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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   ___________ /  3             2       \
  /  3         |-x *sin(x)   3*x *cos(x)|
\/  x *cos(x) *|---------- + -----------|
               \    2             2     /
-----------------------------------------
                 3                       
                x *cos(x)
x3cos⁡(x)(3x2cos⁡(x)2+−x3sin⁡(x)2)x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(\frac{3 x^{2} \cos{\left(x \right)}}{2} + \frac{- x^{3} \sin{\left(x \right)}}{2}\right)}{x^{3} \cos{\left(x \right)}} 
(sqrt(x^3*cos(x))*(((-x^3)*sin(x))/2 + ((3*x^2)*cos(x))/2))/((x^3*cos(x)))
Simplificación general [src] 
   ___________               
  /  3                       
\/  x *cos(x) *(3 - x*tan(x))
-----------------------------
             2*x
x3cos⁡(x)(−xtan⁡(x)+3)2x\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- x \tan{\left(x \right)} + 3\right)}{2 x} 
sqrt(x^3*cos(x))*(3 - x*tan(x))/(2*x)
Respuesta numérica [src] 
(x^3*cos(x))^0.5*(1.5*x^2*cos(x) - 0.5*x^3*sin(x))/(x^3*cos(x))
(x^3*cos(x))^0.5*(1.5*x^2*cos(x) - 0.5*x^3*sin(x))/(x^3*cos(x))
Denominador racional [src] 
   ___________                            
  /  3         /   3             2       \
\/  x *cos(x) *\- x *sin(x) + 3*x *cos(x)/
------------------------------------------
                  3                       
               2*x *cos(x)
x3cos⁡(x)(−x3sin⁡(x)+3x2cos⁡(x))2x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- x^{3} \sin{\left(x \right)} + 3 x^{2} \cos{\left(x \right)}\right)}{2 x^{3} \cos{\left(x \right)}} 
sqrt(x^3*cos(x))*(-x^3*sin(x) + 3*x^2*cos(x))/(2*x^3*cos(x))
Potencias [src] 
   ___________ /   3             2       \
  /  3         |  x *sin(x)   3*x *cos(x)|
\/  x *cos(x) *|- --------- + -----------|
               \      2            2     /
------------------------------------------
                 3                        
                x *cos(x)
x3cos⁡(x)(−x3sin⁡(x)2+3x2cos⁡(x)2)x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- \frac{x^{3} \sin{\left(x \right)}}{2} + \frac{3 x^{2} \cos{\left(x \right)}}{2}\right)}{x^{3} \cos{\left(x \right)}} 
                         /     / I*x    -I*x\                        \
     ___________________ |   2 |e      e    |                        |
    /    / I*x    -I*x\  |3*x *|---- + -----|      3 /   -I*x    I*x\|
   /   3 |e      e    |  |     \ 2       2  /   I*x *\- e     + e   /|
  /   x *|---- + -----| *|------------------- + ---------------------|
\/       \ 2       2  /  \         2                      4          /
----------------------------------------------------------------------
                             / I*x    -I*x\                           
                           3 |e      e    |                           
                          x *|---- + -----|                           
                             \ 2       2  /
x3(eix2+e−ix2)(ix3(eix−e−ix)4+3x2(eix2+e−ix2)2)x3(eix2+e−ix2)\frac{\sqrt{x^{3} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)} \left(\frac{i x^{3} \left(e^{i x} - e^{- i x}\right)}{4} + \frac{3 x^{2} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{2}\right)}{x^{3} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)} 
sqrt(x^3*(exp(i*x)/2 + exp(-i*x)/2))*(3*x^2*(exp(i*x)/2 + exp(-i*x)/2)/2 + i*x^3*(-exp(-i*x) + exp(i*x))/4)/(x^3*(exp(i*x)/2 + exp(-i*x)/2))
Denominador común [src] 
 /       ___________               ___________       \ 
 |      /  3                      /  3               | 
-\- 3*\/  x *cos(x) *cos(x) + x*\/  x *cos(x) *sin(x)/ 
-------------------------------------------------------
                       2*x*cos(x)
−xx3cos⁡(x)sin⁡(x)−3x3cos⁡(x)cos⁡(x)2xcos⁡(x)- \frac{x \sqrt{x^{3} \cos{\left(x \right)}} \sin{\left(x \right)} - 3 \sqrt{x^{3} \cos{\left(x \right)}} \cos{\left(x \right)}}{2 x \cos{\left(x \right)}} 
-(-3*sqrt(x^3*cos(x))*cos(x) + x*sqrt(x^3*cos(x))*sin(x))/(2*x*cos(x))
Combinatoria [src] 
    ___________                        
   /  3                                
-\/  x *cos(x) *(-3*cos(x) + x*sin(x)) 
---------------------------------------
               2*x*cos(x)
−x3cos⁡(x)(xsin⁡(x)−3cos⁡(x))2xcos⁡(x)- \frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)}{2 x \cos{\left(x \right)}} 
-sqrt(x^3*cos(x))*(-3*cos(x) + x*sin(x))/(2*x*cos(x))
Unión de expresiones racionales [src] 
   ___________                      
  /  3                              
\/  x *cos(x) *(3*cos(x) - x*sin(x))
------------------------------------
             2*x*cos(x)
x3cos⁡(x)(−xsin⁡(x)+3cos⁡(x))2xcos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- x \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)}{2 x \cos{\left(x \right)}} 
sqrt(x^3*cos(x))*(3*cos(x) - x*sin(x))/(2*x*cos(x))
Abrimos la expresión [src] 
   ____ /  3             2       \
  /  3  |-x *sin(x)   3*x *cos(x)|
\/  x  *|---------- + -----------|
        \    2             2     /
----------------------------------
           3   ________           
          x *\/ cos(x)
(3x2cos⁡(x)2+−x3sin⁡(x)2)x3x3cos⁡(x)\frac{\left(\frac{3 x^{2} \cos{\left(x \right)}}{2} + \frac{- x^{3} \sin{\left(x \right)}}{2}\right) \sqrt{x^{3}}}{x^{3} \sqrt{\cos{\left(x \right)}}} 
     ___________      ___________       
    /  3             /  3               
3*\/  x *cos(x)    \/  x *cos(x) *sin(x)
---------------- - ---------------------
      2*x                 2*cos(x)
−x3cos⁡(x)sin⁡(x)2cos⁡(x)+3x3cos⁡(x)2x- \frac{\sqrt{x^{3} \cos{\left(x \right)}} \sin{\left(x \right)}}{2 \cos{\left(x \right)}} + \frac{3 \sqrt{x^{3} \cos{\left(x \right)}}}{2 x} 
3*sqrt(x^3*cos(x))/(2*x) - sqrt(x^3*cos(x))*sin(x)/(2*cos(x))
Compilar la expresión [src] 
   ___________ /   3             2       \
  /  3         |  x *sin(x)   3*x *cos(x)|
\/  x *cos(x) *|- --------- + -----------|
               \      2            2     /
------------------------------------------
                 3                        
                x *cos(x)
x3cos⁡(x)(−x3sin⁡(x)2+3x2cos⁡(x)2)x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- \frac{x^{3} \sin{\left(x \right)}}{2} + \frac{3 x^{2} \cos{\left(x \right)}}{2}\right)}{x^{3} \cos{\left(x \right)}} 
sqrt(x^3*cos(x))*(-x^3*sin(x)/2 + 3*x^2*cos(x)/2)/(x^3*cos(x))
Parte trigonométrica [src] 
        ___________________                                                    
       /  3 /        2/x\\                /    3    /x\       2 /        2/x\\\
      /  x *|-1 + cot |-||                |   x *cot|-|    3*x *|-1 + cot |-|||
     /      \         \2//  /       2/x\\ |         \2/         \         \2//|
    /    ----------------- *|1 + cot |-||*|- ----------- + -------------------|
   /               2/x\     \        \2// |         2/x\       /       2/x\\  |
  /         1 + cot |-|                   |  1 + cot |-|     2*|1 + cot |-||  |
\/                  \2/                   \          \2/       \        \2//  /
-------------------------------------------------------------------------------
                                3 /        2/x\\                               
                               x *|-1 + cot |-||                               
                                  \         \2//
x3(cot⁡2(x2)−1)cot⁡2(x2)+1(−x3cot⁡(x2)cot⁡2(x2)+1+3x2(cot⁡2(x2)−1)2(cot⁡2(x2)+1))(cot⁡2(x2)+1)x3(cot⁡2(x2)−1)\frac{\sqrt{\frac{x^{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- \frac{x^{3} \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{3 x^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{x^{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)} 
               /         /    pi\\
   ___________ |    x*cos|x - --||
  /  3         |         \    2 /|
\/  x *cos(x) *|3 - -------------|
               \        cos(x)   /
----------------------------------
               2*x
x3cos⁡(x)(−xcos⁡(x−π2)cos⁡(x)+3)2x\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- \frac{x \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} + 3\right)}{2 x} 
       _____________ /         /pi    \\
      /       3      |    x*csc|-- - x||
     /       x       |         \2     /|
    /   ----------- *|3 - -------------|
   /       /pi    \  \        csc(x)   /
  /     csc|-- - x|                     
\/         \2     /                     
----------------------------------------
                  2*x
x3csc⁡(−x+π2)(−xcsc⁡(−x+π2)csc⁡(x)+3)2x\frac{\sqrt{\frac{x^{3}}{\csc{\left(- x + \frac{\pi}{2} \right)}}} \left(- \frac{x \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} + 3\right)}{2 x} 
     ________                               
    /    3    /      3           2  \       
   /    x     |     x         3*x   |       
  /   ------ *|- -------- + --------|*sec(x)
\/    sec(x)  \  2*csc(x)   2*sec(x)/       
--------------------------------------------
                      3                     
                     x
x3sec⁡(x)(−x32csc⁡(x)+3x22sec⁡(x))sec⁡(x)x3\frac{\sqrt{\frac{x^{3}}{\sec{\left(x \right)}}} \left(- \frac{x^{3}}{2 \csc{\left(x \right)}} + \frac{3 x^{2}}{2 \sec{\left(x \right)}}\right) \sec{\left(x \right)}}{x^{3}} 
   ___________ /   3             2       \
  /  3         |  x *sin(x)   3*x *cos(x)|
\/  x *cos(x) *|- --------- + -----------|
               \      2            2     /
------------------------------------------
                 3                        
                x *cos(x)
x3cos⁡(x)(−x3sin⁡(x)2+3x2cos⁡(x)2)x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- \frac{x^{3} \sin{\left(x \right)}}{2} + \frac{3 x^{2} \cos{\left(x \right)}}{2}\right)}{x^{3} \cos{\left(x \right)}} 
        __________________                                                   
       /  3 /       2/x\\                /    3    /x\       2 /       2/x\\\
      /  x *|1 - tan |-||                |   x *tan|-|    3*x *|1 - tan |-|||
     /      \        \2//  /       2/x\\ |         \2/         \        \2//|
    /    ---------------- *|1 + tan |-||*|- ----------- + ------------------|
   /              2/x\     \        \2// |         2/x\      /       2/x\\  |
  /        1 + tan |-|                   |  1 + tan |-|    2*|1 + tan |-||  |
\/                 \2/                   \          \2/      \        \2//  /
-----------------------------------------------------------------------------
                                3 /       2/x\\                              
                               x *|1 - tan |-||                              
                                  \        \2//
x3(1−tan⁡2(x2))tan⁡2(x2)+1(−x3tan⁡(x2)tan⁡2(x2)+1+3x2(1−tan⁡2(x2))2(tan⁡2(x2)+1))(tan⁡2(x2)+1)x3(1−tan⁡2(x2))\frac{\sqrt{\frac{x^{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- \frac{x^{3} \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{3 x^{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{x^{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)} 
 2                      
x *(3*cos(x) - x*sin(x))
------------------------
         ___________    
        /  3            
    2*\/  x *cos(x)
x2(−xsin⁡(x)+3cos⁡(x))2x3cos⁡(x)\frac{x^{2} \left(- x \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)}{2 \sqrt{x^{3} \cos{\left(x \right)}}} 
               /   3    /    pi\              \
   ___________ |  x *cos|x - --|      2       |
  /  3         |        \    2 /   3*x *cos(x)|
\/  x *cos(x) *|- -------------- + -----------|
               \        2               2     /
-----------------------------------------------
                    3                          
                   x *cos(x)
x3cos⁡(x)(−x3cos⁡(x−π2)2+3x2cos⁡(x)2)x3cos⁡(x)\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- \frac{x^{3} \cos{\left(x - \frac{\pi}{2} \right)}}{2} + \frac{3 x^{2} \cos{\left(x \right)}}{2}\right)}{x^{3} \cos{\left(x \right)}} 
       _____________                         
      /       3                              
     /       x       /       3          x   \
    /   ----------- *|- ----------- + ------|
   /       /pi    \  |     /pi    \   csc(x)|
  /     csc|-- - x|  |  csc|-- - x|         |
\/         \2     /  \     \2     /         /
---------------------------------------------
             /   1           1      \        
         2*x*|------- - ------------|        
             |   2/x\      2/pi   x\|        
             |csc |-|   csc |-- - -||        
             \    \2/       \2    2//
x3csc⁡(−x+π2)(xcsc⁡(x)−3csc⁡(−x+π2))2x(−1csc⁡2(−x2+π2)+1csc⁡2(x2))\frac{\sqrt{\frac{x^{3}}{\csc{\left(- x + \frac{\pi}{2} \right)}}} \left(\frac{x}{\csc{\left(x \right)}} - \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)}{2 x \left(- \frac{1}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)} 
   ___________                            
  /  3         /                 /    pi\\
\/  x *cos(x) *|-3*cos(x) + x*cos|x - --||
               \                 \    2 //
------------------------------------------
           /   2/x   pi\      2/x\\       
       2*x*|cos |- - --| - cos |-||       
           \    \2   2 /       \2//
x3cos⁡(x)(xcos⁡(x−π2)−3cos⁡(x))2x(−cos⁡2(x2)+cos⁡2(x2−π2))\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(x \cos{\left(x - \frac{\pi}{2} \right)} - 3 \cos{\left(x \right)}\right)}{2 x \left(- \cos^{2}{\left(\frac{x}{2} \right)} + \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}\right)} 
    ________________                             
   /  3    /    pi\  /       /    pi\           \
  /  x *sin|x + --| *|- 3*sin|x + --| + x*sin(x)|
\/         \    2 /  \       \    2 /           /
-------------------------------------------------
               /   2/x\      2/pi   x\\          
           2*x*|sin |-| - sin |-- + -||          
               \    \2/       \2    2//
x3sin⁡(x+π2)(xsin⁡(x)−3sin⁡(x+π2))2x(sin⁡2(x2)−sin⁡2(x2+π2))\frac{\sqrt{x^{3} \sin{\left(x + \frac{\pi}{2} \right)}} \left(x \sin{\left(x \right)} - 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)}{2 x \left(\sin^{2}{\left(\frac{x}{2} \right)} - \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}\right)} 
       _____________                                         
      /       3      /      3              2    \            
     /       x       |     x            3*x     |    /pi    \
    /   ----------- *|- -------- + -------------|*csc|-- - x|
   /       /pi    \  |  2*csc(x)        /pi    \|    \2     /
  /     csc|-- - x|  |             2*csc|-- - x||            
\/         \2     /  \                  \2     //            
-------------------------------------------------------------
                               3                             
                              x
x3csc⁡(−x+π2)(−x32csc⁡(x)+3x22csc⁡(−x+π2))csc⁡(−x+π2)x3\frac{\sqrt{\frac{x^{3}}{\csc{\left(- x + \frac{\pi}{2} \right)}}} \left(- \frac{x^{3}}{2 \csc{\left(x \right)}} + \frac{3 x^{2}}{2 \csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}{x^{3}} 
        __________________               
       /  3 /       2/x\\                
      /  x *|1 - tan |-||                
     /      \        \2//                
    /    ---------------- *(3 - x*tan(x))
   /              2/x\                   
  /        1 + tan |-|                   
\/                 \2/                   
-----------------------------------------
                   2*x
x3(1−tan⁡2(x2))tan⁡2(x2)+1(−xtan⁡(x)+3)2x\frac{\sqrt{\frac{x^{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- x \tan{\left(x \right)} + 3\right)}{2 x} 
   ___________                       
  /  3                               
\/  x *cos(x) *(-3*cos(x) + x*sin(x))
-------------------------------------
           /   2/x\      2/x\\       
       2*x*|sin |-| - cos |-||       
           \    \2/       \2//
x3cos⁡(x)(xsin⁡(x)−3cos⁡(x))2x(sin⁡2(x2)−cos⁡2(x2))\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)}{2 x \left(\sin^{2}{\left(\frac{x}{2} \right)} - \cos^{2}{\left(\frac{x}{2} \right)}\right)} 
    ________________ /           2   \
   /  3    /    pi\  |    2*x*sin (x)|
  /  x *sin|x + --| *|3 - -----------|
\/         \    2 /  \      sin(2*x) /
--------------------------------------
                 2*x
x3sin⁡(x+π2)(−2xsin⁡2(x)sin⁡(2x)+3)2x\frac{\sqrt{x^{3} \sin{\left(x + \frac{\pi}{2} \right)}} \left(- \frac{2 x \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + 3\right)}{2 x} 
    ___________                 
   /  3                         
-\/  x *cos(x) *(-3 + x*tan(x)) 
--------------------------------
              2*x
−x3cos⁡(x)(xtan⁡(x)−3)2x- \frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(x \tan{\left(x \right)} - 3\right)}{2 x} 
     ________                         
    /    3                            
   /    x     /    3           x     \
  /   ------ *|- ------ + -----------|
\/    sec(x)  |  sec(x)      /    pi\|
              |           sec|x - --||
              \              \    2 //
--------------------------------------
         /     1            1   \     
     2*x*|------------ - -------|     
         |   2/x   pi\      2/x\|     
         |sec |- - --|   sec |-||     
         \    \2   2 /       \2//
x3sec⁡(x)(xsec⁡(x−π2)−3sec⁡(x))2x(1sec⁡2(x2−π2)−1sec⁡2(x2))\frac{\sqrt{\frac{x^{3}}{\sec{\left(x \right)}}} \left(\frac{x}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{3}{\sec{\left(x \right)}}\right)}{2 x \left(\frac{1}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{1}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)} 
     ________                                    
    /    3    /         3             2  \       
   /    x     |        x           3*x   |       
  /   ------ *|- ------------- + --------|*sec(x)
\/    sec(x)  |       /    pi\   2*sec(x)|       
              |  2*sec|x - --|           |       
              \       \    2 /           /       
-------------------------------------------------
                         3                       
                        x
x3sec⁡(x)(−x32sec⁡(x−π2)+3x22sec⁡(x))sec⁡(x)x3\frac{\sqrt{\frac{x^{3}}{\sec{\left(x \right)}}} \left(- \frac{x^{3}}{2 \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{3 x^{2}}{2 \sec{\left(x \right)}}\right) \sec{\left(x \right)}}{x^{3}} 
     ________                  
    /    3                     
   /    x     /      x*sec(x) \
  /   ------ *|3 - -----------|
\/    sec(x)  |       /    pi\|
              |    sec|x - --||
              \       \    2 //
-------------------------------
              2*x
x3sec⁡(x)(−xsec⁡(x)sec⁡(x−π2)+3)2x\frac{\sqrt{\frac{x^{3}}{\sec{\left(x \right)}}} \left(- \frac{x \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + 3\right)}{2 x} 
                     /                 2    /    pi\\
    ________________ |   3          3*x *sin|x + --||
   /  3    /    pi\  |  x *sin(x)           \    2 /|
  /  x *sin|x + --| *|- --------- + ----------------|
\/         \    2 /  \      2              2        /
-----------------------------------------------------
                     3    /    pi\                   
                    x *sin|x + --|                   
                          \    2 /
x3sin⁡(x+π2)(−x3sin⁡(x)2+3x2sin⁡(x+π2)2)x3sin⁡(x+π2)\frac{\sqrt{x^{3} \sin{\left(x + \frac{\pi}{2} \right)}} \left(- \frac{x^{3} \sin{\left(x \right)}}{2} + \frac{3 x^{2} \sin{\left(x + \frac{\pi}{2} \right)}}{2}\right)}{x^{3} \sin{\left(x + \frac{\pi}{2} \right)}} 
        __________________                                  
       /  3 /       2/x\\  /    /       2/x\\           /x\\
      /  x *|1 - tan |-||  |  3*|1 - tan |-||    2*x*tan|-||
     /      \        \2//  |    \        \2//           \2/|
    /    ---------------- *|- --------------- + -----------|
   /              2/x\     |           2/x\            2/x\|
  /        1 + tan |-|     |    1 + tan |-|     1 + tan |-||
\/                 \2/     \            \2/             \2//
------------------------------------------------------------
              /               2                 \           
              |  /       2/x\\           2/x\   |           
              |  |1 - tan |-||      4*tan |-|   |           
              |  \        \4//            \4/   |           
          2*x*|- -------------- + --------------|           
              |               2                2|           
              |  /       2/x\\    /       2/x\\ |           
              |  |1 + tan |-||    |1 + tan |-|| |           
              \  \        \4//    \        \4// /
x3(1−tan⁡2(x2))tan⁡2(x2)+1(2xtan⁡(x2)tan⁡2(x2)+1−3(1−tan⁡2(x2))tan⁡2(x2)+1)2x(−(1−tan⁡2(x4))2(tan⁡2(x4)+1)2+4tan⁡2(x4)(tan⁡2(x4)+1)2)\frac{\sqrt{\frac{x^{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{2 x \left(- \frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right)} 
        ___________________                                   
       /  3 /        2/x\\  /    /        2/x\\           /x\\
      /  x *|-1 + cot |-||  |  3*|-1 + cot |-||    2*x*cot|-||
     /      \         \2//  |    \         \2//           \2/|
    /    ----------------- *|- ---------------- + -----------|
   /               2/x\     |           2/x\             2/x\|
  /         1 + cot |-|     |    1 + cot |-|      1 + cot |-||
\/                  \2/     \            \2/              \2//
--------------------------------------------------------------
               /                2                 \           
               |  /        2/x\\           2/x\   |           
               |  |-1 + cot |-||      4*cot |-|   |           
               |  \         \4//            \4/   |           
           2*x*|- --------------- + --------------|           
               |                2                2|           
               |   /       2/x\\    /       2/x\\ |           
               |   |1 + cot |-||    |1 + cot |-|| |           
               \   \        \4//    \        \4// /
x3(cot⁡2(x2)−1)cot⁡2(x2)+1(2xcot⁡(x2)cot⁡2(x2)+1−3(cot⁡2(x2)−1)cot⁡2(x2)+1)2x(−(cot⁡2(x4)−1)2(cot⁡2(x4)+1)2+4cot⁡2(x4)(cot⁡2(x4)+1)2)\frac{\sqrt{\frac{x^{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\frac{2 x \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{2 x \left(- \frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right)} 
   ___________               
  /  3                       
\/  x *cos(x) *(3 - x*tan(x))
-----------------------------
             2*x
x3cos⁡(x)(−xtan⁡(x)+3)2x\frac{\sqrt{x^{3} \cos{\left(x \right)}} \left(- x \tan{\left(x \right)} + 3\right)}{2 x} 
        ___________________             
       /  3 /        2/x\\              
      /  x *|-1 + cot |-||              
     /      \         \2//  /      x   \
    /    ----------------- *|3 - ------|
   /               2/x\     \    cot(x)/
  /         1 + cot |-|                 
\/                  \2/                 
----------------------------------------
                  2*x
x3(cot⁡2(x2)−1)cot⁡2(x2)+1(−xcot⁡(x)+3)2x\frac{\sqrt{\frac{x^{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- \frac{x}{\cot{\left(x \right)}} + 3\right)}{2 x} 
sqrt(x^3*(-1 + cot(x/2)^2)/(1 + cot(x/2)^2))*(3 - x/cot(x))/(2*x)
    © Sr Examen – Калькулятор