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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                               /3*pi    \          
                            sin|---- - a|          
              cos(pi + a)      \ 2      /      1   
sin(pi + a) + ----------- - ------------- - -------
                 /pi    \      a*x - 1      a*x + 1
              cos|-- - a|                          
                 \2     /
((sin⁡(a+π)+cos⁡(a+π)cos⁡(−a+π2))−sin⁡(−a+3π2)ax−1)−1ax+1\left(\left(\sin{\left(a + \pi \right)} + \frac{\cos{\left(a + \pi \right)}}{\cos{\left(- a + \frac{\pi}{2} \right)}}\right) - \frac{\sin{\left(- a + \frac{3 \pi}{2} \right)}}{a x - 1}\right) - \frac{1}{a x + 1} 
sin(pi + a) + cos(pi + a)/cos(pi/2 - a) - sin((3*pi)/2 - a)/(a*x - 1) - 1/(a*x + 1)
Simplificación general [src] 
                                                     2  2                
      1        ___    /    pi\                      a *x      2  2       
1 + ------ + \/ 2 *sin|a + --| - a*x + a*x*cos(a) - ------ - a *x *sin(a)
    tan(a)            \    4 /                      tan(a)               
-------------------------------------------------------------------------
                           (1 + a*x)*(-1 + a*x)
−a2x2sin⁡(a)−a2x2tan⁡(a)+axcos⁡(a)−ax+2sin⁡(a+π4)+1+1tan⁡(a)(ax−1)(ax+1)\frac{- a^{2} x^{2} \sin{\left(a \right)} - \frac{a^{2} x^{2}}{\tan{\left(a \right)}} + a x \cos{\left(a \right)} - a x + \sqrt{2} \sin{\left(a + \frac{\pi}{4} \right)} + 1 + \frac{1}{\tan{\left(a \right)}}}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + 1/tan(a) + sqrt(2)*sin(a + pi/4) - a*x + a*x*cos(a) - a^2*x^2/tan(a) - a^2*x^2*sin(a))/((1 + a*x)*(-1 + a*x))
Respuesta numérica [src] 
-1/(1.0 + a*x) + cos(pi + a)/cos(pi/2 - a) - sin((3*pi)/2 - a)/(-1.0 + a*x) + sin(pi + a)
-1/(1.0 + a*x) + cos(pi + a)/cos(pi/2 - a) - sin((3*pi)/2 - a)/(-1.0 + a*x) + sin(pi + a)
Denominador común [src] 
                                2  2                                                                    
-cos(pi + a) + cos(a)*sin(a) + a *x *cos(pi + a) - a*x*sin(a) + a*x*cos(a)*sin(a) + sin(a)              
------------------------------------------------------------------------------------------ + sin(pi + a)
                                             2  2                                                       
                                  -sin(a) + a *x *sin(a)
sin⁡(a+π)+a2x2cos⁡(a+π)+axsin⁡(a)cos⁡(a)−axsin⁡(a)+sin⁡(a)cos⁡(a)+sin⁡(a)−cos⁡(a+π)a2x2sin⁡(a)−sin⁡(a)\sin{\left(a + \pi \right)} + \frac{a^{2} x^{2} \cos{\left(a + \pi \right)} + a x \sin{\left(a \right)} \cos{\left(a \right)} - a x \sin{\left(a \right)} + \sin{\left(a \right)} \cos{\left(a \right)} + \sin{\left(a \right)} - \cos{\left(a + \pi \right)}}{a^{2} x^{2} \sin{\left(a \right)} - \sin{\left(a \right)}} 
(-cos(pi + a) + cos(a)*sin(a) + a^2*x^2*cos(pi + a) - a*x*sin(a) + a*x*cos(a)*sin(a) + sin(a))/(-sin(a) + a^2*x^2*sin(a)) + sin(pi + a)
Denominador racional [src] 
          /    pi\      /    pi\                 /    pi\    2  2                        /    pi\    2  2    /    pi\                      /    pi\
cos(a)*cos|a - --| + cos|a - --|*sin(a) - a*x*cos|a - --| - a *x *cos(a) + a*x*cos(a)*cos|a - --| - a *x *cos|a - --|*sin(a) + cos(a) + cos|a - --|
          \    2 /      \    2 /                 \    2 /                                \    2 /            \    2 /                      \    2 /
---------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                  /    pi\                                                         
                                                          (1 + a*x)*(-1 + a*x)*cos|a - --|                                                         
                                                                                  \    2 /
−a2x2sin⁡(a)cos⁡(a−π2)−a2x2cos⁡(a)+axcos⁡(a)cos⁡(a−π2)−axcos⁡(a−π2)+sin⁡(a)cos⁡(a−π2)+cos⁡(a)cos⁡(a−π2)+cos⁡(a)+cos⁡(a−π2)(ax−1)(ax+1)cos⁡(a−π2)\frac{- a^{2} x^{2} \sin{\left(a \right)} \cos{\left(a - \frac{\pi}{2} \right)} - a^{2} x^{2} \cos{\left(a \right)} + a x \cos{\left(a \right)} \cos{\left(a - \frac{\pi}{2} \right)} - a x \cos{\left(a - \frac{\pi}{2} \right)} + \sin{\left(a \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \cos{\left(a \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \cos{\left(a \right)} + \cos{\left(a - \frac{\pi}{2} \right)}}{\left(a x - 1\right) \left(a x + 1\right) \cos{\left(a - \frac{\pi}{2} \right)}} 
(cos(a)*cos(a - pi/2) + cos(a - pi/2)*sin(a) - a*x*cos(a - pi/2) - a^2*x^2*cos(a) + a*x*cos(a)*cos(a - pi/2) - a^2*x^2*cos(a - pi/2)*sin(a) + cos(a) + cos(a - pi/2))/((1 + a*x)*(-1 + a*x)*cos(a - pi/2))
Abrimos la expresión [src] 
     1                cos(a)   cos(a)
- ------- - sin(a) + ------- - ------
  a*x + 1            a*x - 1   sin(a)
−sin⁡(a)−cos⁡(a)sin⁡(a)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} - \frac{\cos{\left(a \right)}}{\sin{\left(a \right)}} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
-1/(a*x + 1) - sin(a) + cos(a)/(a*x - 1) - cos(a)/sin(a)
Compilar la expresión [src] 
                             /3*pi    \              
                          sin|---- - a|              
     1      cos(pi + a)      \ 2      /              
- ------- + ----------- - ------------- + sin(pi + a)
  1 + a*x      /pi    \      -1 + a*x                
            cos|-- - a|                              
               \2     /
sin⁡(a+π)+cos⁡(a+π)cos⁡(−a+π2)−1ax+1−sin⁡(−a+3π2)ax−1\sin{\left(a + \pi \right)} + \frac{\cos{\left(a + \pi \right)}}{\cos{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{a x + 1} - \frac{\sin{\left(- a + \frac{3 \pi}{2} \right)}}{a x - 1} 
-1/(1 + a*x) + cos(pi + a)/cos(pi/2 - a) - sin((3*pi)/2 - a)/(-1 + a*x) + sin(pi + a)
Unión de expresiones racionales [src] 
          /           /             /pi - 2*a\       \      /pi - 2*a\    /-2*a + 3*pi\\                 /pi - 2*a\
(1 + a*x)*|(-1 + a*x)*|-cos(a) - cos|--------|*sin(a)| - cos|--------|*sin|-----------|| - (-1 + a*x)*cos|--------|
          \           \             \   2    /       /      \   2    /    \     2     //                 \   2    /
-------------------------------------------------------------------------------------------------------------------
                                                                 /pi - 2*a\                                        
                                         (1 + a*x)*(-1 + a*x)*cos|--------|                                        
                                                                 \   2    /
−(ax−1)cos⁡(π−2a2)+(ax+1)((ax−1)(−sin⁡(a)cos⁡(π−2a2)−cos⁡(a))−sin⁡(−2a+3π2)cos⁡(π−2a2))(ax−1)(ax+1)cos⁡(π−2a2)\frac{- \left(a x - 1\right) \cos{\left(\frac{\pi - 2 a}{2} \right)} + \left(a x + 1\right) \left(\left(a x - 1\right) \left(- \sin{\left(a \right)} \cos{\left(\frac{\pi - 2 a}{2} \right)} - \cos{\left(a \right)}\right) - \sin{\left(\frac{- 2 a + 3 \pi}{2} \right)} \cos{\left(\frac{\pi - 2 a}{2} \right)}\right)}{\left(a x - 1\right) \left(a x + 1\right) \cos{\left(\frac{\pi - 2 a}{2} \right)}} 
((1 + a*x)*((-1 + a*x)*(-cos(a) - cos((pi - 2*a)/2)*sin(a)) - cos((pi - 2*a)/2)*sin((-2*a + 3*pi)/2)) - (-1 + a*x)*cos((pi - 2*a)/2))/((1 + a*x)*(-1 + a*x)*cos((pi - 2*a)/2))
Potencias [src] 
     1                cos(a)    cos(a)
- ------- - sin(a) + -------- - ------
  1 + a*x            -1 + a*x   sin(a)
−sin⁡(a)−cos⁡(a)sin⁡(a)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} - \frac{\cos{\left(a \right)}}{\sin{\left(a \right)}} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
             I*(pi + a)    I*(-pi - a)                                        /     /    3*pi\      /     3*pi\\
            e             e                                                   |   I*|a - ----|    I*|-a + ----||
            ----------- + ------------     /   I*(-pi - a)    I*(pi + a)\     |     \     2  /      \      2  /|
     1           2             2         I*\- e            + e          /   I*\- e             + e             /
- ------- + -------------------------- - -------------------------------- + ------------------------------------
  1 + a*x      /    pi\      /pi    \                   2                               2*(-1 + a*x)            
             I*|a - --|    I*|-- - a|                                                                           
               \    2 /      \2     /                                                                           
            e             e                                                                                     
            ----------- + -----------                                                                           
                 2             2
−i(−ei(−a−π)+ei(a+π))2+ei(−a−π)2+ei(a+π)2ei(−a+π2)2+ei(a−π2)2−1ax+1+i(ei(−a+3π2)−ei(a−3π2))2(ax−1)- \frac{i \left(- e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right)}{2} + \frac{\frac{e^{i \left(- a - \pi\right)}}{2} + \frac{e^{i \left(a + \pi\right)}}{2}}{\frac{e^{i \left(- a + \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(a - \frac{\pi}{2}\right)}}{2}} - \frac{1}{a x + 1} + \frac{i \left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)}{2 \left(a x - 1\right)} 
-1/(1 + a*x) + (exp(i*(pi + a))/2 + exp(i*(-pi - a))/2)/(exp(i*(a - pi/2))/2 + exp(i*(pi/2 - a))/2) - i*(-exp(i*(-pi - a)) + exp(i*(pi + a)))/2 + i*(-exp(i*(a - 3*pi/2)) + exp(i*(-a + 3*pi/2)))/(2*(-1 + a*x))
Parte trigonométrica [src] 
                            /a\                 2/a\       
                       2*tan|-|          1 - tan |-|       
     1        1             \2/                  \2/       
- ------- - ------ - ----------- + ------------------------
  1 + a*x   tan(a)          2/a\   /       2/a\\           
                     1 + tan |-|   |1 + tan |-||*(-1 + a*x)
                             \2/   \        \2//
1−tan⁡2(a2)(ax−1)(tan⁡2(a2)+1)−1tan⁡(a)−2tan⁡(a2)tan⁡2(a2)+1−1ax+1\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)} - \frac{1}{\tan{\left(a \right)}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} 
                                                 /    pi\
                                              sec|a - --|
     1           1                1              \    2 /
- ------- - ----------- + ----------------- - -----------
  1 + a*x      /    pi\   (-1 + a*x)*sec(a)      sec(a)  
            sec|a - --|                                  
               \    2 /
−1sec⁡(a−π2)−sec⁡(a−π2)sec⁡(a)−1ax+1+1(ax−1)sec⁡(a)- \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} - \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \sec{\left(a \right)}} 
   /a\                                 /       /a\\             
tan|-|                                 |1 - tan|-||*(1 + sin(a))
   \2/      1                  1       \       \2//             
------ - ------- - sin(a) - -------- + -------------------------
  2      1 + a*x                 /a\    /       /a\\            
                            2*tan|-|    |1 + tan|-||*(-1 + a*x) 
                                 \2/    \       \2//
(1−tan⁡(a2))(sin⁡(a)+1)(ax−1)(tan⁡(a2)+1)−sin⁡(a)+tan⁡(a2)2−12tan⁡(a2)−1ax+1\frac{\left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(\sin{\left(a \right)} + 1\right)}{\left(a x - 1\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)} - \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} 
    1         /a\                                              
- ------ + tan|-|                                              
     /a\      \2/                                      /a   pi\
  tan|-|                               (1 + sin(a))*cot|- + --|
     \2/               1                               \2   4 /
----------------- - ------- - sin(a) + ------------------------
        2           1 + a*x                    -1 + a*x
tan⁡(a2)−1tan⁡(a2)2−sin⁡(a)−1ax+1+(sin⁡(a)+1)cot⁡(a2+π4)ax−1\frac{\tan{\left(\frac{a}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}}}{2} - \sin{\left(a \right)} - \frac{1}{a x + 1} + \frac{\left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{a x - 1} 
                        /a\          /a\                                             
                     cot|-|     2*cot|-|                                             
   1          1         \2/          \2/                        2                    
-------- - ------- - ------ - ----------- + -----------------------------------------
     /a\   1 + a*x     2             2/a\   /         1      \               /a   pi\
2*cot|-|                      1 + cot |-|   |1 + ------------|*(-1 + a*x)*cot|- + --|
     \2/                              \2/   |       2/a   pi\|               \2   4 /
                                            |    cot |- + --||                       
                                            \        \2   4 //
−cot⁡(a2)2+12cot⁡(a2)−2cot⁡(a2)cot⁡2(a2)+1−1ax+1+2(1+1cot⁡2(a2+π4))(ax−1)cot⁡(a2+π4)- \frac{\cot{\left(\frac{a}{2} \right)}}{2} + \frac{1}{2 \cot{\left(\frac{a}{2} \right)}} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(a x - 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
                                                                   /         1      \ /        1   \
                                                                   |1 + ------------|*|-1 + -------|
                                                /a   pi\           |       2/a   pi\| |        2/a\|
                                           2*cot|- + --|           |    cot |- + --|| |     cot |-||
     1               2                          \2   4 /           \        \2   4 // \         \2//
- ------- - -------------------- + ----------------------------- + ---------------------------------
  1 + a*x   /       1   \    /a\   /       2/a   pi\\              /       1   \ /          1      \
            |1 + -------|*cot|-|   |1 + cot |- + --||*(-1 + a*x)   |1 + -------|*|-1 + ------------|
            |       2/a\|    \2/   \        \2   4 //              |       2/a\| |        2/a   pi\|
            |    cot |-||                                          |    cot |-|| |     cot |- + --||
            \        \2//                                          \        \2// \         \2   4 //
(−1+1cot⁡2(a2))(1+1cot⁡2(a2+π4))(−1+1cot⁡2(a2+π4))(1+1cot⁡2(a2))−1ax+1+2cot⁡(a2+π4)(ax−1)(cot⁡2(a2+π4)+1)−2(1+1cot⁡2(a2))cot⁡(a2)\frac{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)}{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)} - \frac{1}{a x + 1} + \frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} - \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)}} 
   /a\                         /a\                   /a   pi\
tan|-|                      cot|-|   (1 + sin(a))*cot|- + --|
   \2/      1                  \2/                   \2   4 /
------ - ------- - sin(a) - ------ + ------------------------
  2      1 + a*x              2              -1 + a*x
−sin⁡(a)+tan⁡(a2)2−cot⁡(a2)2−1ax+1+(sin⁡(a)+1)cot⁡(a2+π4)ax−1- \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{\cot{\left(\frac{a}{2} \right)}}{2} - \frac{1}{a x + 1} + \frac{\left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{a x - 1} 
     1                         cos(a) 
- ------- - cot(a) - sin(a) + --------
  1 + a*x                     -1 + a*x
−sin⁡(a)−cot⁡(a)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} - \cot{\left(a \right)} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                   /a\                 /a   pi\           /       2/a   pi\\ /       2/a\\
              2*cot|-|            2*tan|- + --|           |1 + cot |- + --||*|1 - cot |-||
     1             \2/                 \2   4 /           \        \2   4 // \        \2//
- ------- - ----------- + ----------------------------- + --------------------------------
  1 + a*x          2/a\   /       2/a   pi\\              /       2/a\\ /       2/a   pi\\
            1 + cot |-|   |1 + tan |- + --||*(-1 + a*x)   |1 + cot |-||*|1 - cot |- + --||
                    \2/   \        \2   4 //              \        \2// \        \2   4 //
(1−cot⁡2(a2))(cot⁡2(a2+π4)+1)(1−cot⁡2(a2+π4))(cot⁡2(a2)+1)−2cot⁡(a2)cot⁡2(a2)+1−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)\frac{\left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)}{\left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
   /a\                         /a\                /a   pi\        
tan|-|                      cot|-|           2*tan|- + --|        
   \2/      1                  \2/                \2   4 /        
------ - ------- - sin(a) - ------ + -----------------------------
  2      1 + a*x              2      /       2/a   pi\\           
                                     |1 + tan |- + --||*(-1 + a*x)
                                     \        \2   4 //
−sin⁡(a)+tan⁡(a2)2−cot⁡(a2)2−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)- \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{\cot{\left(\frac{a}{2} \right)}}{2} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
     1      /  1            \    cos(a)
- ------- - |------ + sin(a)| + -------
  a*x + 1   \tan(a)         /   a*x - 1
−(sin⁡(a)+1tan⁡(a))−1ax+1+cos⁡(a)ax−1- (\sin{\left(a \right)} + \frac{1}{\tan{\left(a \right)}}) - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                             /a   pi\          /a\                         /a   pi\              
                          cos|- - --|       cos|-|                    2*cos|- - --|              
     1         /    pi\      \2   2 /          \2/                         \2   4 /              
- ------- - cos|a - --| + ----------- - ------------- + -----------------------------------------
  1 + a*x      \    2 /          /a\         /a   pi\   /       2/a   pi\\                       
                            2*cos|-|    2*cos|- - --|   |    cos |- - --||                       
                                 \2/         \2   2 /   |        \2   4 /|               /a   pi\
                                                        |1 + ------------|*(-1 + a*x)*cos|- + --|
                                                        |       2/a   pi\|               \2   4 /
                                                        |    cos |- + --||                       
                                                        \        \2   4 //
−cos⁡(a2)2cos⁡(a2−π2)−cos⁡(a−π2)+cos⁡(a2−π2)2cos⁡(a2)−1ax+1+2cos⁡(a2−π4)(ax−1)(cos⁡2(a2−π4)cos⁡2(a2+π4)+1)cos⁡(a2+π4)- \frac{\cos{\left(\frac{a}{2} \right)}}{2 \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \cos{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{2 \cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
                             /a   pi\          /a\      /       /    pi\\    /a   pi\
                          cos|- - --|       cos|-|      |1 + cos|a - --||*cos|- + --|
     1         /    pi\      \2   2 /          \2/      \       \    2 //    \2   4 /
- ------- - cos|a - --| + ----------- - ------------- + -----------------------------
  1 + a*x      \    2 /          /a\         /a   pi\                     /a   pi\   
                            2*cos|-|    2*cos|- - --|       (-1 + a*x)*cos|- - --|   
                                 \2/         \2   2 /                     \2   4 /
−cos⁡(a2)2cos⁡(a2−π2)−cos⁡(a−π2)+cos⁡(a2−π2)2cos⁡(a2)−1ax+1+(cos⁡(a−π2)+1)cos⁡(a2+π4)(ax−1)cos⁡(a2−π4)- \frac{\cos{\left(\frac{a}{2} \right)}}{2 \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \cos{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}} 
    1         /a\                                                   
- ------ + tan|-|                                                   
     /a\      \2/                                   /a   pi\        
  tan|-|                                       2*tan|- + --|        
     \2/               1                            \2   4 /        
----------------- - ------- - sin(a) + -----------------------------
        2           1 + a*x            /       2/a   pi\\           
                                       |1 + tan |- + --||*(-1 + a*x)
                                       \        \2   4 //
tan⁡(a2)−1tan⁡(a2)2−sin⁡(a)−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)\frac{\tan{\left(\frac{a}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}}}{2} - \sin{\left(a \right)} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
                                                                   /         1      \ /       1   \
                                                                   |1 + ------------|*|1 - -------|
                                                /a   pi\           |       2/a   pi\| |       2/a\|
                                           2*tan|- + --|           |    tan |- + --|| |    tan |-||
     1               2                          \2   4 /           \        \2   4 // \        \2//
- ------- - -------------------- + ----------------------------- + --------------------------------
  1 + a*x   /       1   \    /a\   /       2/a   pi\\              /       1   \ /         1      \
            |1 + -------|*tan|-|   |1 + tan |- + --||*(-1 + a*x)   |1 + -------|*|1 - ------------|
            |       2/a\|    \2/   \        \2   4 //              |       2/a\| |       2/a   pi\|
            |    tan |-||                                          |    tan |-|| |    tan |- + --||
            \        \2//                                          \        \2// \        \2   4 //
(1−1tan⁡2(a2))(1+1tan⁡2(a2+π4))(1+1tan⁡2(a2))(1−1tan⁡2(a2+π4))−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)−2(1+1tan⁡2(a2))tan⁡(a2)\frac{\left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} - \frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}} 
     1        1                cos(a) 
- ------- - ------ - sin(a) + --------
  1 + a*x   tan(a)            -1 + a*x
−sin⁡(a)−1tan⁡(a)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} - \frac{1}{\tan{\left(a \right)}} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                        2/a\                                        
                     sin |-|                                        
     1                   \2/     sin(a)       (1 + sin(a))*cos(a)   
- ------- - sin(a) + ------- - --------- + -------------------------
  1 + a*x             sin(a)        2/a\                   2/a   pi\
                               4*sin |-|   2*(-1 + a*x)*sin |- + --|
                                     \2/                    \2   4 /
sin⁡2(a2)sin⁡(a)−sin⁡(a)−sin⁡(a)4sin⁡2(a2)−1ax+1+(sin⁡(a)+1)cos⁡(a)2(ax−1)sin⁡2(a2+π4)\frac{\sin^{2}{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} - \sin{\left(a \right)} - \frac{\sin{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{\left(\sin{\left(a \right)} + 1\right) \cos{\left(a \right)}}{2 \left(a x - 1\right) \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
                        /    pi\            
                     sin|a + --|            
     1                  \    2 /    sin(2*a)
- ------- - sin(a) + ----------- - ---------
  1 + a*x              -1 + a*x         2   
                                   2*sin (a)
−sin⁡(a)−sin⁡(2a)2sin⁡2(a)−1ax+1+sin⁡(a+π2)ax−1- \sin{\left(a \right)} - \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}} - \frac{1}{a x + 1} + \frac{\sin{\left(a + \frac{\pi}{2} \right)}}{a x - 1} 
                                   /    3*pi\
                                sin|a + ----|
     1                cos(a)       \     2  /
- ------- - sin(a) + -------- + -------------
  1 + a*x            -1 + a*x    sin(pi - a)
−sin⁡(a)+sin⁡(a+3π2)sin⁡(π−a)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} + \frac{\sin{\left(a + \frac{3 \pi}{2} \right)}}{\sin{\left(\pi - a \right)}} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                                 /a\         /a   pi\                      /a   pi\              
                              sec|-|      sec|- - --|                 2*sec|- + --|              
     1           1               \2/         \2   2 /                      \2   4 /              
- ------- - ----------- + ------------- - ----------- + -----------------------------------------
  1 + a*x      /    pi\        /a   pi\          /a\    /       2/a   pi\\                       
            sec|a - --|   2*sec|- - --|     2*sec|-|    |    sec |- + --||                       
               \    2 /        \2   2 /          \2/    |        \2   4 /|               /a   pi\
                                                        |1 + ------------|*(-1 + a*x)*sec|- - --|
                                                        |       2/a   pi\|               \2   4 /
                                                        |    sec |- - --||                       
                                                        \        \2   4 //
sec⁡(a2)2sec⁡(a2−π2)−1sec⁡(a−π2)−sec⁡(a2−π2)2sec⁡(a2)−1ax+1+2sec⁡(a2+π4)(1+sec⁡2(a2+π4)sec⁡2(a2−π4))(ax−1)sec⁡(a2−π4)\frac{\sec{\left(\frac{a}{2} \right)}}{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \sec{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{2 \sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right) \left(a x - 1\right) \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}} 
                        /pi   a\          /a\                         /  a   pi\              
                     csc|-- - -|       csc|-|                    2*csc|- - + --|              
     1        1         \2    2/          \2/                         \  2   4 /              
- ------- - ------ + ----------- - ------------- + -------------------------------------------
  1 + a*x   csc(a)          /a\         /pi   a\   /       2/  a   pi\\                       
                       2*csc|-|    2*csc|-- - -|   |    csc |- - + --||                       
                            \2/         \2    2/   |        \  2   4 /|               /a   pi\
                                                   |1 + --------------|*(-1 + a*x)*csc|- + --|
                                                   |        2/a   pi\ |               \2   4 /
                                                   |     csc |- + --| |                       
                                                   \         \2   4 / /
−csc⁡(a2)2csc⁡(−a2+π2)−1csc⁡(a)+csc⁡(−a2+π2)2csc⁡(a2)−1ax+1+2csc⁡(−a2+π4)(ax−1)(csc⁡2(−a2+π4)csc⁡2(a2+π4)+1)csc⁡(a2+π4)- \frac{\csc{\left(\frac{a}{2} \right)}}{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} + \frac{\csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{2 \csc{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right) \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
   /a\                               /a\                 /a   pi\        
tan|-|                          2*tan|-|            2*tan|- + --|        
   \2/      1         1              \2/                 \2   4 /        
------ - ------- - -------- - ----------- + -----------------------------
  2      1 + a*x        /a\          2/a\   /       2/a   pi\\           
                   2*tan|-|   1 + tan |-|   |1 + tan |- + --||*(-1 + a*x)
                        \2/           \2/   \        \2   4 //
tan⁡(a2)2−12tan⁡(a2)−2tan⁡(a2)tan⁡2(a2)+1−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)\frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
                                            /           /a\ \            
                                            |      2*cot|-| |            
                                            |           \2/ |    /a   pi\
                                            |1 + -----------|*cot|- + --|
                        /a\          /a\    |           2/a\|    \2   4 /
                     cot|-|     2*cot|-|    |    1 + cot |-||            
   1          1         \2/          \2/    \            \2//            
-------- - ------- - ------ - ----------- + -----------------------------
     /a\   1 + a*x     2             2/a\              -1 + a*x          
2*cot|-|                      1 + cot |-|                                
     \2/                              \2/
(1+2cot⁡(a2)cot⁡2(a2)+1)cot⁡(a2+π4)ax−1−cot⁡(a2)2+12cot⁡(a2)−2cot⁡(a2)cot⁡2(a2)+1−1ax+1\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{a x - 1} - \frac{\cot{\left(\frac{a}{2} \right)}}{2} + \frac{1}{2 \cot{\left(\frac{a}{2} \right)}} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} 
   /a\                                                       
tan|-|                                                       
   \2/      1                  1             1 + sin(a)      
------ - ------- - sin(a) - -------- + ----------------------
  2      1 + a*x                 /a\                 /a   pi\
                            2*tan|-|   (-1 + a*x)*tan|- + --|
                                 \2/                 \2   4 /
−sin⁡(a)+tan⁡(a2)2−12tan⁡(a2)−1ax+1+sin⁡(a)+1(ax−1)tan⁡(a2+π4)- \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{\sin{\left(a \right)} + 1}{\left(a x - 1\right) \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} 
                   /a\                 /a   pi\           /       2/a   pi\\ /        2/a\\
              2*tan|-|            2*cot|- + --|           |1 + tan |- + --||*|-1 + tan |-||
     1             \2/                 \2   4 /           \        \2   4 // \         \2//
- ------- - ----------- + ----------------------------- + ---------------------------------
  1 + a*x          2/a\   /       2/a   pi\\              /       2/a\\ /        2/a   pi\\
            1 + tan |-|   |1 + cot |- + --||*(-1 + a*x)   |1 + tan |-||*|-1 + tan |- + --||
                    \2/   \        \2   4 //              \        \2// \         \2   4 //
(tan⁡2(a2)−1)(tan⁡2(a2+π4)+1)(tan⁡2(a2)+1)(tan⁡2(a2+π4)−1)−2tan⁡(a2)tan⁡2(a2)+1−1ax+1+2cot⁡(a2+π4)(ax−1)(cot⁡2(a2+π4)+1)\frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} + \frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
                                   2/a\                 
                                sin |-|                 
     1                cos(a)        \2/       sin(a)    
- ------- - sin(a) + -------- + ------- - --------------
  1 + a*x            -1 + a*x    sin(a)   2*(1 - cos(a))
sin⁡2(a2)sin⁡(a)−sin⁡(a)−1ax+1+cos⁡(a)ax−1−sin⁡(a)2(1−cos⁡(a))\frac{\sin^{2}{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} - \sin{\left(a \right)} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} - \frac{\sin{\left(a \right)}}{2 \left(1 - \cos{\left(a \right)}\right)} 
                        /    pi\         
                     sin|a + --|         
     1                  \    2 /   cos(a)
- ------- - sin(a) + ----------- - ------
  1 + a*x              -1 + a*x    sin(a)
−sin⁡(a)−cos⁡(a)sin⁡(a)−1ax+1+sin⁡(a+π2)ax−1- \sin{\left(a \right)} - \frac{\cos{\left(a \right)}}{\sin{\left(a \right)}} - \frac{1}{a x + 1} + \frac{\sin{\left(a + \frac{\pi}{2} \right)}}{a x - 1} 
                                                        /         1     \    /a   pi\
                                                        |1 + -----------|*sec|- - --|
                                 /a\         /a   pi\   |       /    pi\|    \2   4 /
                              sec|-|      sec|- - --|   |    sec|a - --||            
     1           1               \2/         \2   2 /   \       \    2 //            
- ------- - ----------- + ------------- - ----------- + -----------------------------
  1 + a*x      /    pi\        /a   pi\          /a\                      /a   pi\   
            sec|a - --|   2*sec|- - --|     2*sec|-|        (-1 + a*x)*sec|- + --|   
               \    2 /        \2   2 /          \2/                      \2   4 /
(1+1sec⁡(a−π2))sec⁡(a2−π4)(ax−1)sec⁡(a2+π4)+sec⁡(a2)2sec⁡(a2−π2)−1sec⁡(a−π2)−sec⁡(a2−π2)2sec⁡(a2)−1ax+1\frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\left(a x - 1\right) \sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + \frac{\sec{\left(\frac{a}{2} \right)}}{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \sec{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} 
   /a\                                              /a   pi\        
tan|-|                                         2*tan|- + --|        
   \2/      1                  1                    \2   4 /        
------ - ------- - sin(a) - -------- + -----------------------------
  2      1 + a*x                 /a\   /       2/a   pi\\           
                            2*tan|-|   |1 + tan |- + --||*(-1 + a*x)
                                 \2/   \        \2   4 //
−sin⁡(a)+tan⁡(a2)2−12tan⁡(a2)−1ax+1+2tan⁡(a2+π4)(ax−1)(tan⁡2(a2+π4)+1)- \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
     1        1                1                 csc(a)  
- ------- - ------ + ---------------------- - -----------
  1 + a*x   csc(a)                 /pi    \      /pi    \
                     (-1 + a*x)*csc|-- - a|   csc|-- - a|
                                   \2     /      \2     /
−csc⁡(a)csc⁡(−a+π2)−1csc⁡(a)−1ax+1+1(ax−1)csc⁡(−a+π2)- \frac{\csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} - \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}} 
     1        1              1              csc(a)  
- ------- - ------ + ----------------- - -----------
  1 + a*x   csc(a)   (-1 + a*x)*sec(a)      /pi    \
                                         csc|-- - a|
                                            \2     /
−csc⁡(a)csc⁡(−a+π2)−1csc⁡(a)−1ax+1+1(ax−1)sec⁡(a)- \frac{\csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} - \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \sec{\left(a \right)}} 
     1                cos(a)       cos(a)  
- ------- - sin(a) + -------- - -----------
  1 + a*x            -1 + a*x      /    pi\
                                cos|a - --|
                                   \    2 /
−sin⁡(a)−cos⁡(a)cos⁡(a−π2)−1ax+1+cos⁡(a)ax−1- \sin{\left(a \right)} - \frac{\cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                        2/a\                                2/a   pi\            
                     sin |-|                           4*sin |- + --|            
     1                   \2/     sin(a)                      \2   4 /            
- ------- - sin(a) + ------- - --------- + --------------------------------------
  1 + a*x             sin(a)        2/a\   /         4/a   pi\\                  
                               4*sin |-|   |    4*sin |- + --||                  
                                     \2/   |          \2   4 /|                  
                                           |1 + --------------|*(-1 + a*x)*cos(a)
                                           |          2       |                  
                                           \       cos (a)    /
sin⁡2(a2)sin⁡(a)−sin⁡(a)−sin⁡(a)4sin⁡2(a2)−1ax+1+4sin⁡2(a2+π4)(ax−1)(4sin⁡4(a2+π4)cos⁡2(a)+1)cos⁡(a)\frac{\sin^{2}{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} - \sin{\left(a \right)} - \frac{\sin{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} + \frac{4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(a \right)}} + 1\right) \cos{\left(a \right)}} 
     1      cos(pi - a)   cos(a)      /    pi\
- ------- - ----------- - ------ + cos|a + --|
  1 + a*x     -1 + a*x    sin(a)      \    2 /
cos⁡(a+π2)−cos⁡(a)sin⁡(a)−1ax+1−cos⁡(π−a)ax−1\cos{\left(a + \frac{\pi}{2} \right)} - \frac{\cos{\left(a \right)}}{\sin{\left(a \right)}} - \frac{1}{a x + 1} - \frac{\cos{\left(\pi - a \right)}}{a x - 1} 
     1           1                1              csc(a)
----------- - ------- - ---------------------- - ------
   /    pi\   1 + a*x   (-1 + a*x)*sec(pi - a)   sec(a)
sec|a + --|                                            
   \    2 /
−csc⁡(a)sec⁡(a)+1sec⁡(a+π2)−1ax+1−1(ax−1)sec⁡(π−a)- \frac{\csc{\left(a \right)}}{\sec{\left(a \right)}} + \frac{1}{\sec{\left(a + \frac{\pi}{2} \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \sec{\left(\pi - a \right)}} 
   /a\                                              /       /a\\
tan|-|                                 (1 - sin(a))*|1 + tan|-||
   \2/      1                  1                    \       \2//
------ - ------- - sin(a) - -------- + -------------------------
  2      1 + a*x                 /a\    /       /a\\            
                            2*tan|-|    |1 - tan|-||*(-1 + a*x) 
                                 \2/    \       \2//
(1−sin⁡(a))(tan⁡(a2)+1)(1−tan⁡(a2))(ax−1)−sin⁡(a)+tan⁡(a2)2−12tan⁡(a2)−1ax+1\frac{\left(1 - \sin{\left(a \right)}\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)}{\left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(a x - 1\right)} - \sin{\left(a \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} 
     1        1                1              csc(a)
- ------- - ------ + ---------------------- - ------
  1 + a*x   csc(a)                 /pi    \   sec(a)
                     (-1 + a*x)*csc|-- - a|         
                                   \2     /
−csc⁡(a)sec⁡(a)−1csc⁡(a)−1ax+1+1(ax−1)csc⁡(−a+π2)- \frac{\csc{\left(a \right)}}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}} - \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}} 
                                                          /a\     
                                                     2*tan|-|     
                                                          \2/     
                                               1 + -----------    
   /a\                               /a\                  2/a\    
tan|-|                          2*tan|-|           1 + tan |-|    
   \2/      1         1              \2/                   \2/    
------ - ------- - -------- - ----------- + ----------------------
  2      1 + a*x        /a\          2/a\                 /a   pi\
                   2*tan|-|   1 + tan |-|   (-1 + a*x)*tan|- + --|
                        \2/           \2/                 \2   4 /
1+2tan⁡(a2)tan⁡2(a2)+1(ax−1)tan⁡(a2+π4)+tan⁡(a2)2−12tan⁡(a2)−2tan⁡(a2)tan⁡2(a2)+1−1ax+1\frac{1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}}{\left(a x - 1\right) \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + \frac{\tan{\left(\frac{a}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{a}{2} \right)}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} 
     1         /    pi\    cos(a)       cos(a)  
- ------- - cos|a - --| + -------- - -----------
  1 + a*x      \    2 /   -1 + a*x      /    pi\
                                     cos|a - --|
                                        \    2 /
−cos⁡(a)cos⁡(a−π2)−cos⁡(a−π2)−1ax+1+cos⁡(a)ax−1- \frac{\cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} - \frac{1}{a x + 1} + \frac{\cos{\left(a \right)}}{a x - 1} 
                                            /pi    \
                                         sec|-- - a|
     1        1              1              \2     /
- ------- - ------ + ----------------- - -----------
  1 + a*x   csc(a)   (-1 + a*x)*sec(a)      sec(a)
−sec⁡(−a+π2)sec⁡(a)−1csc⁡(a)−1ax+1+1(ax−1)sec⁡(a)- \frac{\sec{\left(- a + \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}} - \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \sec{\left(a \right)}} 
                        /pi   a\          /a\      /      1   \    /a   pi\
                     csc|-- - -|       csc|-|      |1 + ------|*csc|- + --|
     1        1         \2    2/          \2/      \    csc(a)/    \2   4 /
- ------- - ------ + ----------- - ------------- + ------------------------
  1 + a*x   csc(a)          /a\         /pi   a\                 /  a   pi\
                       2*csc|-|    2*csc|-- - -|   (-1 + a*x)*csc|- - + --|
                            \2/         \2    2/                 \  2   4 /
(1+1csc⁡(a))csc⁡(a2+π4)(ax−1)csc⁡(−a2+π4)−csc⁡(a2)2csc⁡(−a2+π2)−1csc⁡(a)+csc⁡(−a2+π2)2csc⁡(a2)−1ax+1\frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{\csc{\left(\frac{a}{2} \right)}}{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} + \frac{\csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{2 \csc{\left(\frac{a}{2} \right)}} - \frac{1}{a x + 1} 
                            /a\                  2/a\      
                       2*cot|-|          -1 + cot |-|      
     1                      \2/                   \2/      
- ------- - cot(a) - ----------- + ------------------------
  1 + a*x                   2/a\   /       2/a\\           
                     1 + cot |-|   |1 + cot |-||*(-1 + a*x)
                             \2/   \        \2//
−cot⁡(a)−2cot⁡(a2)cot⁡2(a2)+1−1ax+1+cot⁡2(a2)−1(ax−1)(cot⁡2(a2)+1)- \cot{\left(a \right)} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - \frac{1}{a x + 1} + \frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\left(a x - 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
-1/(1 + a*x) - cot(a) - 2*cot(a/2)/(1 + cot(a/2)^2) + (-1 + cot(a/2)^2)/((1 + cot(a/2)^2)*(-1 + a*x))
Combinatoria [src] 
 /     2                                                      2  2    2       2  2                           \ 
-\- sin (a) - cos(a) - sin(a) - cos(a)*sin(a) + a*x*sin(a) + a *x *sin (a) + a *x *cos(a) - a*x*cos(a)*sin(a)/ 
---------------------------------------------------------------------------------------------------------------
                                          (1 + a*x)*(-1 + a*x)*sin(a)
−a2x2sin⁡2(a)+a2x2cos⁡(a)−axsin⁡(a)cos⁡(a)+axsin⁡(a)−sin⁡2(a)−sin⁡(a)cos⁡(a)−sin⁡(a)−cos⁡(a)(ax−1)(ax+1)sin⁡(a)- \frac{a^{2} x^{2} \sin^{2}{\left(a \right)} + a^{2} x^{2} \cos{\left(a \right)} - a x \sin{\left(a \right)} \cos{\left(a \right)} + a x \sin{\left(a \right)} - \sin^{2}{\left(a \right)} - \sin{\left(a \right)} \cos{\left(a \right)} - \sin{\left(a \right)} - \cos{\left(a \right)}}{\left(a x - 1\right) \left(a x + 1\right) \sin{\left(a \right)}} 
-(-sin(a)^2 - cos(a) - sin(a) - cos(a)*sin(a) + a*x*sin(a) + a^2*x^2*sin(a)^2 + a^2*x^2*cos(a) - a*x*cos(a)*sin(a))/((1 + a*x)*(-1 + a*x)*sin(a))
    © Sr Examen – Калькулятор