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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)

¿Cómo vas a descomponer esta tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   4/x\                                
tan |-|                                
    \2/     ___    3/x\ /         2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
    ___             \2/ \          \2//
2*\/ x
xtan⁡3(x2)(2tan⁡2(x2)+2)+tan⁡4(x2)2x\sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^4/((2*sqrt(x))) + (sqrt(x)*tan(x/2)^3)*(2 + 2*tan(x/2)^2)
Simplificación general [src] 
   3/x\ /   8*x          /x\\
tan |-|*|---------- + tan|-||
    \2/ \1 + cos(x)      \2//
-----------------------------
               ___           
           2*\/ x
(8xcos⁡(x)+1+tan⁡(x2))tan⁡3(x2)2x\frac{\left(\frac{8 x}{\cos{\left(x \right)} + 1} + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^3*(8*x/(1 + cos(x)) + tan(x/2))/(2*sqrt(x))
Respuesta numérica [src] 
0.5*x^(-0.5)*tan(x/2)^4 + x^0.5*tan(x/2)^3*(2.0 + 2.0*tan(x/2)^2)
0.5*x^(-0.5)*tan(x/2)^4 + x^0.5*tan(x/2)^3*(2.0 + 2.0*tan(x/2)^2)
Denominador común [src] 
   4/x\          3/x\          5/x\
tan |-| + 4*x*tan |-| + 4*x*tan |-|
    \2/           \2/           \2/
-----------------------------------
                  ___              
              2*\/ x
4xtan⁡5(x2)+4xtan⁡3(x2)+tan⁡4(x2)2x\frac{4 x \tan^{5}{\left(\frac{x}{2} \right)} + 4 x \tan^{3}{\left(\frac{x}{2} \right)} + \tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
(tan(x/2)^4 + 4*x*tan(x/2)^3 + 4*x*tan(x/2)^5)/(2*sqrt(x))
Combinatoria [src] 
   3/x\ /             2/x\      /x\\
tan |-|*|4*x + 4*x*tan |-| + tan|-||
    \2/ \              \2/      \2//
------------------------------------
                  ___               
              2*\/ x
(4xtan⁡2(x2)+4x+tan⁡(x2))tan⁡3(x2)2x\frac{\left(4 x \tan^{2}{\left(\frac{x}{2} \right)} + 4 x + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^3*(4*x + 4*x*tan(x/2)^2 + tan(x/2))/(2*sqrt(x))
Abrimos la expresión [src] 
   4/x\                                    
tan |-|                                    
    \2/       ___    3/x\       ___    5/x\
------- + 2*\/ x *tan |-| + 2*\/ x *tan |-|
    ___               \2/               \2/
2*\/ x
2xtan⁡5(x2)+2xtan⁡3(x2)+tan⁡4(x2)2x2 \sqrt{x} \tan^{5}{\left(\frac{x}{2} \right)} + 2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^4/(2*sqrt(x)) + 2*sqrt(x)*tan(x/2)^3 + 2*sqrt(x)*tan(x/2)^5
Potencias [src] 
                                                      /                       2\
                                                    3 |      /   I*x    -I*x \ |
                                   /   I*x    -I*x \  |      |   ---    -----| |
                                   |   ---    -----|  |      |    2       2  | |
                               ___ |    2       2  |  |    2*\- e    + e     / |
                           I*\/ x *\- e    + e     / *|2 - --------------------|
                    4                                 |                     2  |
   /   I*x    -I*x \                                  |      / I*x    -I*x \   |
   |   ---    -----|                                  |      | ---    -----|   |
   |    2       2  |                                  |      |  2       2  |   |
   \- e    + e     /                                  \      \e    + e     /   /
------------------------ - -----------------------------------------------------
                       4                                     3                  
        / I*x    -I*x \                       / I*x    -I*x \                   
        | ---    -----|                       | ---    -----|                   
    ___ |  2       2  |                       |  2       2  |                   
2*\/ x *\e    + e     /                       \e    + e     /
−ix(−2(−eix2+e−ix2)2(eix2+e−ix2)2+2)(−eix2+e−ix2)3(eix2+e−ix2)3+(−eix2+e−ix2)42x(eix2+e−ix2)4- \frac{i \sqrt{x} \left(- \frac{2 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 2\right) \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3}} + \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{2 \sqrt{x} \left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} 
   4/x\                                
tan |-|                                
    \2/     ___    3/x\ /         2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
    ___             \2/ \          \2//
2*\/ x
x(2tan⁡2(x2)+2)tan⁡3(x2)+tan⁡4(x2)2x\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^4/(2*sqrt(x)) + sqrt(x)*tan(x/2)^3*(2 + 2*tan(x/2)^2)
Unión de expresiones racionales [src] 
   3/x\ /    /       2/x\\      /x\\
tan |-|*|4*x*|1 + tan |-|| + tan|-||
    \2/ \    \        \2//      \2//
------------------------------------
                  ___               
              2*\/ x
(4x(tan⁡2(x2)+1)+tan⁡(x2))tan⁡3(x2)2x\frac{\left(4 x \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) + \tan{\left(\frac{x}{2} \right)}\right) \tan^{3}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^3*(4*x*(1 + tan(x/2)^2) + tan(x/2))/(2*sqrt(x))
Parte trigonométrica [src] 
   4/x\                          
tan |-|                          
    \2/       ___    5/x\    3/x\
------- + 2*\/ x *sec |-|*sin |-|
    ___               \2/     \2/
2*\/ x
2xsin⁡3(x2)sec⁡5(x2)+tan⁡4(x2)2x2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)} \sec^{5}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                    ___ /       2   \
                  \/ x *|2 + -------|
                        |       2/x\|
                        |    cot |-||
       1                \        \2//
--------------- + -------------------
    ___    4/x\            3/x\      
2*\/ x *cot |-|         cot |-|      
            \2/             \2/
x(2+2cot⁡2(x2))cot⁡3(x2)+12xcot⁡4(x2)\frac{\sqrt{x} \left(2 + \frac{2}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)}{\cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}} 
                                2        
   4/x\        ___ /       2/x\\     3/x\
tan |-|   16*\/ x *|1 + tan |-|| *tan |-|
    \2/            \        \4//      \4/
------- + -------------------------------
    ___                         5        
2*\/ x             /       2/x\\         
                   |1 - tan |-||         
                   \        \4//
16x(tan⁡2(x4)+1)2tan⁡3(x4)(1−tan⁡2(x4))5+tan⁡4(x2)2x\frac{16 \sqrt{x} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan^{3}{\left(\frac{x}{4} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{5}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                               ___          
       1                   4*\/ x           
--------------- + --------------------------
    ___    4/x\   /            2/x\\        
2*\/ x *cot |-|   |    -1 + cot |-||        
            \2/   |             \2/|    3/x\
                  |1 + ------------|*cot |-|
                  |           2/x\ |     \2/
                  |    1 + cot |-| |        
                  \            \2/ /
4x(cot⁡2(x2)−1cot⁡2(x2)+1+1)cot⁡3(x2)+12xcot⁡4(x2)\frac{4 \sqrt{x}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}} 
   4/x\           ___    3/x\   
tan |-|      16*\/ x *tan |-|   
    \2/                   \4/   
------- + ----------------------
    ___                5        
2*\/ x    /       2/x\\     4/x\
          |1 - tan |-|| *cos |-|
          \        \4//      \4/
16xtan⁡3(x4)(1−tan⁡2(x4))5cos⁡4(x4)+tan⁡4(x2)2x\frac{16 \sqrt{x} \tan^{3}{\left(\frac{x}{4} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{5} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                                     /         2/x   pi\\
                                     |    2*cos |- - --||
                    ___    3/x   pi\ |          \2   2 /|
                  \/ x *cos |- - --|*|2 + --------------|
     4/x   pi\              \2   2 / |          2/x\    |
  cos |- - --|                       |       cos |-|    |
      \2   2 /                       \           \2/    /
--------------- + ---------------------------------------
    ___    4/x\                      3/x\                
2*\/ x *cos |-|                   cos |-|                
            \2/                       \2/
x(2+2cos⁡2(x2−π2)cos⁡2(x2))cos⁡3(x2−π2)cos⁡3(x2)+cos⁡4(x2−π2)2xcos⁡4(x2)\frac{\sqrt{x} \left(2 + \frac{2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}} 
     4/pi   x\        ___    5/pi   x\
  csc |-- - -|    2*\/ x *csc |-- - -|
      \2    2/                \2    2/
--------------- + --------------------
    ___    4/x\            3/x\       
2*\/ x *csc |-|         csc |-|       
            \2/             \2/
2xcsc⁡5(−x2+π2)csc⁡3(x2)+csc⁡4(−x2+π2)2xcsc⁡4(x2)\frac{2 \sqrt{x} \csc^{5}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}} 
                                        2
                       ___ /       2/x\\ 
                   2*\/ x *|1 + cot |-|| 
       1                   \        \4// 
--------------- + -----------------------
    ___    4/x\                 2        
2*\/ x *cot |-|   /        2/x\\     3/x\
            \2/   |-1 + cot |-|| *cot |-|
                  \         \4//      \2/
2x(cot⁡2(x4)+1)2(cot⁡2(x4)−1)2cot⁡3(x2)+12xcot⁡4(x2)\frac{2 \sqrt{x} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \cot^{3}{\left(\frac{x}{2} \right)}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}} 
       8/x\               ___    6/x\    
  8*sin |-|          32*\/ x *sin |-|    
        \2/                       \2/    
------------- + -------------------------
  ___    4      /       /    pi\\    3   
\/ x *sin (x)   |1 + sin|x + --||*sin (x)
                \       \    2 //
32xsin⁡6(x2)(sin⁡(x+π2)+1)sin⁡3(x)+8sin⁡8(x2)xsin⁡4(x)\frac{32 \sqrt{x} \sin^{6}{\left(\frac{x}{2} \right)}}{\left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right) \sin^{3}{\left(x \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}} 
   4/x\       ___    3/x\
tan |-|   2*\/ x *sin |-|
    \2/               \2/
------- + ---------------
    ___          5/x\    
2*\/ x        cos |-|    
                  \2/
2xsin⁡3(x2)cos⁡5(x2)+tan⁡4(x2)2x\frac{2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)}}{\cos^{5}{\left(\frac{x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                               2        
   4/x\       ___ /       2/x\\     3/x\
tan |-|   2*\/ x *|1 + tan |-|| *tan |-|
    \2/           \        \4//      \2/
------- + ------------------------------
    ___                        2        
2*\/ x            /       2/x\\         
                  |1 - tan |-||         
                  \        \4//
2x(tan⁡2(x4)+1)2tan⁡3(x2)(1−tan⁡2(x4))2+tan⁡4(x2)2x\frac{2 \sqrt{x} \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
     4/x   pi\        ___    3/x   pi\
  cos |- - --|    4*\/ x *cos |- - --|
      \2   2 /                \2   2 /
--------------- + --------------------
    ___    4/x\                   3/x\
2*\/ x *cos |-|   (1 + cos(x))*cos |-|
            \2/                    \2/
4xcos⁡3(x2−π2)(cos⁡(x)+1)cos⁡3(x2)+cos⁡4(x2−π2)2xcos⁡4(x2)\frac{4 \sqrt{x} \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(\cos{\left(x \right)} + 1\right) \cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}} 
         4/x\              ___    5/x\
      sec |-|          2*\/ x *sec |-|
          \2/                      \2/
-------------------- + ---------------
    ___    4/x   pi\        3/x   pi\ 
2*\/ x *sec |- - --|     sec |- - --| 
            \2   2 /         \2   2 /
2xsec⁡5(x2)sec⁡3(x2−π2)+sec⁡4(x2)2xsec⁡4(x2−π2)\frac{2 \sqrt{x} \sec^{5}{\left(\frac{x}{2} \right)}}{\sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
   4/x\       ___    3/x\
tan |-|   2*\/ x *tan |-|
    \2/               \2/
------- + ---------------
    ___          2/x\    
2*\/ x        cos |-|    
                  \2/
2xtan⁡3(x2)cos⁡2(x2)+tan⁡4(x2)2x\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
   4/x\       ___    3/x\
tan |-|   4*\/ x *tan |-|
    \2/               \2/
------- + ---------------
    ___      1 + cos(x)  
2*\/ x
4xtan⁡3(x2)cos⁡(x)+1+tan⁡4(x2)2x\frac{4 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\cos{\left(x \right)} + 1} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
   4/x\            ___    3/x\   
tan |-|       16*\/ x *cot |-|   
    \2/                    \4/   
------- + -----------------------
    ___                 5        
2*\/ x    /        2/x\\     4/x\
          |-1 + cot |-|| *sin |-|
          \         \4//      \4/
16xcot⁡3(x4)(cot⁡2(x4)−1)5sin⁡4(x4)+tan⁡4(x2)2x\frac{16 \sqrt{x} \cot^{3}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{5} \sin^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                                /         2/x\\
                                |    2*sin |-||
                    ___    3/x\ |          \2/|
                  \/ x *sin |-|*|2 + ---------|
       4/x\                 \2/ |        2/x\ |
    sin |-|                     |     cos |-| |
        \2/                     \         \2/ /
--------------- + -----------------------------
    ___    4/x\                 3/x\           
2*\/ x *cos |-|              cos |-|           
            \2/                  \2/
x(2sin⁡2(x2)cos⁡2(x2)+2)sin⁡3(x2)cos⁡3(x2)+sin⁡4(x2)2xcos⁡4(x2)\frac{\sqrt{x} \left(\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}} + 2\right) \sin^{3}{\left(\frac{x}{2} \right)}}{\cos^{3}{\left(\frac{x}{2} \right)}} + \frac{\sin^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}} 
                                        2        
                       ___ /       2/x\\     3/x\
                  16*\/ x *|1 + cot |-|| *cot |-|
       1                   \        \4//      \4/
--------------- + -------------------------------
    ___    4/x\                         5        
2*\/ x *cot |-|           /        2/x\\         
            \2/           |-1 + cot |-||         
                          \         \4//
16x(cot⁡2(x4)+1)2cot⁡3(x4)(cot⁡2(x4)−1)5+12xcot⁡4(x2)\frac{16 \sqrt{x} \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot^{3}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{5}} + \frac{1}{2 \sqrt{x} \cot^{4}{\left(\frac{x}{2} \right)}} 
         4/x\                   ___    3/x\     
      sec |-|               4*\/ x *sec |-|     
          \2/                           \2/     
-------------------- + -------------------------
    ___    4/x   pi\   /      1   \    3/x   pi\
2*\/ x *sec |- - --|   |1 + ------|*sec |- - --|
            \2   2 /   \    sec(x)/     \2   2 /
4xsec⁡3(x2)(1+1sec⁡(x))sec⁡3(x2−π2)+sec⁡4(x2)2xsec⁡4(x2−π2)\frac{4 \sqrt{x} \sec^{3}{\left(\frac{x}{2} \right)}}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
                                     /          2/x\  \
                                     |     2*sec |-|  |
                         ___    3/x\ |           \2/  |
                       \/ x *sec |-|*|2 + ------------|
         4/x\                    \2/ |       2/x   pi\|
      sec |-|                        |    sec |- - --||
          \2/                        \        \2   2 //
-------------------- + --------------------------------
    ___    4/x   pi\                3/x   pi\          
2*\/ x *sec |- - --|             sec |- - --|          
            \2   2 /                 \2   2 /
x(2sec⁡2(x2)sec⁡2(x2−π2)+2)sec⁡3(x2)sec⁡3(x2−π2)+sec⁡4(x2)2xsec⁡4(x2−π2)\frac{\sqrt{x} \left(\frac{2 \sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 2\right) \sec^{3}{\left(\frac{x}{2} \right)}}{\sec^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
       8/x\            ___    6/x\  
  8*sin |-|       16*\/ x *sin |-|  
        \2/                    \2/  
------------- + --------------------
  ___    4         3       2/pi   x\
\/ x *sin (x)   sin (x)*sin |-- + -|
                            \2    2/
16xsin⁡6(x2)sin⁡3(x)sin⁡2(x2+π2)+8sin⁡8(x2)xsin⁡4(x)\frac{16 \sqrt{x} \sin^{6}{\left(\frac{x}{2} \right)}}{\sin^{3}{\left(x \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}} 
                                /         4/x\\
                                |    8*sin |-||
                    ___    6/x\ |          \2/|
       8/x\     8*\/ x *sin |-|*|2 + ---------|
  8*sin |-|                 \2/ |        2    |
        \2/                     \     sin (x) /
------------- + -------------------------------
  ___    4                     3               
\/ x *sin (x)               sin (x)
8x(8sin⁡4(x2)sin⁡2(x)+2)sin⁡6(x2)sin⁡3(x)+8sin⁡8(x2)xsin⁡4(x)\frac{8 \sqrt{x} \left(\frac{8 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 2\right) \sin^{6}{\left(\frac{x}{2} \right)}}{\sin^{3}{\left(x \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}} 
    ___    3/x\          8/x\  
2*\/ x *sin |-|     8*sin |-|  
            \2/           \2/  
--------------- + -------------
     5/pi   x\      ___    4   
  sin |-- + -|    \/ x *sin (x)
      \2    2/
2xsin⁡3(x2)sin⁡5(x2+π2)+8sin⁡8(x2)xsin⁡4(x)\frac{2 \sqrt{x} \sin^{3}{\left(\frac{x}{2} \right)}}{\sin^{5}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{8 \sin^{8}{\left(\frac{x}{2} \right)}}{\sqrt{x} \sin^{4}{\left(x \right)}} 
                                /         2/x\\
                                |    2*sec |-||
                    ___    3/x\ |          \2/|
                  \/ x *sec |-|*|2 + ---------|
       4/x\                 \2/ |        2/x\ |
    sec |-|                     |     csc |-| |
        \2/                     \         \2/ /
--------------- + -----------------------------
    ___    4/x\                 3/x\           
2*\/ x *csc |-|              csc |-|           
            \2/                  \2/
x(2+2sec⁡2(x2)csc⁡2(x2))sec⁡3(x2)csc⁡3(x2)+sec⁡4(x2)2xcsc⁡4(x2)\frac{\sqrt{x} \left(2 + \frac{2 \sec^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \sec^{3}{\left(\frac{x}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\sec^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}} 
   4/x\       ___    3/x\
tan |-|   4*\/ x *tan |-|
    \2/               \2/
------- + ---------------
    ___              2/x\
2*\/ x        1 - tan |-|
                      \2/
          1 + -----------
                     2/x\
              1 + tan |-|
                      \2/
4xtan⁡3(x2)1−tan⁡2(x2)tan⁡2(x2)+1+1+tan⁡4(x2)2x\frac{4 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
                                     /         2/pi   x\\
                                     |    2*csc |-- - -||
                    ___    3/pi   x\ |          \2    2/|
                  \/ x *csc |-- - -|*|2 + --------------|
     4/pi   x\              \2    2/ |          2/x\    |
  csc |-- - -|                       |       csc |-|    |
      \2    2/                       \           \2/    /
--------------- + ---------------------------------------
    ___    4/x\                      3/x\                
2*\/ x *csc |-|                   csc |-|                
            \2/                       \2/
x(2+2csc⁡2(−x2+π2)csc⁡2(x2))csc⁡3(−x2+π2)csc⁡3(x2)+csc⁡4(−x2+π2)2xcsc⁡4(x2)\frac{\sqrt{x} \left(2 + \frac{2 \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc^{3}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}} 
     4/x   pi\        ___    3/x   pi\
  cos |- - --|    2*\/ x *cos |- - --|
      \2   2 /                \2   2 /
--------------- + --------------------
    ___    4/x\            5/x\       
2*\/ x *cos |-|         cos |-|       
            \2/             \2/
2xcos⁡3(x2−π2)cos⁡5(x2)+cos⁡4(x2−π2)2xcos⁡4(x2)\frac{2 \sqrt{x} \cos^{3}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{5}{\left(\frac{x}{2} \right)}} + \frac{\cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{x} \cos^{4}{\left(\frac{x}{2} \right)}} 
   4/x\           ___    3/x\    
tan |-|       2*\/ x *tan |-|    
    \2/                   \2/    
------- + -----------------------
    ___                 2        
2*\/ x    /        2/x\\     4/x\
          |-1 + cot |-|| *sin |-|
          \         \4//      \4/
2xtan⁡3(x2)(cot⁡2(x4)−1)2sin⁡4(x4)+tan⁡4(x2)2x\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
     4/pi   x\           ___    3/pi   x\  
  csc |-- - -|       4*\/ x *csc |-- - -|  
      \2    2/                   \2    2/  
--------------- + -------------------------
    ___    4/x\   /         1     \    3/x\
2*\/ x *csc |-|   |1 + -----------|*csc |-|
            \2/   |       /pi    \|     \2/
                  |    csc|-- - x||        
                  \       \2     //
4xcsc⁡3(−x2+π2)(1+1csc⁡(−x+π2))csc⁡3(x2)+csc⁡4(−x2+π2)2xcsc⁡4(x2)\frac{4 \sqrt{x} \csc^{3}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc^{3}{\left(\frac{x}{2} \right)}} + \frac{\csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{2 \sqrt{x} \csc^{4}{\left(\frac{x}{2} \right)}} 
   4/x\                                
tan |-|                                
    \2/     ___    3/x\ /         2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
    ___             \2/ \          \2//
2*\/ x
x(2tan⁡2(x2)+2)tan⁡3(x2)+tan⁡4(x2)2x\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
   4/x\          ___    3/x\    
tan |-|      2*\/ x *tan |-|    
    \2/                  \2/    
------- + ----------------------
    ___                2        
2*\/ x    /       2/x\\     4/x\
          |1 - tan |-|| *cos |-|
          \        \4//      \4/
2xtan⁡3(x2)(1−tan⁡2(x4))2cos⁡4(x4)+tan⁡4(x2)2x\frac{2 \sqrt{x} \tan^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \cos^{4}{\left(\frac{x}{4} \right)}} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^4/(2*sqrt(x)) + 2*sqrt(x)*tan(x/2)^3/((1 - tan(x/4)^2)^2*cos(x/4)^4)
Compilar la expresión [src] 
   4/x\                                
tan |-|                                
    \2/     ___    3/x\ /         2/x\\
------- + \/ x *tan |-|*|2 + 2*tan |-||
    ___             \2/ \          \2//
2*\/ x
x(2tan⁡2(x2)+2)tan⁡3(x2)+tan⁡4(x2)2x\sqrt{x} \left(2 \tan^{2}{\left(\frac{x}{2} \right)} + 2\right) \tan^{3}{\left(\frac{x}{2} \right)} + \frac{\tan^{4}{\left(\frac{x}{2} \right)}}{2 \sqrt{x}} 
tan(x/2)^4/(2*sqrt(x)) + sqrt(x)*tan(x/2)^3*(2 + 2*tan(x/2)^2)
Denominador racional [src] 
  ___    4/x\      3/2    3/x\      3/2    5/x\
\/ x *tan |-| + 4*x   *tan |-| + 4*x   *tan |-|
          \2/              \2/              \2/
-----------------------------------------------
                      2*x
4x32tan⁡5(x2)+4x32tan⁡3(x2)+xtan⁡4(x2)2x\frac{4 x^{\frac{3}{2}} \tan^{5}{\left(\frac{x}{2} \right)} + 4 x^{\frac{3}{2}} \tan^{3}{\left(\frac{x}{2} \right)} + \sqrt{x} \tan^{4}{\left(\frac{x}{2} \right)}}{2 x} 
(sqrt(x)*tan(x/2)^4 + 4*x^(3/2)*tan(x/2)^3 + 4*x^(3/2)*tan(x/2)^5)/(2*x)
    © Sr Examen – Калькулятор