec |-- - x|
   1          \2     /
------- + ------------
   5            7     
sec (x)    6*sec (x)
1sec⁡5(x)+sec⁡2(−x+π2)6sec⁡7(x)\frac{1}{\sec^{5}{\left(x \right)}} + \frac{\sec^{2}{\left(- x + \frac{\pi}{2} \right)}}{6 \sec^{7}{\left(x \right)}} 
                                           3             3       
      5/x   pi\    5/x   pi\   (1 - sin(x)) *(1 + sin(x)) *cos(x)
32*cos |- + --|*sin |- + --| + ----------------------------------
       \2   4 /     \2   4 /            3*(1 - cos(2*x))
(1−sin⁡(x))3(sin⁡(x)+1)3cos⁡(x)3(1−cos⁡(2x))+32sin⁡5(x2+π4)cos⁡5(x2+π4)\frac{\left(1 - \sin{\left(x \right)}\right)^{3} \left(\sin{\left(x \right)} + 1\right)^{3} \cos{\left(x \right)}}{3 \left(1 - \cos{\left(2 x \right)}\right)} + 32 \sin^{5}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} \cos^{5}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} 
             5              10                7              10
/       2/x\\  /       2/x\\     /       2/x\\  /       2/x\\  
|1 - tan |-|| *|1 - tan |-||     |1 - tan |-|| *|1 - tan |-||  
\        \2//  \        \4//     \        \2//  \        \4//  
------------------------------ + ------------------------------
                    10                             10          
       /       2/x\\                  /       2/x\\      2/x\  
       |1 + tan |-||               24*|1 + tan |-||  *tan |-|  
       \        \4//                  \        \4//       \2/
(1−tan⁡2(x4))10(1−tan⁡2(x2))724(tan⁡2(x4)+1)10tan⁡2(x2)+(1−tan⁡2(x4))10(1−tan⁡2(x2))5(tan⁡2(x4)+1)10\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{10} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{7}}{24 \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10} \tan^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{10} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{5}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} 
                   5                              7         
     /        2/x\\     10/x\       /        2/x\\     10/x\
1024*|-1 + cot |-|| *cot  |-|   128*|-1 + cot |-|| *cot  |-|
     \         \2//       \4/       \         \2//       \4/
----------------------------- + ----------------------------
                    10                          10          
       /       2/x\\               /       2/x\\      2/x\  
       |1 + cot |-||             3*|1 + cot |-||  *cot |-|  
       \        \4//               \        \4//       \2/
128(cot⁡2(x2)−1)7cot⁡10(x4)3(cot⁡2(x4)+1)10cot⁡2(x2)+1024(cot⁡2(x2)−1)5cot⁡10(x4)(cot⁡2(x4)+1)10\frac{128 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{7} \cot^{10}{\left(\frac{x}{4} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10} \cot^{2}{\left(\frac{x}{2} \right)}} + \frac{1024 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{5} \cot^{10}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{10}} 
                     2       
     1            csc (x)    
------------ + --------------
   5/pi    \        7/pi    \
csc |-- - x|   6*csc |-- - x|
    \2     /         \2     /
csc⁡2(x)6csc⁡7(−x+π2)+1csc⁡5(−x+π2)\frac{\csc^{2}{\left(x \right)}}{6 \csc^{7}{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{5}{\left(- x + \frac{\pi}{2} \right)}} 
                  7/    pi\
               sin |x + --|
   5/    pi\       \    2 /
sin |x + --| + ------------
    \    2 /         2     
                6*sin (x)
sin⁡5(x+π2)+sin⁡7(x+π2)6sin⁡2(x)\sin^{5}{\left(x + \frac{\pi}{2} \right)} + \frac{\sin^{7}{\left(x + \frac{\pi}{2} \right)}}{6 \sin^{2}{\left(x \right)}} 
             5                      7     
/       2/x\\          /       2/x\\      
|1 - tan |-||          |1 - tan |-||      
\        \2//          \        \2//      
-------------- + -------------------------
             5                   5        
/       2/x\\       /       2/x\\     2/x\
|1 + tan |-||    24*|1 + tan |-|| *tan |-|
\        \2//       \        \2//      \2/
(1−tan⁡2(x2))724(tan⁡2(x2)+1)5tan⁡2(x2)+(1−tan⁡2(x2))5(tan⁡2(x2)+1)5\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{7}}{24 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{5} \tan^{2}{\left(\frac{x}{2} \right)}} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{5}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{5}} 
                   5                      7        
/        2/x   pi\\    /        2/x   pi\\         
|     sec |- - --||    |     sec |- - --||         
|         \2   2 /|    |         \2   2 /|     2/x\
|-1 + ------------|    |-1 + ------------| *sec |-|
|          2/x\   |    |          2/x\   |      \2/
|       sec |-|   |    |       sec |-|   |         
\           \2/   /    \           \2/   /         
-------------------- + ----------------------------
      10/x   pi\                   12/x   pi\      
   sec  |- - --|             24*sec  |- - --|      
        \2   2 /                     \2   2 /
(−1+sec⁡2(x2−π2)sec⁡2(x2))7sec⁡2(x2)24sec⁡12(x2−π2)+(−1+sec⁡2(x2−π2)sec⁡2(x2))5sec⁡10(x2−π2)\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \sec^{2}{\left(\frac{x}{2} \right)}}{24 \sec^{12}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{5}}{\sec^{10}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
                                                7                      
                                 /         4/x\\                       
                                 |    4*sin |-||                       
               5                 |          \2/|     2       10/pi   x\
/         4/x\\                  |1 - ---------| *sin (x)*sin  |-- + -|
|    4*sin |-||                  |        2    |               \2    2/
|          \2/|     10/pi   x\   \     sin (x) /                       
|1 - ---------| *sin  |-- + -| + --------------------------------------
|        2    |       \2    2/                       4/x\              
\     sin (x) /                                96*sin |-|              
                                                      \2/
(−4sin⁡4(x2)sin⁡2(x)+1)7sin⁡2(x)sin⁡10(x2+π2)96sin⁡4(x2)+(−4sin⁡4(x2)sin⁡2(x)+1)5sin⁡10(x2+π2)\frac{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{7} \sin^{2}{\left(x \right)} \sin^{10}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{96 \sin^{4}{\left(\frac{x}{2} \right)}} + \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{5} \sin^{10}{\left(\frac{x}{2} + \frac{\pi}{2} \right)} 
      5       10/x\                         
32*cos (x)*cos  |-|                 3       
                \2/   (1 + cos(2*x)) *cos(x)
------------------- + ----------------------
               5        24*(1 - cos(2*x))   
   (1 + cos(x))
32cos⁡10(x2)cos⁡5(x)(cos⁡(x)+1)5+(cos⁡(2x)+1)3cos⁡(x)24(1−cos⁡(2x))\frac{32 \cos^{10}{\left(\frac{x}{2} \right)} \cos^{5}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{5}} + \frac{\left(\cos{\left(2 x \right)} + 1\right)^{3} \cos{\left(x \right)}}{24 \left(1 - \cos{\left(2 x \right)}\right)} 
      5       10/x\         7       12/x\    2/x\
32*cos (x)*cos  |-|   16*cos (x)*cos  |-|*csc |-|
                \2/                   \2/     \2/
------------------- + ---------------------------
               5                          7      
   (1 + cos(x))             3*(1 + cos(x))
32cos⁡10(x2)cos⁡5(x)(cos⁡(x)+1)5+16cos⁡12(x2)cos⁡7(x)csc⁡2(x2)3(cos⁡(x)+1)7\frac{32 \cos^{10}{\left(\frac{x}{2} \right)} \cos^{5}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{5}} + \frac{16 \cos^{12}{\left(\frac{x}{2} \right)} \cos^{7}{\left(x \right)} \csc^{2}{\left(\frac{x}{2} \right)}}{3 \left(\cos{\left(x \right)} + 1\right)^{7}} 
                  5                     7        
/       2/pi   x\\    /       2/pi   x\\         
|    csc |-- - -||    |    csc |-- - -||         
|        \2    2/|    |        \2    2/|     2/x\
|1 - ------------|    |1 - ------------| *csc |-|
|         2/x\   |    |         2/x\   |      \2/
|      csc |-|   |    |      csc |-|   |         
\          \2/   /    \          \2/   /         
------------------- + ---------------------------
      10/pi   x\                  12/pi   x\     
   csc  |-- - -|            24*csc  |-- - -|     
        \2    2/                    \2    2/
(1−csc⁡2(−x2+π2)csc⁡2(x2))7csc⁡2(x2)24csc⁡12(−x2+π2)+(1−csc⁡2(−x2+π2)csc⁡2(x2))5csc⁡10(−x2+π2)\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{7} \csc^{2}{\left(\frac{x}{2} \right)}}{24 \csc^{12}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{5}}{\csc^{10}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} 
                                       7         
                          /       2/x\\     12/x\
             5            |1 - tan |-|| *cos  |-|
/       2/x\\     10/x\   \        \2//       \2/
|1 - tan |-|| *cos  |-| + -----------------------
\        \2//       \2/       12*(1 - cos(x))
(1−tan⁡2(x2))5cos⁡10(x2)+(1−tan⁡2(x2))7cos⁡12(x2)12(1−cos⁡(x))\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{5} \cos^{10}{\left(\frac{x}{2} \right)} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{7} \cos^{12}{\left(\frac{x}{2} \right)}}{12 \left(1 - \cos{\left(x \right)}\right)} 
(1 - tan(x/2)^2)^5*cos(x/2)^10 + (1 - tan(x/2)^2)^7*cos(x/2)^12/(12*(1 - cos(x)))
Denominador racional [src] 
   7           5       2   
cos (x) + 6*cos (x)*sin (x)
---------------------------
              2            
         6*sin (x)
6sin⁡2(x)cos⁡5(x)+cos⁡7(x)6sin⁡2(x)\frac{6 \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)} + \cos^{7}{\left(x \right)}}{6 \sin^{2}{\left(x \right)}} 
(cos(x)^7 + 6*cos(x)^5*sin(x)^2)/(6*sin(x)^2)
    © Sr Examen – Калькулятор