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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(pi/((6*(x^2+1))))/5-pi*x^2*cos(pi/(6*(x^2+1)))/(15*(x^2+1)^2)

¿Cómo vas a descomponer esta sin(pi/((6*(x^2+1))))/5-pi*x^2*cos(pi/(6*(x^2+1)))/(15*(x^2+1)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /    pi    \       2    /    pi    \
sin|----------|   pi*x *cos|----------|
   |  / 2    \|            |  / 2    \|
   \6*\x  + 1//            \6*\x  + 1//
--------------- - ---------------------
       5                          2    
                          / 2    \     
                       15*\x  + 1/
−πx2cos⁡(π6(x2+1))15(x2+1)2+sin⁡(π6(x2+1))5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{5} 
sin(pi/((6*(x^2 + 1))))/5 - (pi*x^2)*cos(pi/((6*(x^2 + 1))))/(15*(x^2 + 1)^2)
Denominador racional [src] 
           2                                      
   /     2\     /   pi   \         2    /   pi   \
15*\1 + x / *sin|--------| - 5*pi*x *cos|--------|
                |       2|              |       2|
                \6 + 6*x /              \6 + 6*x /
--------------------------------------------------
                              2                   
                      /     2\                    
                   75*\1 + x /
−5πx2cos⁡(π6x2+6)+15(x2+1)2sin⁡(π6x2+6)75(x2+1)2\frac{- 5 \pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)} + 15 \left(x^{2} + 1\right)^{2} \sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{75 \left(x^{2} + 1\right)^{2}} 
(15*(1 + x^2)^2*sin(pi/(6 + 6*x^2)) - 5*pi*x^2*cos(pi/(6 + 6*x^2)))/(75*(1 + x^2)^2)
Combinatoria [src] 
     /   pi   \      4    /   pi   \      2    /   pi   \       2    /   pi   \
3*sin|--------| + 3*x *sin|--------| + 6*x *sin|--------| - pi*x *cos|--------|
     |       2|           |       2|           |       2|            |       2|
     \6 + 6*x /           \6 + 6*x /           \6 + 6*x /            \6 + 6*x /
-------------------------------------------------------------------------------
                                             2                                 
                                     /     2\                                  
                                  15*\1 + x /
3x4sin⁡(π6x2+6)+6x2sin⁡(π6x2+6)−πx2cos⁡(π6x2+6)+3sin⁡(π6x2+6)15(x2+1)2\frac{3 x^{4} \sin{\left(\frac{\pi}{6 x^{2} + 6} \right)} + 6 x^{2} \sin{\left(\frac{\pi}{6 x^{2} + 6} \right)} - \pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)} + 3 \sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} 
(3*sin(pi/(6 + 6*x^2)) + 3*x^4*sin(pi/(6 + 6*x^2)) + 6*x^2*sin(pi/(6 + 6*x^2)) - pi*x^2*cos(pi/(6 + 6*x^2)))/(15*(1 + x^2)^2)
Unión de expresiones racionales [src] 
          2                                    
  /     2\     /   pi   \       2    /   pi   \
3*\1 + x / *sin|--------| - pi*x *cos|--------|
               |       2|            |       2|
               \6 + 6*x /            \6 + 6*x /
-----------------------------------------------
                             2                 
                     /     2\                  
                  15*\1 + x /
−πx2cos⁡(π6x2+6)+3(x2+1)2sin⁡(π6x2+6)15(x2+1)2\frac{- \pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)} + 3 \left(x^{2} + 1\right)^{2} \sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} 
(3*(1 + x^2)^2*sin(pi/(6 + 6*x^2)) - pi*x^2*cos(pi/(6 + 6*x^2)))/(15*(1 + x^2)^2)
Potencias [src] 
                                      /   pi*I       -pi*I  \
                                      | --------    --------|
    /    -pi*I        pi*I  \         |        2           2|
    |   --------    --------|         | 6 + 6*x     6 + 6*x |
    |          2           2|       2 |e           e        |
    |   6 + 6*x     6 + 6*x |   pi*x *|--------- + ---------|
  I*\- e         + e        /         \    2           2    /
- --------------------------- - -----------------------------
               10                                   2        
                                            /     2\         
                                         15*\1 + x /
−πx2(eiπ6x2+62+e−iπ6x2+62)15(x2+1)2−i(eiπ6x2+6−e−iπ6x2+6)10- \frac{\pi x^{2} \left(\frac{e^{\frac{i \pi}{6 x^{2} + 6}}}{2} + \frac{e^{- \frac{i \pi}{6 x^{2} + 6}}}{2}\right)}{15 \left(x^{2} + 1\right)^{2}} - \frac{i \left(e^{\frac{i \pi}{6 x^{2} + 6}} - e^{- \frac{i \pi}{6 x^{2} + 6}}\right)}{10} 
   /   pi   \       2    /   pi   \
sin|--------|   pi*x *cos|--------|
   |       2|            |       2|
   \6 + 6*x /            \6 + 6*x /
------------- - -------------------
      5                        2   
                       /     2\    
                    15*\1 + x /
−πx2cos⁡(π6x2+6)15(x2+1)2+sin⁡(π6x2+6)5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{5} 
sin(pi/(6 + 6*x^2))/5 - pi*x^2*cos(pi/(6 + 6*x^2))/(15*(1 + x^2)^2)
Respuesta numérica [src] 
0.2*sin(pi/((6*(x^2 + 1)))) - 0.20943951023932*x^2*cos(pi/((6*(x^2 + 1))))/(1.0 + x^2)^2
0.2*sin(pi/((6*(x^2 + 1)))) - 0.20943951023932*x^2*cos(pi/((6*(x^2 + 1))))/(1.0 + x^2)^2
Denominador común [src] 
   /    pi    \       2    /    pi    \
sin|----------|   pi*x *cos|----------|
   |  /     2\|            |  /     2\|
   \6*\1 + x //            \6*\1 + x //
--------------- - ---------------------
       5                     4       2 
                    15 + 15*x  + 30*x
−πx2cos⁡(π6(x2+1))15x4+30x2+15+sin⁡(π6(x2+1))5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{15 x^{4} + 30 x^{2} + 15} + \frac{\sin{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{5} 
sin(pi/(6*(1 + x^2)))/5 - pi*x^2*cos(pi/(6*(1 + x^2)))/(15 + 15*x^4 + 30*x^2)
Abrimos la expresión [src] 
   /   pi   \       2    /   pi   \
sin|--------|   pi*x *cos|--------|
   |       2|            |       2|
   \6 + 6*x /            \6 + 6*x /
------------- - -------------------
      5                   4       2
                 15 + 15*x  + 30*x
−πx2cos⁡(π6x2+6)15x4+30x2+15+sin⁡(π6x2+6)5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 x^{4} + 30 x^{2} + 15} + \frac{\sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{5} 
sin(pi/(6 + 6*x^2))/5 - pi*x^2*cos(pi/(6 + 6*x^2))/(15 + 15*x^4 + 30*x^2)
Parte trigonométrica [src] 
        /     pi     \               2 /       2/     pi     \\   
   2*tan|------------|           pi*x *|1 - tan |------------||   
        |  /       2\|                 |        |  /       2\||   
        \2*\6 + 6*x //                 \        \2*\6 + 6*x ///   
-------------------------- - -------------------------------------
  /       2/     pi     \\              2                         
5*|1 + tan |------------||      /     2\  /       2/     pi     \\
  |        |  /       2\||   15*\1 + x / *|1 + tan |------------||
  \        \2*\6 + 6*x ///                |        |  /       2\||
                                          \        \2*\6 + 6*x ///
−πx2(1−tan⁡2(π2(6x2+6)))15(x2+1)2(tan⁡2(π2(6x2+6))+1)+2tan⁡(π2(6x2+6))5(tan⁡2(π2(6x2+6))+1)- \frac{\pi x^{2} \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)}\right)}{15 \left(x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)} + 1\right)} + \frac{2 \tan{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)}}{5 \left(\tan^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)} + 1\right)} 
        /     pi     \              2 /        2/     pi     \\   
   2*cot|------------|          pi*x *|-1 + cot |------------||   
        |  /       2\|                |         |  /       2\||   
        \2*\6 + 6*x //                \         \2*\6 + 6*x ///   
-------------------------- - -------------------------------------
  /       2/     pi     \\              2                         
5*|1 + cot |------------||      /     2\  /       2/     pi     \\
  |        |  /       2\||   15*\1 + x / *|1 + cot |------------||
  \        \2*\6 + 6*x ///                |        |  /       2\||
                                          \        \2*\6 + 6*x ///
−πx2(cot⁡2(π2(6x2+6))−1)15(x2+1)2(cot⁡2(π2(6x2+6))+1)+2cot⁡(π2(6x2+6))5(cot⁡2(π2(6x2+6))+1)- \frac{\pi x^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)} - 1\right)}{15 \left(x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)} + 1\right)} + \frac{2 \cot{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)}}{5 \left(\cot^{2}{\left(\frac{\pi}{2 \left(6 x^{2} + 6\right)} \right)} + 1\right)} 
                                               2 /            2        \
                                           pi*x *|1 - -----------------|
                                                 |       2/     pi    \|
                                                 |    csc |-----------||
                                                 |        |   /     2\||
                   2                             \        \12*\1 + x ///
---------------------------------------- - -----------------------------
     /     pi    \    /pi        pi    \                       2        
5*csc|-----------|*csc|-- - -----------|               /     2\         
     |   /     2\|    |2       /     2\|            15*\1 + x /         
     \12*\1 + x //    \     12*\1 + x //
−πx2(1−2csc⁡2(π12(x2+1)))15(x2+1)2+25csc⁡(π12(x2+1))csc⁡(π2−π12(x2+1))- \frac{\pi x^{2} \left(1 - \frac{2}{\csc^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{2}{5 \csc{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}} 
                                       2           
          1                        pi*x            
---------------------- - --------------------------
     /  pi      pi   \              2              
5*sec|- -- + --------|      /     2\     /   pi   \
     |  2           2|   15*\1 + x / *sec|--------|
     \       6 + 6*x /                   |       2|
                                         \6 + 6*x /
−πx215(x2+1)2sec⁡(π6x2+6)+15sec⁡(−π2+π6x2+6)- \frac{\pi x^{2}}{15 \left(x^{2} + 1\right)^{2} \sec{\left(\frac{\pi}{6 x^{2} + 6} \right)}} + \frac{1}{5 \sec{\left(- \frac{\pi}{2} + \frac{\pi}{6 x^{2} + 6} \right)}} 
     /     pi    \    /pi        pi    \       2 /         2/     pi    \\
2*sin|-----------|*sin|-- + -----------|   pi*x *|1 - 2*sin |-----------||
     |   /     2\|    |2       /     2\|         |          |   /     2\||
     \12*\1 + x //    \     12*\1 + x //         \          \12*\1 + x ///
---------------------------------------- - -------------------------------
                   5                                            2         
                                                        /     2\          
                                                     15*\1 + x /
−πx2(1−2sin⁡2(π12(x2+1)))15(x2+1)2+2sin⁡(π12(x2+1))sin⁡(π2+π12(x2+1))5- \frac{\pi x^{2} \left(1 - 2 \sin^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{2 \sin{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}{5} 
   /  pi      pi   \       2    /   pi   \
cos|- -- + --------|   pi*x *cos|--------|
   |  2           2|            |       2|
   \       6 + 6*x /            \6 + 6*x /
-------------------- - -------------------
         5                            2   
                              /     2\    
                           15*\1 + x /
−πx2cos⁡(π6x2+6)15(x2+1)2+cos⁡(−π2+π6x2+6)5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{6 x^{2} + 6} \right)}}{5} 
     /     pi    \    /     pi    \       2 /         2/     pi    \\
2*cos|-----------|*sin|-----------|   pi*x *|1 - 2*sin |-----------||
     |   /     2\|    |   /     2\|         |          |   /     2\||
     \12*\1 + x //    \12*\1 + x //         \          \12*\1 + x ///
----------------------------------- - -------------------------------
                 5                                         2         
                                                   /     2\          
                                                15*\1 + x /
−πx2(1−2sin⁡2(π12(x2+1)))15(x2+1)2+2sin⁡(π12(x2+1))cos⁡(π12(x2+1))5- \frac{\pi x^{2} \left(1 - 2 \sin^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{2 \sin{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} \cos{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}{5} 
                                          2            
           1                          pi*x             
------------------------ - ----------------------------
     /  pi       pi    \              2                
5*sec|- -- + ----------|      /     2\     /    pi    \
     |  2      /     2\|   15*\1 + x / *sec|----------|
     \       6*\1 + x //                   |  /     2\|
                                           \6*\1 + x //
−πx215(x2+1)2sec⁡(π6(x2+1))+15sec⁡(−π2+π6(x2+1))- \frac{\pi x^{2}}{15 \left(x^{2} + 1\right)^{2} \sec{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}} + \frac{1}{5 \sec{\left(- \frac{\pi}{2} + \frac{\pi}{6 \left(x^{2} + 1\right)} \right)}} 
   /    pi    \       2    /pi       pi    \
sin|----------|   pi*x *sin|-- + ----------|
   |  /     2\|            |2      /     2\|
   \6*\1 + x //            \     6*\1 + x //
--------------- - --------------------------
       5                            2       
                            /     2\        
                         15*\1 + x /
−πx2sin⁡(π2+π6(x2+1))15(x2+1)2+sin⁡(π6(x2+1))5- \frac{\pi x^{2} \sin{\left(\frac{\pi}{2} + \frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{5} 
                                                    /           2/     pi    \   \
                                                    |      8*cot |-----------|   |
                                                    |            |   /     2\|   |
                                                  2 |            \24*\1 + x //   |
                                              pi*x *|1 - ------------------------|
                                                    |                           2|
  /        2/     pi    \\    /     pi    \         |    /       2/     pi    \\ |
4*|-1 + cot |-----------||*cot|-----------|         |    |1 + cot |-----------|| |
  |         |   /     2\||    |   /     2\|         |    |        |   /     2\|| |
  \         \24*\1 + x ///    \24*\1 + x //         \    \        \24*\1 + x /// /
------------------------------------------- - ------------------------------------
                                  2                                  2            
           /       2/     pi    \\                           /     2\             
         5*|1 + cot |-----------||                        15*\1 + x /             
           |        |   /     2\||                                                
           \        \24*\1 + x ///
−πx2(1−8cot⁡2(π24(x2+1))(cot⁡2(π24(x2+1))+1)2)15(x2+1)2+4(cot⁡2(π24(x2+1))−1)cot⁡(π24(x2+1))5(cot⁡2(π24(x2+1))+1)2- \frac{\pi x^{2} \left(1 - \frac{8 \cot^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)}}{\left(\cot^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)} + 1\right)^{2}}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{4 \left(\cot^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)} - 1\right) \cot{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)}}{5 \left(\cot^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)} + 1\right)^{2}} 
   /   pi   \       2    /pi      pi   \
sin|--------|   pi*x *sin|-- + --------|
   |       2|            |2           2|
   \6 + 6*x /            \     6 + 6*x /
------------- - ------------------------
      5                          2      
                         /     2\       
                      15*\1 + x /
−πx2sin⁡(π2+π6x2+6)15(x2+1)2+sin⁡(π6x2+6)5- \frac{\pi x^{2} \sin{\left(\frac{\pi}{2} + \frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{5} 
                                      2              
        1                         pi*x               
----------------- - ---------------------------------
     /    pi    \              2                     
5*csc|----------|      /     2\     /pi       pi    \
     |  /     2\|   15*\1 + x / *csc|-- - ----------|
     \6*\1 + x //                   |2      /     2\|
                                    \     6*\1 + x //
−πx215(x2+1)2csc⁡(π2−π6(x2+1))+15csc⁡(π6(x2+1))- \frac{\pi x^{2}}{15 \left(x^{2} + 1\right)^{2} \csc{\left(\frac{\pi}{2} - \frac{\pi}{6 \left(x^{2} + 1\right)} \right)}} + \frac{1}{5 \csc{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}} 
                                   2             
       1                       pi*x              
--------------- - -------------------------------
     /   pi   \              2                   
5*csc|--------|      /     2\     /pi      pi   \
     |       2|   15*\1 + x / *csc|-- - --------|
     \6 + 6*x /                   |2           2|
                                  \     6 + 6*x /
−πx215(x2+1)2csc⁡(π2−π6x2+6)+15csc⁡(π6x2+6)- \frac{\pi x^{2}}{15 \left(x^{2} + 1\right)^{2} \csc{\left(\frac{\pi}{2} - \frac{\pi}{6 x^{2} + 6} \right)}} + \frac{1}{5 \csc{\left(\frac{\pi}{6 x^{2} + 6} \right)}} 
         /     pi    \             2 /       2/     pi    \\    
    2*tan|-----------|         pi*x *|1 - tan |-----------||    
         |   /     2\|               |        |   /     2\||    
         \12*\1 + x //               \        \12*\1 + x ///    
------------------------- - ------------------------------------
  /       2/     pi    \\              2                        
5*|1 + tan |-----------||      /     2\  /       2/     pi    \\
  |        |   /     2\||   15*\1 + x / *|1 + tan |-----------||
  \        \12*\1 + x ///                |        |   /     2\||
                                         \        \12*\1 + x ///
−πx2(1−tan⁡2(π12(x2+1)))15(x2+1)2(tan⁡2(π12(x2+1))+1)+2tan⁡(π12(x2+1))5(tan⁡2(π12(x2+1))+1)- \frac{\pi x^{2} \left(1 - \tan^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}\right)}{15 \left(x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} + 1\right)} + \frac{2 \tan{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}{5 \left(\tan^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} + 1\right)} 
   /   pi   \       2    /   pi   \
sin|--------|   pi*x *cos|--------|
   |       2|            |       2|
   \6 + 6*x /            \6 + 6*x /
------------- - -------------------
      5                        2   
                       /     2\    
                    15*\1 + x /
−πx2cos⁡(π6x2+6)15(x2+1)2+sin⁡(π6x2+6)5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{\pi}{6 x^{2} + 6} \right)}}{5} 
                                                   /           2/     pi    \   \
                                                   |      8*tan |-----------|   |
                                                   |            |   /     2\|   |
                                                 2 |            \24*\1 + x //   |
                                             pi*x *|1 - ------------------------|
                                                   |                           2|
  /       2/     pi    \\    /     pi    \         |    /       2/     pi    \\ |
4*|1 - tan |-----------||*tan|-----------|         |    |1 + tan |-----------|| |
  |        |   /     2\||    |   /     2\|         |    |        |   /     2\|| |
  \        \24*\1 + x ///    \24*\1 + x //         \    \        \24*\1 + x /// /
------------------------------------------ - ------------------------------------
                                 2                                  2            
          /       2/     pi    \\                           /     2\             
        5*|1 + tan |-----------||                        15*\1 + x /             
          |        |   /     2\||                                                
          \        \24*\1 + x ///
−πx2(1−8tan⁡2(π24(x2+1))(tan⁡2(π24(x2+1))+1)2)15(x2+1)2+4(1−tan⁡2(π24(x2+1)))tan⁡(π24(x2+1))5(tan⁡2(π24(x2+1))+1)2- \frac{\pi x^{2} \left(1 - \frac{8 \tan^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)} + 1\right)^{2}}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)}\right) \tan{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)}}{5 \left(\tan^{2}{\left(\frac{\pi}{24 \left(x^{2} + 1\right)} \right)} + 1\right)^{2}} 
   /  pi       pi    \       2    /    pi    \
cos|- -- + ----------|   pi*x *cos|----------|
   |  2      /     2\|            |  /     2\|
   \       6*\1 + x //            \6*\1 + x //
---------------------- - ---------------------
          5                              2    
                                 /     2\     
                              15*\1 + x /
−πx2cos⁡(π6(x2+1))15(x2+1)2+cos⁡(−π2+π6(x2+1))5- \frac{\pi x^{2} \cos{\left(\frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{15 \left(x^{2} + 1\right)^{2}} + \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{6 \left(x^{2} + 1\right)} \right)}}{5} 
         /     pi    \             2 /        2/     pi    \\   
    2*cot|-----------|         pi*x *|-1 + cot |-----------||   
         |   /     2\|               |         |   /     2\||   
         \12*\1 + x //               \         \12*\1 + x ///   
------------------------- - ------------------------------------
  /       2/     pi    \\              2                        
5*|1 + cot |-----------||      /     2\  /       2/     pi    \\
  |        |   /     2\||   15*\1 + x / *|1 + cot |-----------||
  \        \12*\1 + x ///                |        |   /     2\||
                                         \        \12*\1 + x ///
−πx2(cot⁡2(π12(x2+1))−1)15(x2+1)2(cot⁡2(π12(x2+1))+1)+2cot⁡(π12(x2+1))5(cot⁡2(π12(x2+1))+1)- \frac{\pi x^{2} \left(\cot^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} - 1\right)}{15 \left(x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} + 1\right)} + \frac{2 \cot{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}{5 \left(\cot^{2}{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} + 1\right)} 
                                2           
       1                    pi*x            
--------------- - --------------------------
     /   pi   \              2              
5*csc|--------|      /     2\     /   pi   \
     |       2|   15*\1 + x / *sec|--------|
     \6 + 6*x /                   |       2|
                                  \6 + 6*x /
−πx215(x2+1)2sec⁡(π6x2+6)+15csc⁡(π6x2+6)- \frac{\pi x^{2}}{15 \left(x^{2} + 1\right)^{2} \sec{\left(\frac{\pi}{6 x^{2} + 6} \right)}} + \frac{1}{5 \csc{\left(\frac{\pi}{6 x^{2} + 6} \right)}} 
     /     pi    \    /  pi        pi    \       2 /         2/  pi        pi    \\
2*cos|-----------|*cos|- -- + -----------|   pi*x *|1 - 2*cos |- -- + -----------||
     |   /     2\|    |  2       /     2\|         |          |  2       /     2\||
     \12*\1 + x //    \       12*\1 + x //         \          \       12*\1 + x ///
------------------------------------------ - --------------------------------------
                    5                                                2             
                                                             /     2\              
                                                          15*\1 + x /
−πx2(1−2cos⁡2(−π2+π12(x2+1)))15(x2+1)2+2cos⁡(π12(x2+1))cos⁡(−π2+π12(x2+1))5- \frac{\pi x^{2} \left(1 - 2 \cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{2 \cos{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}{5} 
                                                 2 /               2            \
                                             pi*x *|1 - ------------------------|
                                                   |       2/  pi        pi    \|
                                                   |    sec |- -- + -----------||
                                                   |        |  2       /     2\||
                    2                              \        \       12*\1 + x ///
------------------------------------------ - ------------------------------------
     /     pi    \    /  pi        pi    \                          2            
5*sec|-----------|*sec|- -- + -----------|                  /     2\             
     |   /     2\|    |  2       /     2\|               15*\1 + x /             
     \12*\1 + x //    \       12*\1 + x //
−πx2(1−2sec⁡2(−π2+π12(x2+1)))15(x2+1)2+25sec⁡(π12(x2+1))sec⁡(−π2+π12(x2+1))- \frac{\pi x^{2} \left(1 - \frac{2}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}}\right)}{15 \left(x^{2} + 1\right)^{2}} + \frac{2}{5 \sec{\left(\frac{\pi}{12 \left(x^{2} + 1\right)} \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{12 \left(x^{2} + 1\right)} \right)}} 
2/(5*sec(pi/(12*(1 + x^2)))*sec(-pi/2 + pi/(12*(1 + x^2)))) - pi*x^2*(1 - 2/sec(-pi/2 + pi/(12*(1 + x^2)))^2)/(15*(1 + x^2)^2)
    © Sr Examen – Калькулятор