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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                   3                          
              2*cot (x)   2*cos(x)    2*cos(x)
cot(x)*(-2) - --------- - -------- + ---------
                  3       3*sin(x)        3   
                                     3*sin (x)
(((−2)cot⁡(x)−2cot⁡3(x)3)−2cos⁡(x)3sin⁡(x))+2cos⁡(x)3sin⁡3(x)\left(\left(\left(-2\right) \cot{\left(x \right)} - \frac{2 \cot^{3}{\left(x \right)}}{3}\right) - \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}}\right) + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
cot(x)*(-2) - 2*cot(x)^3/3 - 2*cos(x)/(3*sin(x)) + (2*cos(x))/((3*sin(x)^3))
Simplificación general [src] 
 -2   
------
tan(x)
−2tan⁡(x)- \frac{2}{\tan{\left(x \right)}} 
-2/tan(x)
Respuesta numérica [src] 
-2.0*cot(x) - 0.666666666666667*cot(x)^3 + 0.666666666666667*cos(x)/sin(x)^3 - 0.666666666666667*cos(x)/sin(x)
-2.0*cot(x) - 0.666666666666667*cot(x)^3 + 0.666666666666667*cos(x)/sin(x)^3 - 0.666666666666667*cos(x)/sin(x)
Denominador racional [src] 
     3    /              /                 3   \       \                   
3*sin (x)*\-6*cos(x) + 3*\-6*cot(x) - 2*cot (x)/*sin(x)/ + 18*cos(x)*sin(x)
---------------------------------------------------------------------------
                                       4                                   
                                 27*sin (x)
3(3(−2cot⁡3(x)−6cot⁡(x))sin⁡(x)−6cos⁡(x))sin⁡3(x)+18sin⁡(x)cos⁡(x)27sin⁡4(x)\frac{3 \left(3 \left(- 2 \cot^{3}{\left(x \right)} - 6 \cot{\left(x \right)}\right) \sin{\left(x \right)} - 6 \cos{\left(x \right)}\right) \sin^{3}{\left(x \right)} + 18 \sin{\left(x \right)} \cos{\left(x \right)}}{27 \sin^{4}{\left(x \right)}} 
(3*sin(x)^3*(-6*cos(x) + 3*(-6*cot(x) - 2*cot(x)^3)*sin(x)) + 18*cos(x)*sin(x))/(27*sin(x)^4)
Potencias [src] 
                 3           / I*x    -I*x\       / I*x    -I*x\
            2*cot (x)    8*I*\e    + e    /   2*I*\e    + e    /
-2*cot(x) - --------- - ------------------- - ------------------
                3                         3     /   -I*x    I*x\
                          /   -I*x    I*x\    3*\- e     + e   /
                        3*\- e     + e   /
−2cot⁡3(x)3−2cot⁡(x)−2i(eix+e−ix)3(eix−e−ix)−8i(eix+e−ix)3(eix−e−ix)3- \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} - \frac{2 i \left(e^{i x} + e^{- i x}\right)}{3 \left(e^{i x} - e^{- i x}\right)} - \frac{8 i \left(e^{i x} + e^{- i x}\right)}{3 \left(e^{i x} - e^{- i x}\right)^{3}} 
                 3                          
            2*cot (x)   2*cos(x)    2*cos(x)
-2*cot(x) - --------- - -------- + ---------
                3       3*sin(x)        3   
                                   3*sin (x)
−2cot⁡3(x)3−2cot⁡(x)−2cos⁡(x)3sin⁡(x)+2cos⁡(x)3sin⁡3(x)- \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
-2*cot(x) - 2*cot(x)^3/3 - 2*cos(x)/(3*sin(x)) + 2*cos(x)/(3*sin(x)^3)
Unión de expresiones racionales [src] 
  /   2    /          /        2   \              \         \
2*\sin (x)*\-cos(x) + \-3 - cot (x)/*cot(x)*sin(x)/ + cos(x)/
-------------------------------------------------------------
                               3                             
                          3*sin (x)
2(((−cot⁡2(x)−3)sin⁡(x)cot⁡(x)−cos⁡(x))sin⁡2(x)+cos⁡(x))3sin⁡3(x)\frac{2 \left(\left(\left(- \cot^{2}{\left(x \right)} - 3\right) \sin{\left(x \right)} \cot{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)} + \cos{\left(x \right)}\right)}{3 \sin^{3}{\left(x \right)}} 
2*(sin(x)^2*(-cos(x) + (-3 - cot(x)^2)*cot(x)*sin(x)) + cos(x))/(3*sin(x)^3)
Denominador común [src] 
                 3                       2          
            2*cot (x)   -2*cos(x) + 2*sin (x)*cos(x)
-2*cot(x) - --------- - ----------------------------
                3                     3             
                                 3*sin (x)
−2sin⁡2(x)cos⁡(x)−2cos⁡(x)3sin⁡3(x)−2cot⁡3(x)3−2cot⁡(x)- \frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} 
-2*cot(x) - 2*cot(x)^3/3 - (-2*cos(x) + 2*sin(x)^2*cos(x))/(3*sin(x)^3)
Abrimos la expresión [src] 
       3                                        
  2*cot (x)                 2*cos(x)    2*cos(x)
- --------- + cot(x)*(-2) - -------- + ---------
      3                     3*sin(x)        3   
                                       3*sin (x)
−2cot⁡3(x)3+(−2)cot⁡(x)−2cos⁡(x)3sin⁡(x)+2cos⁡(x)3sin⁡3(x)- \frac{2 \cot^{3}{\left(x \right)}}{3} + \left(-2\right) \cot{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
                   3                          
              2*cot (x)   2*cos(x)    2*cos(x)
cot(x)*(-2) - --------- - -------- + ---------
                  3       3*sin(x)        3   
                                     3*sin (x)
(−2)cot⁡(x)−2cot⁡3(x)3−2cos⁡(x)3sin⁡(x)+2cos⁡(x)3sin⁡3(x)\left(-2\right) \cot{\left(x \right)} - \frac{2 \cot^{3}{\left(x \right)}}{3} - \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
cot(x)*(-2) - 2*cot(x)^3/3 - 2*cos(x)/(3*sin(x)) + 2*cos(x)/(3*sin(x)^3)
Compilar la expresión [src] 
                 3                          
            2*cot (x)   2*cos(x)    2*cos(x)
-2*cot(x) - --------- - -------- + ---------
                3       3*sin(x)        3   
                                   3*sin (x)
−2cot⁡3(x)3−2cot⁡(x)−2cos⁡(x)3sin⁡(x)+2cos⁡(x)3sin⁡3(x)- \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
-2*cot(x) - 2*cot(x)^3/3 - 2*cos(x)/(3*sin(x)) + 2*cos(x)/(3*sin(x)^3)
Parte trigonométrica [src] 
                                     /x\   /       2/x\\    /x\
                                  tan|-|   |1 - tan |-||*tan|-|
    2          2          1          \2/   \        \2//    \2/
- ------ - --------- - -------- + ------ + --------------------
  tan(x)        3           /x\     3             4/x\    4/x\ 
           3*tan (x)   3*tan|-|            192*cos |-|*sin |-| 
                            \2/                    \4/     \4/
(1−tan⁡2(x2))tan⁡(x2)192sin⁡4(x4)cos⁡4(x4)+tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{192 \sin^{4}{\left(\frac{x}{4} \right)} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                                     /x\                           
                                  tan|-|                           
    2          2          1          \2/           8*cos(x)        
- ------ - --------- - -------- + ------ - ------------------------
  tan(x)        3           /x\     3      3*(-3*sin(x) + sin(3*x))
           3*tan (x)   3*tan|-|                                    
                            \2/
tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)−8cos⁡(x)3(−3sin⁡(x)+sin⁡(3x))\frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} - \frac{8 \cos{\left(x \right)}}{3 \left(- 3 \sin{\left(x \right)} + \sin{\left(3 x \right)}\right)} 
                                     /x\   /       2/x\\    /x\
                                  tan|-|   |1 - tan |-||*sec|-|
    2          2          1          \2/   \        \2//    \2/
- ------ - --------- - -------- + ------ + --------------------
  tan(x)        3           /x\     3                 3/x\     
           3*tan (x)   3*tan|-|                 12*sin |-|     
                            \2/                        \2/
(1−tan⁡2(x2))sec⁡(x2)12sin⁡3(x2)+tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \sec{\left(\frac{x}{2} \right)}}{12 \sin^{3}{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                                                                              /         2/x\   \       
                                                                              |      sec |-|   |       
                                                                    3/x   pi\ |          \2/   |    /x\
                                                                 sec |- - --|*|1 - ------------|*sec|-|
       /    pi\        3/    pi\      /x   pi\          /x\          \2   2 / |       2/x   pi\|    \2/
  2*sec|x - --|   2*sec |x - --|   sec|- - --|       sec|-|                   |    sec |- - --||       
       \    2 /         \    2 /      \2   2 /          \2/                   \        \2   2 //       
- ------------- - -------------- - ----------- + ------------- + --------------------------------------
      sec(x)             3                /x\         /x   pi\                     12                  
                    3*sec (x)        3*sec|-|    3*sec|- - --|                                         
                                          \2/         \2   2 /
(−sec⁡2(x2)sec⁡2(x2−π2)+1)sec⁡(x2)sec⁡3(x2−π2)12+sec⁡(x2)3sec⁡(x2−π2)−2sec⁡(x−π2)sec⁡(x)−2sec⁡3(x−π2)3sec⁡3(x)−sec⁡(x2−π2)3sec⁡(x2)\frac{\left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} \right)} \sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{12} + \frac{\sec{\left(\frac{x}{2} \right)}}{3 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{2 \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} - \frac{2 \sec^{3}{\left(x - \frac{\pi}{2} \right)}}{3 \sec^{3}{\left(x \right)}} - \frac{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \sec{\left(\frac{x}{2} \right)}} 
                                     /x\                           
                                  tan|-|                           
    2          2          1          \2/           8*cos(x)        
- ------ - --------- - -------- + ------ + ------------------------
  tan(x)        3           /x\     3      3*(-sin(3*x) + 3*sin(x))
           3*tan (x)   3*tan|-|                                    
                            \2/
tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)+8cos⁡(x)3(3sin⁡(x)−sin⁡(3x))\frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} + \frac{8 \cos{\left(x \right)}}{3 \left(3 \sin{\left(x \right)} - \sin{\left(3 x \right)}\right)} 
                  3               
  8*cos(x)   2*cos (x)    2*cos(x)
- -------- - --------- + ---------
  3*sin(x)        3           3   
             3*sin (x)   3*sin (x)
−8cos⁡(x)3sin⁡(x)−2cos⁡3(x)3sin⁡3(x)+2cos⁡(x)3sin⁡3(x)- \frac{8 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} - \frac{2 \cos^{3}{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
                                                  2              
                              2/x\   /       2/x\\  /       2/x\\
                       1 - tan |-|   |1 + tan |-|| *|1 - tan |-||
    2          2               \2/   \        \2//  \        \2//
- ------ - --------- - ----------- + ----------------------------
  tan(x)        3             /x\                   3/x\         
           3*tan (x)     3*tan|-|             12*tan |-|         
                              \2/                    \2/
(1−tan⁡2(x2))(tan⁡2(x2)+1)212tan⁡3(x2)−1−tan⁡2(x2)3tan⁡(x2)−2tan⁡(x)−23tan⁡3(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{12 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan{\left(\frac{x}{2} \right)}} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} 
                                                        4                       
                                           /       2/x\\     3/x\ /        1   \
                                           |1 + tan |-|| *tan |-|*|-1 + -------|
                                     /x\   \        \4//      \2/ |        2/x\|
                                  tan|-|                          |     tan |-||
    2          2          1          \2/                          \         \2//
- ------ - --------- - -------- + ------ + -------------------------------------
  tan(x)        3           /x\     3                          4/x\             
           3*tan (x)   3*tan|-|                         192*tan |-|             
                            \2/                                 \4/
(−1+1tan⁡2(x2))(tan⁡2(x4)+1)4tan⁡3(x2)192tan⁡4(x4)+tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \tan^{3}{\left(\frac{x}{2} \right)}}{192 \tan^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                                   2/x\    
                            1 - tan |-|    
     8           2                  \2/    
- -------- - --------- + ------------------
  3*tan(x)        3            4/x\    3/x\
             3*tan (x)   12*cos |-|*tan |-|
                                \2/     \2/
1−tan⁡2(x2)12cos⁡4(x2)tan⁡3(x2)−83tan⁡(x)−23tan⁡3(x)\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{12 \cos^{4}{\left(\frac{x}{2} \right)} \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{8}{3 \tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} 
                                                         4                      
                                            /       2/x\\     3/x\ /       1   \
                                            |1 + cot |-|| *cot |-|*|1 - -------|
                           /x\              \        \4//      \2/ |       2/x\|
                 3      cot|-|                                     |    cot |-||
            2*cot (x)      \2/      1                              \        \2//
-2*cot(x) - --------- - ------ + -------- + ------------------------------------
                3         3           /x\                             4         
                                 3*cot|-|               /        2/x\\          
                                      \2/            12*|-1 + cot |-||          
                                                        \         \4//
(1−1cot⁡2(x2))(cot⁡2(x4)+1)4cot⁡3(x2)12(cot⁡2(x4)−1)4−cot⁡(x2)3−2cot⁡3(x)3−2cot⁡(x)+13cot⁡(x2)\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \cot^{3}{\left(\frac{x}{2} \right)}}{12 \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4}} - \frac{\cot{\left(\frac{x}{2} \right)}}{3} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} + \frac{1}{3 \cot{\left(\frac{x}{2} \right)}} 
                         3                       
     8*cos(x)       2*cos (x)         2*cos(x)   
- ------------- - -------------- + --------------
       /    pi\        3/    pi\        3/    pi\
  3*cos|x - --|   3*cos |x - --|   3*cos |x - --|
       \    2 /         \    2 /         \    2 /
−2cos⁡3(x)3cos⁡3(x−π2)−8cos⁡(x)3cos⁡(x−π2)+2cos⁡(x)3cos⁡3(x−π2)- \frac{2 \cos^{3}{\left(x \right)}}{3 \cos^{3}{\left(x - \frac{\pi}{2} \right)}} - \frac{8 \cos{\left(x \right)}}{3 \cos{\left(x - \frac{\pi}{2} \right)}} + \frac{2 \cos{\left(x \right)}}{3 \cos^{3}{\left(x - \frac{\pi}{2} \right)}} 
                                     /x\                     2/x\           
                                  tan|-|              1 - tan |-|           
    2          2          1          \2/                      \2/           
- ------ - --------- - -------- + ------ + ---------------------------------
  tan(x)        3           /x\     3                      4                
           3*tan (x)   3*tan|-|               /       2/x\\     8/x\    3/x\
                            \2/            12*|1 - tan |-|| *cos |-|*tan |-|
                                              \        \4//      \4/     \2/
tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)+1−tan⁡2(x2)12(1−tan⁡2(x4))4cos⁡8(x4)tan⁡3(x2)\frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{12 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \cos^{8}{\left(\frac{x}{4} \right)} \tan^{3}{\left(\frac{x}{2} \right)}} 
     8           2        2*cos(x)
- -------- - --------- + ---------
  3*tan(x)        3           3   
             3*tan (x)   3*sin (x)
−83tan⁡(x)−23tan⁡3(x)+2cos⁡(x)3sin⁡3(x)- \frac{8}{3 \tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} 
                           /x\      /x\   /       2/x\\    /x\
                 3      cot|-|   tan|-|   |1 - tan |-||*tan|-|
            2*cot (x)      \2/      \2/   \        \2//    \2/
-2*cot(x) - --------- - ------ + ------ + --------------------
                3         3        3             4/x\    4/x\ 
                                          192*cos |-|*sin |-| 
                                                  \4/     \4/
(1−tan⁡2(x2))tan⁡(x2)192sin⁡4(x4)cos⁡4(x4)+tan⁡(x2)3−cot⁡(x2)3−2cot⁡3(x)3−2cot⁡(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{192 \sin^{4}{\left(\frac{x}{4} \right)} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{\cot{\left(\frac{x}{2} \right)}}{3} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} 
                                                    2               
                                2/x\   /       2/x\\  /        2/x\\
                 3      -1 + cot |-|   |1 + cot |-|| *|-1 + cot |-||
            2*cot (x)            \2/   \        \2//  \         \2//
-2*cot(x) - --------- - ------------ + -----------------------------
                3              /x\                     3/x\         
                          3*cot|-|               12*cot |-|         
                               \2/                      \2/
(cot⁡2(x2)−1)(cot⁡2(x2)+1)212cot⁡3(x2)−cot⁡2(x2)−13cot⁡(x2)−2cot⁡3(x)3−2cot⁡(x)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{12 \cot^{3}{\left(\frac{x}{2} \right)}} - \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{3 \cot{\left(\frac{x}{2} \right)}} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} 
                                                        4              
                                     /x\   /       2/x\\  /       2/x\\
                                  tan|-|   |1 + tan |-|| *|1 - tan |-||
    2          2          1          \2/   \        \4//  \        \2//
- ------ - --------- - -------- + ------ + ----------------------------
  tan(x)        3           /x\     3                       4          
           3*tan (x)   3*tan|-|                /       2/x\\     3/x\  
                            \2/             12*|1 - tan |-|| *tan |-|  
                                               \        \4//      \2/
tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)+(1−tan⁡2(x2))(tan⁡2(x4)+1)412(1−tan⁡2(x4))4tan⁡3(x2)\frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}}{12 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \tan^{3}{\left(\frac{x}{2} \right)}} 
                                           /        1   \    /x\
                                           |-1 + -------|*csc|-|
                                     /x\   |        2/x\|    \2/
                                  tan|-|   |     tan |-||       
    2          2          1          \2/   \         \2//       
- ------ - --------- - -------- + ------ + ---------------------
  tan(x)        3           /x\     3                  3/x\     
           3*tan (x)   3*tan|-|                  12*cos |-|     
                            \2/                         \2/
(−1+1tan⁡2(x2))csc⁡(x2)12cos⁡3(x2)+tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}{12 \cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                            2/x\                                            2/x\
                       2*sin |-|                                       2*sin |-|
    2          2             \2/       sin(x)              1                 \2/
- ------ - --------- - --------- - -------------- + ---------------- + ---------
  tan(x)        3           3      3*(1 - cos(x))               2/x\    3*sin(x)
           3*tan (x)   3*sin (x)                    6*sin(x)*sin |-|            
                                                                 \2/
2sin⁡2(x2)3sin⁡(x)−2sin⁡2(x2)3sin⁡3(x)−2tan⁡(x)−23tan⁡3(x)+16sin⁡2(x2)sin⁡(x)−sin⁡(x)3(1−cos⁡(x))\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin{\left(x \right)}} - \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} + \frac{1}{6 \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)}} - \frac{\sin{\left(x \right)}}{3 \left(1 - \cos{\left(x \right)}\right)} 
                                                                                                  2/x\
                                                                                             2*sin |-|
    2                 2                  2                  2                   sin(x)             \2/
- ------ - ----------------------- - --------- + ------------------------ - -------------- + ---------
  tan(x)   3*(2*sin(x) + sin(2*x))        3      3*(-sin(2*x) + 2*sin(x))   3*(1 - cos(x))    3*sin(x)
                                     3*tan (x)
2sin⁡2(x2)3sin⁡(x)−2tan⁡(x)−23tan⁡3(x)−23(2sin⁡(x)+sin⁡(2x))+23(2sin⁡(x)−sin⁡(2x))−sin⁡(x)3(1−cos⁡(x))\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin{\left(x \right)}} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{2}{3 \left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right)} + \frac{2}{3 \left(2 \sin{\left(x \right)} - \sin{\left(2 x \right)}\right)} - \frac{\sin{\left(x \right)}}{3 \left(1 - \cos{\left(x \right)}\right)} 
                           3                  
  sin(2*x)   2*cos(x)   sin (2*x)     2*cos(x)
- -------- - -------- - ---------- + ---------
     2       3*sin(x)         6           3   
  sin (x)               12*sin (x)   3*sin (x)
−2cos⁡(x)3sin⁡(x)−sin⁡(2x)sin⁡2(x)+2cos⁡(x)3sin⁡3(x)−sin⁡3(2x)12sin⁡6(x)- \frac{2 \cos{\left(x \right)}}{3 \sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{\sin^{3}{\left(2 x \right)}}{12 \sin^{6}{\left(x \right)}} 
                                 /    pi\
                  3         2*sin|x + --|
  4*sin(2*x)   sin (2*x)         \    2 /
- ---------- - ---------- + -------------
       2             6             3     
  3*sin (x)    12*sin (x)     3*sin (x)
−4sin⁡(2x)3sin⁡2(x)+2sin⁡(x+π2)3sin⁡3(x)−sin⁡3(2x)12sin⁡6(x)- \frac{4 \sin{\left(2 x \right)}}{3 \sin^{2}{\left(x \right)}} + \frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{\sin^{3}{\left(2 x \right)}}{12 \sin^{6}{\left(x \right)}} 
                                      2               
                         /       2/x\\  /        2/x\\
                  3      |1 + cot |-|| *|-1 + cot |-||
  8*cot(x)   2*cot (x)   \        \2//  \         \2//
- -------- - --------- + -----------------------------
     3           3                       3/x\         
                                   12*cot |-|         
                                          \2/
(cot⁡2(x2)−1)(cot⁡2(x2)+1)212cot⁡3(x2)−2cot⁡3(x)3−8cot⁡(x)3\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{12 \cot^{3}{\left(\frac{x}{2} \right)}} - \frac{2 \cot^{3}{\left(x \right)}}{3} - \frac{8 \cot{\left(x \right)}}{3} 
                           /x\      /x\        3/x\ /       2/x\\   
                 3      cot|-|   tan|-|     cot |-|*|1 - tan |-||   
            2*cot (x)      \2/      \2/         \2/ \        \2//   
-2*cot(x) - --------- - ------ + ------ + --------------------------
                3         3        3                       4        
                                             /        2/x\\     8/x\
                                          12*|-1 + cot |-|| *sin |-|
                                             \         \4//      \4/
(1−tan⁡2(x2))cot⁡3(x2)12(cot⁡2(x4)−1)4sin⁡8(x4)+tan⁡(x2)3−cot⁡(x2)3−2cot⁡3(x)3−2cot⁡(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \cot^{3}{\left(\frac{x}{2} \right)}}{12 \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{x}{4} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{\cot{\left(\frac{x}{2} \right)}}{3} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} 
                  /    pi\                     /    pi\
             2*sin|x + --|      3         2*sin|x + --|
  sin(2*x)        \    2 /   sin (2*x)         \    2 /
- -------- - ------------- - ---------- + -------------
     2          3*sin(x)           6             3     
  sin (x)                    12*sin (x)     3*sin (x)
−2sin⁡(x+π2)3sin⁡(x)−sin⁡(2x)sin⁡2(x)+2sin⁡(x+π2)3sin⁡3(x)−sin⁡3(2x)12sin⁡6(x)- \frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{3 \sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \sin{\left(x + \frac{\pi}{2} \right)}}{3 \sin^{3}{\left(x \right)}} - \frac{\sin^{3}{\left(2 x \right)}}{12 \sin^{6}{\left(x \right)}} 
                                                                            /          2/x\   \       
                                                                            |       csc |-|   |       
                                                                  3/pi   x\ |           \2/   |    /x\
                                                               csc |-- - -|*|-1 + ------------|*csc|-|
                                        /x\         /pi   x\       \2    2/ |        2/pi   x\|    \2/
                       3             csc|-|      csc|-- - -|                |     csc |-- - -||       
    2*csc(x)      2*csc (x)             \2/         \2    2/                \         \2    2//       
- ----------- - -------------- - ------------- + ----------- + ---------------------------------------
     /pi    \        3/pi    \        /pi   x\          /x\                       12                  
  csc|-- - x|   3*csc |-- - x|   3*csc|-- - -|     3*csc|-|                                           
     \2     /         \2     /        \2    2/          \2/
(csc⁡2(x2)csc⁡2(−x2+π2)−1)csc⁡(x2)csc⁡3(−x2+π2)12−csc⁡(x2)3csc⁡(−x2+π2)−2csc⁡3(x)3csc⁡3(−x+π2)−2csc⁡(x)csc⁡(−x+π2)+csc⁡(−x2+π2)3csc⁡(x2)\frac{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right) \csc{\left(\frac{x}{2} \right)} \csc^{3}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{12} - \frac{\csc{\left(\frac{x}{2} \right)}}{3 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{2 \csc^{3}{\left(x \right)}}{3 \csc^{3}{\left(- x + \frac{\pi}{2} \right)}} - \frac{2 \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{3 \csc{\left(\frac{x}{2} \right)}} 
                                                                         2/x   pi\   
                                                                      cos |- - --|   
                                                                          \2   2 /   
                                                                  1 - ------------   
                                        /x\         /x   pi\               2/x\      
                       3             cos|-|      cos|- - --|            cos |-|      
    2*cos(x)      2*cos (x)             \2/         \2   2 /                \2/      
- ----------- - -------------- - ------------- + ----------- + ----------------------
     /    pi\        3/    pi\        /x   pi\          /x\          /x\    3/x   pi\
  cos|x - --|   3*cos |x - --|   3*cos|- - --|     3*cos|-|    12*cos|-|*cos |- - --|
     \    2 /         \    2 /        \2   2 /          \2/          \2/     \2   2 /
1−cos⁡2(x2−π2)cos⁡2(x2)12cos⁡(x2)cos⁡3(x2−π2)−cos⁡(x2)3cos⁡(x2−π2)−2cos⁡3(x)3cos⁡3(x−π2)−2cos⁡(x)cos⁡(x−π2)+cos⁡(x2−π2)3cos⁡(x2)\frac{1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}}{12 \cos{\left(\frac{x}{2} \right)} \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{\cos{\left(\frac{x}{2} \right)}}{3 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{2 \cos^{3}{\left(x \right)}}{3 \cos^{3}{\left(x - \frac{\pi}{2} \right)}} - \frac{2 \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \cos{\left(\frac{x}{2} \right)}} 
                                     /x\             2/x\    
                                  tan|-|      1 - tan |-|    
    2          2          1          \2/              \2/    
- ------ - --------- - -------- + ------ + ------------------
  tan(x)        3           /x\     3            4/x\    3/x\
           3*tan (x)   3*tan|-|            12*cos |-|*tan |-|
                            \2/                   \2/     \2/
1−tan⁡2(x2)12cos⁡4(x2)tan⁡3(x2)+tan⁡(x2)3−2tan⁡(x)−23tan⁡3(x)−13tan⁡(x2)\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{12 \cos^{4}{\left(\frac{x}{2} \right)} \tan^{3}{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2}{\tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                                                                         /        2/x   pi\\            
                                                                         |     sec |- - --||            
                                                                    3/x\ |         \2   2 /|    /x   pi\
                                                                 sec |-|*|-1 + ------------|*sec|- - --|
       /    pi\        3/    pi\      /x   pi\          /x\          \2/ |          2/x\   |    \2   2 /
  2*sec|x - --|   2*sec |x - --|   sec|- - --|       sec|-|              |       sec |-|   |            
       \    2 /         \    2 /      \2   2 /          \2/              \           \2/   /            
- ------------- - -------------- - ----------- + ------------- + ---------------------------------------
      sec(x)             3                /x\         /x   pi\                      12                  
                    3*sec (x)        3*sec|-|    3*sec|- - --|                                          
                                          \2/         \2   2 /
(−1+sec⁡2(x2−π2)sec⁡2(x2))sec⁡3(x2)sec⁡(x2−π2)12+sec⁡(x2)3sec⁡(x2−π2)−2sec⁡(x−π2)sec⁡(x)−2sec⁡3(x−π2)3sec⁡3(x)−sec⁡(x2−π2)3sec⁡(x2)\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec^{3}{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{12} + \frac{\sec{\left(\frac{x}{2} \right)}}{3 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{2 \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} - \frac{2 \sec^{3}{\left(x - \frac{\pi}{2} \right)}}{3 \sec^{3}{\left(x \right)}} - \frac{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \sec{\left(\frac{x}{2} \right)}} 
                         3                3     
     8*csc(x)       2*csc (x)        2*csc (x)  
- ------------- - -------------- + -------------
       /pi    \        3/pi    \        /pi    \
  3*csc|-- - x|   3*csc |-- - x|   3*csc|-- - x|
       \2     /         \2     /        \2     /
2csc⁡3(x)3csc⁡(−x+π2)−2csc⁡3(x)3csc⁡3(−x+π2)−8csc⁡(x)3csc⁡(−x+π2)\frac{2 \csc^{3}{\left(x \right)}}{3 \csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{2 \csc^{3}{\left(x \right)}}{3 \csc^{3}{\left(- x + \frac{\pi}{2} \right)}} - \frac{8 \csc{\left(x \right)}}{3 \csc{\left(- x + \frac{\pi}{2} \right)}} 
                                                            /         2    \
                                                       2/x\ |      sin (x) |
                                                  2*sin |-|*|-1 + ---------|
                                           2/x\         \2/ |          4/x\|
                            3         2*sin |-|             |     4*sin |-||
  sin(2*x)     sin(x)    sin (2*x)          \2/             \           \2//
- -------- - --------- - ---------- + --------- + --------------------------
     2            2/x\         6       3*sin(x)                3            
  sin (x)    6*sin |-|   12*sin (x)                       3*sin (x)         
                   \2/
2(−1+sin⁡2(x)4sin⁡4(x2))sin⁡2(x2)3sin⁡3(x)+2sin⁡2(x2)3sin⁡(x)−sin⁡(2x)sin⁡2(x)−sin⁡3(2x)12sin⁡6(x)−sin⁡(x)6sin⁡2(x2)\frac{2 \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin^{3}{\left(x \right)}} + \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} - \frac{\sin^{3}{\left(2 x \right)}}{12 \sin^{6}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{6 \sin^{2}{\left(\frac{x}{2} \right)}} 
                                                         4               
                           /x\              /       2/x\\  /        2/x\\
                 3      cot|-|              |1 + cot |-|| *|-1 + cot |-||
            2*cot (x)      \2/      1       \        \4//  \         \2//
-2*cot(x) - --------- - ------ + -------- + -----------------------------
                3         3           /x\               3/x\    4/x\     
                                 3*cot|-|        192*cot |-|*cot |-|     
                                      \2/                \2/     \4/
(cot⁡2(x4)+1)4(cot⁡2(x2)−1)192cot⁡4(x4)cot⁡3(x2)−cot⁡(x2)3−2cot⁡3(x)3−2cot⁡(x)+13cot⁡(x2)\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{192 \cot^{4}{\left(\frac{x}{4} \right)} \cot^{3}{\left(\frac{x}{2} \right)}} - \frac{\cot{\left(\frac{x}{2} \right)}}{3} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} + \frac{1}{3 \cot{\left(\frac{x}{2} \right)}} 
                                                                       /       2/pi   x\\            
                                                                       |    csc |-- - -||            
                                                                  3/x\ |        \2    2/|    /pi   x\
                                                               csc |-|*|1 - ------------|*csc|-- - -|
                                        /x\         /pi   x\       \2/ |         2/x\   |    \2    2/
                       3             csc|-|      csc|-- - -|           |      csc |-|   |            
    2*csc(x)      2*csc (x)             \2/         \2    2/           \          \2/   /            
- ----------- - -------------- - ------------- + ----------- + --------------------------------------
     /pi    \        3/pi    \        /pi   x\          /x\                      12                  
  csc|-- - x|   3*csc |-- - x|   3*csc|-- - -|     3*csc|-|                                          
     \2     /         \2     /        \2    2/          \2/
(1−csc⁡2(−x2+π2)csc⁡2(x2))csc⁡3(x2)csc⁡(−x2+π2)12−csc⁡(x2)3csc⁡(−x2+π2)−2csc⁡3(x)3csc⁡3(−x+π2)−2csc⁡(x)csc⁡(−x+π2)+csc⁡(−x2+π2)3csc⁡(x2)\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc^{3}{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{12} - \frac{\csc{\left(\frac{x}{2} \right)}}{3 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{2 \csc^{3}{\left(x \right)}}{3 \csc^{3}{\left(- x + \frac{\pi}{2} \right)}} - \frac{2 \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{3 \csc{\left(\frac{x}{2} \right)}} 
                  3           3   
  8*csc(x)   2*csc (x)   2*csc (x)
- -------- - --------- + ---------
  3*sec(x)        3       3*sec(x)
             3*sec (x)
2csc⁡3(x)3sec⁡(x)−2csc⁡3(x)3sec⁡3(x)−8csc⁡(x)3sec⁡(x)\frac{2 \csc^{3}{\left(x \right)}}{3 \sec{\left(x \right)}} - \frac{2 \csc^{3}{\left(x \right)}}{3 \sec^{3}{\left(x \right)}} - \frac{8 \csc{\left(x \right)}}{3 \sec{\left(x \right)}} 
                            3/x\ /        2/x\\
                  3      tan |-|*|-1 + cot |-||
  8*cot(x)   2*cot (x)       \2/ \         \2//
- -------- - --------- + ----------------------
     3           3                   4/x\      
                               12*sin |-|      
                                      \2/
(cot⁡2(x2)−1)tan⁡3(x2)12sin⁡4(x2)−2cot⁡3(x)3−8cot⁡(x)3\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \tan^{3}{\left(\frac{x}{2} \right)}}{12 \sin^{4}{\left(\frac{x}{2} \right)}} - \frac{2 \cot^{3}{\left(x \right)}}{3} - \frac{8 \cot{\left(x \right)}}{3} 
                                      /x\      3/x\ /        2/x\\
                 3                 tan|-|   tan |-|*|-1 + cot |-||
            2*cot (x)      1          \2/       \2/ \         \2//
-2*cot(x) - --------- - -------- + ------ + ----------------------
                3            /x\     3                  4/x\      
                        3*tan|-|                  12*sin |-|      
                             \2/                         \2/
(cot⁡2(x2)−1)tan⁡3(x2)12sin⁡4(x2)+tan⁡(x2)3−2cot⁡3(x)3−2cot⁡(x)−13tan⁡(x2)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \tan^{3}{\left(\frac{x}{2} \right)}}{12 \sin^{4}{\left(\frac{x}{2} \right)}} + \frac{\tan{\left(\frac{x}{2} \right)}}{3} - \frac{2 \cot^{3}{\left(x \right)}}{3} - 2 \cot{\left(x \right)} - \frac{1}{3 \tan{\left(\frac{x}{2} \right)}} 
                                                          /         4/x\\
                                                          |    4*sin |-||
                                                     3    |          \2/|
                                           2/x\   sin (x)*|1 - ---------|
                            3         2*sin |-|           |        2    |
  sin(2*x)     sin(x)    sin (2*x)          \2/           \     sin (x) /
- -------- - --------- - ---------- + --------- + -----------------------
     2            2/x\         6       3*sin(x)         6/x\    4/pi   x\
  sin (x)    6*sin |-|   12*sin (x)               96*sin |-|*sin |-- + -|
                   \2/                                   \2/     \2    2/
(−4sin⁡4(x2)sin⁡2(x)+1)sin⁡3(x)96sin⁡6(x2)sin⁡4(x2+π2)+2sin⁡2(x2)3sin⁡(x)−sin⁡(2x)sin⁡2(x)−sin⁡3(2x)12sin⁡6(x)−sin⁡(x)6sin⁡2(x2)\frac{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin^{3}{\left(x \right)}}{96 \sin^{6}{\left(\frac{x}{2} \right)} \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} - \frac{\sin^{3}{\left(2 x \right)}}{12 \sin^{6}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{6 \sin^{2}{\left(\frac{x}{2} \right)}} 
       /    pi\        3/    pi\        3/    pi\
  8*sec|x - --|   2*sec |x - --|   2*sec |x - --|
       \    2 /         \    2 /         \    2 /
- ------------- - -------------- + --------------
     3*sec(x)            3            3*sec(x)   
                    3*sec (x)
2sec⁡3(x−π2)3sec⁡(x)−8sec⁡(x−π2)3sec⁡(x)−2sec⁡3(x−π2)3sec⁡3(x)\frac{2 \sec^{3}{\left(x - \frac{\pi}{2} \right)}}{3 \sec{\left(x \right)}} - \frac{8 \sec{\left(x - \frac{\pi}{2} \right)}}{3 \sec{\left(x \right)}} - \frac{2 \sec^{3}{\left(x - \frac{\pi}{2} \right)}}{3 \sec^{3}{\left(x \right)}} 
                                                                           2/x\      
                                                                        cos |-|      
                                                                            \2/      
                                                                 -1 + ------------   
                                        /x\         /x   pi\             2/x   pi\   
                       3             cos|-|      cos|- - --|          cos |- - --|   
    2*cos(x)      2*cos (x)             \2/         \2   2 /              \2   2 /   
- ----------- - -------------- - ------------- + ----------- + ----------------------
     /    pi\        3/    pi\        /x   pi\          /x\          3/x\    /x   pi\
  cos|x - --|   3*cos |x - --|   3*cos|- - --|     3*cos|-|    12*cos |-|*cos|- - --|
     \    2 /         \    2 /        \2   2 /          \2/           \2/    \2   2 /
cos⁡2(x2)cos⁡2(x2−π2)−112cos⁡3(x2)cos⁡(x2−π2)−cos⁡(x2)3cos⁡(x2−π2)−2cos⁡3(x)3cos⁡3(x−π2)−2cos⁡(x)cos⁡(x−π2)+cos⁡(x2−π2)3cos⁡(x2)\frac{\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1}{12 \cos^{3}{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{\cos{\left(\frac{x}{2} \right)}}{3 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{2 \cos^{3}{\left(x \right)}}{3 \cos^{3}{\left(x - \frac{\pi}{2} \right)}} - \frac{2 \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \cos{\left(\frac{x}{2} \right)}} 
                                      2              
                         /       2/x\\  /       2/x\\
                         |1 + tan |-|| *|1 - tan |-||
     8           2       \        \2//  \        \2//
- -------- - --------- + ----------------------------
  3*tan(x)        3                     3/x\         
             3*tan (x)            12*tan |-|         
                                         \2/
(1−tan⁡2(x2))(tan⁡2(x2)+1)212tan⁡3(x2)−83tan⁡(x)−23tan⁡3(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{12 \tan^{3}{\left(\frac{x}{2} \right)}} - \frac{8}{3 \tan{\left(x \right)}} - \frac{2}{3 \tan^{3}{\left(x \right)}} 
-8/(3*tan(x)) - 2/(3*tan(x)^3) + (1 + tan(x/2)^2)^2*(1 - tan(x/2)^2)/(12*tan(x/2)^3)
Combinatoria [src] 
   /             3       3         2                  3          \
-2*\-cos(x) + cot (x)*sin (x) + sin (x)*cos(x) + 3*sin (x)*cot(x)/
------------------------------------------------------------------
                                 3                                
                            3*sin (x)
−2(sin⁡3(x)cot⁡3(x)+3sin⁡3(x)cot⁡(x)+sin⁡2(x)cos⁡(x)−cos⁡(x))3sin⁡3(x)- \frac{2 \left(\sin^{3}{\left(x \right)} \cot^{3}{\left(x \right)} + 3 \sin^{3}{\left(x \right)} \cot{\left(x \right)} + \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \cos{\left(x \right)}\right)}{3 \sin^{3}{\left(x \right)}} 
-2*(-cos(x) + cot(x)^3*sin(x)^3 + sin(x)^2*cos(x) + 3*sin(x)^3*cot(x))/(3*sin(x)^3)
    © Sr Examen – Калькулятор