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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
        2                          
     cos (x)        2*cos(x)*sin(x)
----------------- - ---------------
/     2\     2          acot(x)    
\1 + x /*acot (x)
−sin⁡(x)2cos⁡(x)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{\sin{\left(x \right)} 2 \cos{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
cos(x)^2/(((1 + x^2)*acot(x)^2)) - (2*cos(x))*sin(x)/acot(x)
Simplificación general [src] 
/    /     2\                        \       
\- 2*\1 + x /*acot(x)*sin(x) + cos(x)/*cos(x)
---------------------------------------------
              /     2\     2                 
              \1 + x /*acot (x)
(−2(x2+1)sin⁡(x)acot⁡(x)+cos⁡(x))cos⁡(x)(x2+1)acot⁡2(x)\frac{\left(- 2 \left(x^{2} + 1\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} + \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
(-2*(1 + x^2)*acot(x)*sin(x) + cos(x))*cos(x)/((1 + x^2)*acot(x)^2)
Respuesta numérica [src] 
cos(x)^2/((1.0 + x^2)*acot(x)^2) - 2.0*cos(x)*sin(x)/acot(x)
cos(x)^2/((1.0 + x^2)*acot(x)^2) - 2.0*cos(x)*sin(x)/acot(x)
Combinatoria [src] 
 /                                2               \        
-\-cos(x) + 2*acot(x)*sin(x) + 2*x *acot(x)*sin(x)/*cos(x) 
-----------------------------------------------------------
                     /     2\     2                        
                     \1 + x /*acot (x)
−(2x2sin⁡(x)acot⁡(x)+2sin⁡(x)acot⁡(x)−cos⁡(x))cos⁡(x)(x2+1)acot⁡2(x)- \frac{\left(2 x^{2} \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} + 2 \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
-(-cos(x) + 2*acot(x)*sin(x) + 2*x^2*acot(x)*sin(x))*cos(x)/((1 + x^2)*acot(x)^2)
Unión de expresiones racionales [src] 
/    /     2\                        \       
\- 2*\1 + x /*acot(x)*sin(x) + cos(x)/*cos(x)
---------------------------------------------
              /     2\     2                 
              \1 + x /*acot (x)
(−2(x2+1)sin⁡(x)acot⁡(x)+cos⁡(x))cos⁡(x)(x2+1)acot⁡2(x)\frac{\left(- 2 \left(x^{2} + 1\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)} + \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
(-2*(1 + x^2)*acot(x)*sin(x) + cos(x))*cos(x)/((1 + x^2)*acot(x)^2)
Potencias [src] 
        2                          
     cos (x)        2*cos(x)*sin(x)
----------------- - ---------------
/     2\     2          acot(x)    
\1 + x /*acot (x)
−2sin⁡(x)cos⁡(x)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
               2                                     
 / I*x    -I*x\                                      
 |e      e    |                                      
 |---- + -----|       /   -I*x    I*x\ / I*x    -I*x\
 \ 2       2  /     I*\- e     + e   /*\e    + e    /
----------------- + ---------------------------------
/     2\     2                  2*acot(x)            
\1 + x /*acot (x)
i(eix−e−ix)(eix+e−ix)2acot⁡(x)+(eix2+e−ix2)2(x2+1)acot⁡2(x)\frac{i \left(e^{i x} - e^{- i x}\right) \left(e^{i x} + e^{- i x}\right)}{2 \operatorname{acot}{\left(x \right)}} + \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
(exp(i*x)/2 + exp(-i*x)/2)^2/((1 + x^2)*acot(x)^2) + i*(-exp(-i*x) + exp(i*x))*(exp(i*x) + exp(-i*x))/(2*acot(x))
Abrimos la expresión [src] 
          2                             
       cos (x)           2*cos(x)*sin(x)
---------------------- - ---------------
    2       2     2          acot(x)    
acot (x) + x *acot (x)
−sin⁡(x)2cos⁡(x)acot⁡(x)+cos⁡2(x)x2acot⁡2(x)+acot⁡2(x)- \frac{\sin{\left(x \right)} 2 \cos{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{x^{2} \operatorname{acot}^{2}{\left(x \right)} + \operatorname{acot}^{2}{\left(x \right)}} 
cos(x)^2/(acot(x)^2 + x^2*acot(x)^2) - (2*cos(x))*sin(x)/acot(x)
Denominador común [src] 
 /     2                                   2                      \ 
-\- cos (x) + 2*acot(x)*cos(x)*sin(x) + 2*x *acot(x)*cos(x)*sin(x)/ 
--------------------------------------------------------------------
                           2       2     2                          
                       acot (x) + x *acot (x)
−2x2sin⁡(x)cos⁡(x)acot⁡(x)+2sin⁡(x)cos⁡(x)acot⁡(x)−cos⁡2(x)x2acot⁡2(x)+acot⁡2(x)- \frac{2 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} - \cos^{2}{\left(x \right)}}{x^{2} \operatorname{acot}^{2}{\left(x \right)} + \operatorname{acot}^{2}{\left(x \right)}} 
-(-cos(x)^2 + 2*acot(x)*cos(x)*sin(x) + 2*x^2*acot(x)*cos(x)*sin(x))/(acot(x)^2 + x^2*acot(x)^2)
Compilar la expresión [src] 
        2                          
     cos (x)        2*cos(x)*sin(x)
----------------- - ---------------
/     2\     2          acot(x)    
\1 + x /*acot (x)
−2sin⁡(x)cos⁡(x)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
cos(x)^2/((1 + x^2)*acot(x)^2) - 2*cos(x)*sin(x)/acot(x)
Parte trigonométrica [src] 
            1                         1            
- --------------------- + -------------------------
             /      pi\   /     2\     2       2   
  acot(x)*sec|2*x - --|   \1 + x /*acot (x)*sec (x)
             \      2 /
−1acot⁡(x)sec⁡(2x−π2)+1(x2+1)acot⁡2(x)sec⁡2(x)- \frac{1}{\operatorname{acot}{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)} \sec^{2}{\left(x \right)}} 
                     2        
  sin(2*x)        cos (x)     
- -------- + -----------------
  acot(x)    /     2\     2   
             \1 + x /*acot (x)
−sin⁡(2x)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{\sin{\left(2 x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
     /      pi\                    
  cos|2*x - --|           2        
     \      2 /        cos (x)     
- ------------- + -----------------
     acot(x)      /     2\     2   
                  \1 + x /*acot (x)
−cos⁡(2x−π2)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
   2            1           sin(2*x)
cos (x)*----------------- - --------
        /     2\     2      acot(x) 
        \1 + x /*acot (x)
1(x2+1)acot⁡2(x)cos⁡2(x)−sin⁡(2x)acot⁡(x)\frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} \cos^{2}{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{\operatorname{acot}{\left(x \right)}} 
                                                2         
                                   /       2/x\\          
                                   |1 - tan |-||          
         2*tan(x)                  \        \2//          
- --------------------- + --------------------------------
  /       2   \                                 2         
  \1 + tan (x)/*acot(x)   /     2\ /       2/x\\      2   
                          \1 + x /*|1 + tan |-|| *acot (x)
                                   \        \2//
(1−tan⁡2(x2))2(x2+1)(tan⁡2(x2)+1)2acot⁡2(x)−2tan⁡(x)(tan⁡2(x)+1)acot⁡(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(x^{2} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} - \frac{2 \tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}} 
                      2                                  
         /       2/x\\               /       2/x\\    /x\
         |1 - tan |-||             4*|1 - tan |-||*tan|-|
         \        \2//               \        \2//    \2/
-------------------------------- - ----------------------
                      2                         2        
/     2\ /       2/x\\      2      /       2/x\\         
\1 + x /*|1 + tan |-|| *acot (x)   |1 + tan |-|| *acot(x)
         \        \2//             \        \2//
(1−tan⁡2(x2))2(x2+1)(tan⁡2(x2)+1)2acot⁡2(x)−4(1−tan⁡2(x2))tan⁡(x2)(tan⁡2(x2)+1)2acot⁡(x)\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(x^{2} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} - \frac{4 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} 
                                1       
                      1 + ------------- 
                             /pi      \ 
                          csc|-- - 2*x| 
         1                   \2       / 
- ---------------- + -------------------
  acot(x)*csc(2*x)     /     2\     2   
                     2*\1 + x /*acot (x)
1+1csc⁡(−2x+π2)2(x2+1)acot⁡2(x)−1acot⁡(x)csc⁡(2x)\frac{1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} - \frac{1}{\operatorname{acot}{\left(x \right)} \csc{\left(2 x \right)}} 
              2                            
      -1 + cot (x)                         
  1 + ------------                         
             2                             
      1 + cot (x)            2*cot(x)      
------------------- - ---------------------
  /     2\     2      /       2   \        
2*\1 + x /*acot (x)   \1 + cot (x)/*acot(x)
−2cot⁡(x)(cot⁡2(x)+1)acot⁡(x)+cot⁡2(x)−1cot⁡2(x)+1+12(x2+1)acot⁡2(x)- \frac{2 \cot{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
             2                             
      1 - tan (x)                          
  1 + -----------                          
             2                             
      1 + tan (x)            2*tan(x)      
------------------- - ---------------------
  /     2\     2      /       2   \        
2*\1 + x /*acot (x)   \1 + tan (x)/*acot(x)
−2tan⁡(x)(tan⁡2(x)+1)acot⁡(x)+1−tan⁡2(x)tan⁡2(x)+1+12(x2+1)acot⁡2(x)- \frac{2 \tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
        2                          
     cos (x)        2*cos(x)*sin(x)
----------------- - ---------------
/     2\     2          acot(x)    
\1 + x /*acot (x)
−2sin⁡(x)cos⁡(x)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
                      2                                   
        /        2/x\\               /        2/x\\    /x\
        |-1 + cot |-||             4*|-1 + cot |-||*cot|-|
        \         \2//               \         \2//    \2/
-------------------------------- - -----------------------
                      2                          2        
/     2\ /       2/x\\      2       /       2/x\\         
\1 + x /*|1 + cot |-|| *acot (x)    |1 + cot |-|| *acot(x)
         \        \2//              \        \2//
−4(cot⁡2(x2)−1)cot⁡(x2)(cot⁡2(x2)+1)2acot⁡(x)+(cot⁡2(x2)−1)2(x2+1)(cot⁡2(x2)+1)2acot⁡2(x)- \frac{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(x^{2} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} 
                                                2         
                                  /        2/x\\          
                                  |-1 + cot |-||          
         2*cot(x)                 \         \2//          
- --------------------- + --------------------------------
  /       2   \                                 2         
  \1 + cot (x)/*acot(x)   /     2\ /       2/x\\      2   
                          \1 + x /*|1 + cot |-|| *acot (x)
                                   \        \2//
−2cot⁡(x)(cot⁡2(x)+1)acot⁡(x)+(cot⁡2(x2)−1)2(x2+1)(cot⁡2(x2)+1)2acot⁡2(x)- \frac{2 \cot{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(x^{2} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} 
                   2/    pi\  
                sin |x + --|  
  sin(2*x)          \    2 /  
- -------- + -----------------
  acot(x)    /     2\     2   
             \1 + x /*acot (x)
−sin⁡(2x)acot⁡(x)+sin⁡2(x+π2)(x2+1)acot⁡2(x)- \frac{\sin{\left(2 x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
      2/    pi\                 /    pi\
   sin |x + --|     2*sin(x)*sin|x + --|
       \    2 /                 \    2 /
----------------- - --------------------
/     2\     2            acot(x)       
\1 + x /*acot (x)
−2sin⁡(x)sin⁡(x+π2)acot⁡(x)+sin⁡2(x+π2)(x2+1)acot⁡2(x)- \frac{2 \sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
              1                              2             
------------------------------ - --------------------------
/     2\     2       2/pi    \                     /pi    \
\1 + x /*acot (x)*csc |-- - x|   acot(x)*csc(x)*csc|-- - x|
                      \2     /                     \2     /
−2acot⁡(x)csc⁡(x)csc⁡(−x+π2)+1(x2+1)acot⁡2(x)csc⁡2(−x+π2)- \frac{2}{\operatorname{acot}{\left(x \right)} \csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}} 
            1                           2             
------------------------- - --------------------------
/     2\     2       2                        /    pi\
\1 + x /*acot (x)*sec (x)   acot(x)*sec(x)*sec|x - --|
                                              \    2 /
−2acot⁡(x)sec⁡(x)sec⁡(x−π2)+1(x2+1)acot⁡2(x)sec⁡2(x)- \frac{2}{\operatorname{acot}{\left(x \right)} \sec{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)} \sec^{2}{\left(x \right)}} 
     /      pi\                      
  cos|2*x - --|                      
     \      2 /       1 + cos(2*x)   
- ------------- + -------------------
     acot(x)        /     2\     2   
                  2*\1 + x /*acot (x)
−cos⁡(2x−π2)acot⁡(x)+cos⁡(2x)+12(x2+1)acot⁡2(x)- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos{\left(2 x \right)} + 1}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
                     /pi      \ 
              1 + sin|-- + 2*x| 
  sin(2*x)           \2       / 
- -------- + -------------------
  acot(x)      /     2\     2   
             2*\1 + x /*acot (x)
−sin⁡(2x)acot⁡(x)+sin⁡(2x+π2)+12(x2+1)acot⁡2(x)- \frac{\sin{\left(2 x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
                                     1       
                              1 + --------   
            1                     sec(2*x)   
- --------------------- + -------------------
             /      pi\     /     2\     2   
  acot(x)*sec|2*x - --|   2*\1 + x /*acot (x)
             \      2 /
1+1sec⁡(2x)2(x2+1)acot⁡2(x)−1acot⁡(x)sec⁡(2x−π2)\frac{1 + \frac{1}{\sec{\left(2 x \right)}}}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} - \frac{1}{\operatorname{acot}{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} 
                                /    pi\
        2           2*cos(x)*cos|x - --|
     cos (x)                    \    2 /
----------------- - --------------------
/     2\     2            acot(x)       
\1 + x /*acot (x)
−2cos⁡(x)cos⁡(x−π2)acot⁡(x)+cos⁡2(x)(x2+1)acot⁡2(x)- \frac{2 \cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
  sin(2*x)       1 + cos(2*x)   
- -------- + -------------------
  acot(x)      /     2\     2   
             2*\1 + x /*acot (x)
−sin⁡(2x)acot⁡(x)+cos⁡(2x)+12(x2+1)acot⁡2(x)- \frac{\sin{\left(2 x \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{\cos{\left(2 x \right)} + 1}{2 \left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} 
            1                         2          
------------------------- - ---------------------
/     2\     2       2      acot(x)*csc(x)*sec(x)
\1 + x /*acot (x)*sec (x)
−2acot⁡(x)csc⁡(x)sec⁡(x)+1(x2+1)acot⁡2(x)sec⁡2(x)- \frac{2}{\operatorname{acot}{\left(x \right)} \csc{\left(x \right)} \sec{\left(x \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)} \sec^{2}{\left(x \right)}} 
         1                         1               
- ---------------- + ------------------------------
  acot(x)*csc(2*x)   /     2\     2       2/pi    \
                     \1 + x /*acot (x)*csc |-- - x|
                                           \2     /
−1acot⁡(x)csc⁡(2x)+1(x2+1)acot⁡2(x)csc⁡2(−x+π2)- \frac{1}{\operatorname{acot}{\left(x \right)} \csc{\left(2 x \right)}} + \frac{1}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}} 
-1/(acot(x)*csc(2*x)) + 1/((1 + x^2)*acot(x)^2*csc(pi/2 - x)^2)
Denominador racional [src] 
   2                    2    /     2\              
cos (x)*acot(x) - 2*acot (x)*\1 + x /*cos(x)*sin(x)
---------------------------------------------------
                 /     2\     3                    
                 \1 + x /*acot (x)
−2(x2+1)sin⁡(x)cos⁡(x)acot⁡2(x)+cos⁡2(x)acot⁡(x)(x2+1)acot⁡3(x)\frac{- 2 \left(x^{2} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{acot}^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{3}{\left(x \right)}} 
(cos(x)^2*acot(x) - 2*acot(x)^2*(1 + x^2)*cos(x)*sin(x))/((1 + x^2)*acot(x)^3)
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