Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ (-sin(x)/cos(2*x)^(1/4)+cos(x)*sin(2*x)/(2*cos(2*x)^(5/4)))/(1+cos(x)^2/sqrt(cos(2*x)))

¿Cómo vas a descomponer esta (-sin(x)/cos(2*x)^(1/4)+cos(x)*sin(2*x)/(2*cos(2*x)^(5/4)))/(1+cos(x)^2/sqrt(cos(2*x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  -sin(x)      cos(x)*sin(2*x)
------------ + ---------------
4 __________         5/4      
\/ cos(2*x)     2*cos   (2*x) 
------------------------------
                2             
             cos (x)          
       1 + ------------       
             __________       
           \/ cos(2*x)
sin⁡(2x)cos⁡(x)2cos⁡54(2x)+(−1)sin⁡(x)cos⁡(2x)4cos⁡2(x)cos⁡(2x)+1\frac{\frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}} + \frac{\left(-1\right) \sin{\left(x \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
((-sin(x))/cos(2*x)^(1/4) + (cos(x)*sin(2*x))/((2*cos(2*x)^(5/4))))/(1 + cos(x)^2/sqrt(cos(2*x)))
Simplificación general [src] 
                 3                  
              sin (x)               
------------------------------------
/   2        __________\    3/4     
\cos (x) + \/ cos(2*x) /*cos   (2*x)
sin⁡3(x)(cos⁡2(x)+cos⁡(2x))cos⁡34(2x)\frac{\sin^{3}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + \sqrt{\cos{\left(2 x \right)}}\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
sin(x)^3/((cos(x)^2 + sqrt(cos(2*x)))*cos(2*x)^(3/4))
Potencias [src] 
                              / I*x    -I*x\                     
                              |e      e    | /   -2*I*x    2*I*x\
      /   -I*x    I*x\      I*|---- + -----|*\- e       + e     /
    I*\- e     + e   /        \ 2       2  /                     
------------------------- - -------------------------------------
       __________________                              5/4       
      /  -2*I*x    2*I*x             / -2*I*x    2*I*x\          
     /  e         e                  |e         e     |          
2*4 /   ------- + ------           4*|------- + ------|          
  \/       2        2                \   2        2   /          
-----------------------------------------------------------------
                                         2                       
                           / I*x    -I*x\                        
                           |e      e    |                        
                           |---- + -----|                        
                           \ 2       2  /                        
                   1 + -----------------------                   
                            __________________                   
                           /  -2*I*x    2*I*x                    
                          /  e         e                         
                         /   ------- + ------                    
                       \/       2        2
−i(eix2+e−ix2)(e2ix−e−2ix)4(e2ix2+e−2ix2)54+i(eix−e−ix)2e2ix2+e−2ix24(eix2+e−ix2)2e2ix2+e−2ix2+1\frac{- \frac{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{2 i x} - e^{- 2 i x}\right)}{4 \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)^{\frac{5}{4}}} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \sqrt[4]{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}}}}{\frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\sqrt{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}}} + 1} 
     sin(x)      cos(x)*sin(2*x)
- ------------ + ---------------
  4 __________         5/4      
  \/ cos(2*x)     2*cos   (2*x) 
--------------------------------
                 2              
              cos (x)           
        1 + ------------        
              __________        
            \/ cos(2*x)
−sin⁡(x)cos⁡(2x)4+sin⁡(2x)cos⁡(x)2cos⁡54(2x)cos⁡2(x)cos⁡(2x)+1\frac{- \frac{\sin{\left(x \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
(-sin(x)/cos(2*x)^(1/4) + cos(x)*sin(2*x)/(2*cos(2*x)^(5/4)))/(1 + cos(x)^2/sqrt(cos(2*x)))
Combinatoria [src] 
-(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x)) 
----------------------------------------
   /   2        __________\    3/4      
 2*\cos (x) + \/ cos(2*x) /*cos   (2*x)
−2sin⁡(x)cos⁡(2x)−sin⁡(2x)cos⁡(x)2(cos⁡2(x)+cos⁡(2x))cos⁡34(2x)- \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \left(\cos^{2}{\left(x \right)} + \sqrt{\cos{\left(2 x \right)}}\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
-(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x))/(2*(cos(x)^2 + sqrt(cos(2*x)))*cos(2*x)^(3/4))
Denominador común [src] 
-(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x)) 
----------------------------------------
      5/4             2       3/4       
 2*cos   (2*x) + 2*cos (x)*cos   (2*x)
−2sin⁡(x)cos⁡(2x)−sin⁡(2x)cos⁡(x)2cos⁡2(x)cos⁡34(2x)+2cos⁡54(2x)- \frac{2 \sin{\left(x \right)} \cos{\left(2 x \right)} - \sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \cos^{\frac{3}{4}}{\left(2 x \right)} + 2 \cos^{\frac{5}{4}}{\left(2 x \right)}} 
-(-cos(x)*sin(2*x) + 2*cos(2*x)*sin(x))/(2*cos(2*x)^(5/4) + 2*cos(x)^2*cos(2*x)^(3/4))
Denominador racional [src] 
     7/4                  3    4 __________               3/4                             2       5/4            
2*cos   (2*x)*sin(x) + cos (x)*\/ cos(2*x) *sin(2*x) - cos   (2*x)*cos(x)*sin(2*x) - 2*cos (x)*cos   (2*x)*sin(x)
-----------------------------------------------------------------------------------------------------------------
                                           /   4              \                                                  
                                         2*\cos (x) - cos(2*x)/*cos(2*x)
−2sin⁡(x)cos⁡2(x)cos⁡54(2x)+2sin⁡(x)cos⁡74(2x)+sin⁡(2x)cos⁡3(x)cos⁡(2x)4−sin⁡(2x)cos⁡(x)cos⁡34(2x)2(cos⁡4(x)−cos⁡(2x))cos⁡(2x)\frac{- 2 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \cos^{\frac{5}{4}}{\left(2 x \right)} + 2 \sin{\left(x \right)} \cos^{\frac{7}{4}}{\left(2 x \right)} + \sin{\left(2 x \right)} \cos^{3}{\left(x \right)} \sqrt[4]{\cos{\left(2 x \right)}} - \sin{\left(2 x \right)} \cos{\left(x \right)} \cos^{\frac{3}{4}}{\left(2 x \right)}}{2 \left(\cos^{4}{\left(x \right)} - \cos{\left(2 x \right)}\right) \cos{\left(2 x \right)}} 
(2*cos(2*x)^(7/4)*sin(x) + cos(x)^3*cos(2*x)^(1/4)*sin(2*x) - cos(2*x)^(3/4)*cos(x)*sin(2*x) - 2*cos(x)^2*cos(2*x)^(5/4)*sin(x))/(2*(cos(x)^4 - cos(2*x))*cos(2*x))
Unión de expresiones racionales [src] 
 cos(x)*sin(2*x) - 2*cos(2*x)*sin(x)  
--------------------------------------
  /   2        __________\    3/4     
2*\cos (x) + \/ cos(2*x) /*cos   (2*x)
−2sin⁡(x)cos⁡(2x)+sin⁡(2x)cos⁡(x)2(cos⁡2(x)+cos⁡(2x))cos⁡34(2x)\frac{- 2 \sin{\left(x \right)} \cos{\left(2 x \right)} + \sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \left(\cos^{2}{\left(x \right)} + \sqrt{\cos{\left(2 x \right)}}\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
(cos(x)*sin(2*x) - 2*cos(2*x)*sin(x))/(2*(cos(x)^2 + sqrt(cos(2*x)))*cos(2*x)^(3/4))
Abrimos la expresión [src] 
  -sin(x)      cos(x)*sin(2*x)
------------ + ---------------
4 __________         5/4      
\/ cos(2*x)     2*cos   (2*x) 
------------------------------
                2             
             cos (x)          
       1 + ------------       
             __________       
           \/ cos(2*x)
(−1)sin⁡(x)cos⁡(2x)4+sin⁡(2x)cos⁡(x)2cos⁡54(2x)cos⁡2(x)cos⁡(2x)+1\frac{\frac{\left(-1\right) \sin{\left(x \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
                                                                                           2                                                   
                    sin(x)                                                              cos (x)*sin(x)                                         
- ----------------------------------------- + -------------------------------------------------------------------------------------------------
     ________________            2                 ________________            2                      4                ________________        
  4 /           2             cos (x)           4 /           2             cos (x)              2*cos (x)          4 /           2        2   
  \/  -1 + 2*cos (x)  + -------------------   - \/  -1 + 2*cos (x)  - ------------------- + ------------------- + 2*\/  -1 + 2*cos (x) *cos (x)
                           ________________                              ________________      ________________                                
                        4 /           2                               4 /           2       4 /           2                                    
                        \/  -1 + 2*cos (x)                            \/  -1 + 2*cos (x)    \/  -1 + 2*cos (x)
sin⁡(x)cos⁡2(x)22cos⁡2(x)−14cos⁡2(x)−2cos⁡2(x)−14+2cos⁡4(x)2cos⁡2(x)−14−cos⁡2(x)2cos⁡2(x)−14−sin⁡(x)2cos⁡2(x)−14+cos⁡2(x)2cos⁡2(x)−14\frac{\sin{\left(x \right)} \cos^{2}{\left(x \right)}}{2 \sqrt[4]{2 \cos^{2}{\left(x \right)} - 1} \cos^{2}{\left(x \right)} - \sqrt[4]{2 \cos^{2}{\left(x \right)} - 1} + \frac{2 \cos^{4}{\left(x \right)}}{\sqrt[4]{2 \cos^{2}{\left(x \right)} - 1}} - \frac{\cos^{2}{\left(x \right)}}{\sqrt[4]{2 \cos^{2}{\left(x \right)} - 1}}} - \frac{\sin{\left(x \right)}}{\sqrt[4]{2 \cos^{2}{\left(x \right)} - 1} + \frac{\cos^{2}{\left(x \right)}}{\sqrt[4]{2 \cos^{2}{\left(x \right)} - 1}}} 
-sin(x)/((-1 + 2*cos(x)^2)^(1/4) + cos(x)^2/(-1 + 2*cos(x)^2)^(1/4)) + cos(x)^2*sin(x)/(-(-1 + 2*cos(x)^2)^(1/4) - cos(x)^2/(-1 + 2*cos(x)^2)^(1/4) + 2*cos(x)^4/(-1 + 2*cos(x)^2)^(1/4) + 2*(-1 + 2*cos(x)^2)^(1/4)*cos(x)^2)
Compilar la expresión [src] 
     sin(x)      cos(x)*sin(2*x)
- ------------ + ---------------
  4 __________         5/4      
  \/ cos(2*x)     2*cos   (2*x) 
--------------------------------
                 2              
              cos (x)           
        1 + ------------        
              __________        
            \/ cos(2*x)
−sin⁡(x)cos⁡(2x)4+sin⁡(2x)cos⁡(x)2cos⁡54(2x)cos⁡2(x)cos⁡(2x)+1\frac{- \frac{\sin{\left(x \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
(-sin(x)/cos(2*x)^(1/4) + cos(x)*sin(2*x)/(2*cos(2*x)^(5/4)))/(1 + cos(x)^2/sqrt(cos(2*x)))
Respuesta numérica [src] 
(-cos(2*x)^(-0.25)*sin(x) + 0.5*cos(2*x)^(-1.25)*cos(x)*sin(2*x))/(1.0 + cos(x)^2*cos(2*x)^(-0.5))
(-cos(2*x)^(-0.25)*sin(x) + 0.5*cos(2*x)^(-1.25)*cos(x)*sin(2*x))/(1.0 + cos(x)^2*cos(2*x)^(-0.5))
Parte trigonométrica [src] 
                  3                  
               sin (x)               
-------------------------------------
               5/4 /         2      \
/         2   \    |      cos (x)   |
\1 - 2*sin (x)/   *|1 + ------------|
                   |      __________|
                   \    \/ cos(2*x) /
sin⁡3(x)(1−2sin⁡2(x))54(cos⁡2(x)cos⁡(2x)+1)\frac{\sin^{3}{\left(x \right)}}{\left(1 - 2 \sin^{2}{\left(x \right)}\right)^{\frac{5}{4}} \left(\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1\right)} 
              3               
           sin (x)            
------------------------------
/         2      \            
|      cos (x)   |    5/4     
|1 + ------------|*cos   (2*x)
|      __________|            
\    \/ cos(2*x) /
sin⁡3(x)(cos⁡2(x)cos⁡(2x)+1)cos⁡54(2x)\frac{\sin^{3}{\left(x \right)}}{\left(\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1\right) \cos^{\frac{5}{4}}{\left(2 x \right)}} 
                                        3/x\                                    
                                   8*cot |-|                                    
                                         \2/                                    
--------------------------------------------------------------------------------
                                   5/4 /                            2          \
               /           2/x\   \    |              /        2/x\\           |
             3 |      8*cot |-|   |    |              |-1 + cot |-||           |
/       2/x\\  |            \2/   |    |              \         \2//           |
|1 + cot |-|| *|1 - --------------|   *|1 + -----------------------------------|
\        \2//  |                 2|    |          ______________               |
               |    /       2/x\\ |    |         /         2                  2|
               |    |1 + cot |-|| |    |        /  -1 + cot (x)  /       2/x\\ |
               \    \        \2// /    |       /   ------------ *|1 + cot |-|| |
                                       |      /           2      \        \2// |
                                       \    \/     1 + cot (x)                 /
8cot⁡3(x2)(1−8cot⁡2(x2)(cot⁡2(x2)+1)2)54(1+(cot⁡2(x2)−1)2cot⁡2(x)−1cot⁡2(x)+1(cot⁡2(x2)+1)2)(cot⁡2(x2)+1)3\frac{8 \cot^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \frac{8 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right)^{\frac{5}{4}} \left(1 + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\sqrt{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{3}} 
                                      /3*x\           /x\                               
                                 2*cot|---|      6*cot|-|                               
                                      \ 2 /           \2/                               
                             - ------------- + -----------                              
                                      2/3*x\          2/x\                              
                               1 + cot |---|   1 + cot |-|                              
                                       \ 2 /           \2/                              
----------------------------------------------------------------------------------------
                    /                                              2                   \
                3/4 |           ______________   /            2/x\\      /        2/x\\|
  /        2   \    |          /         2       |    -1 + cot |-||    2*|-1 + cot |-|||
  |-1 + cot (x)|    |         /  -1 + cot (x)    |             \2/|      \         \2//|
4*|------------|   *|-1 +    /   ------------  + |1 - ------------|  + ----------------|
  |       2    |    |       /           2        |           2/x\ |             2/x\   |
  \1 + cot (x) /    |     \/     1 + cot (x)     |    1 + cot |-| |      1 + cot |-|   |
                    \                            \            \2/ /              \2/   /
−2cot⁡(3x2)cot⁡2(3x2)+1+6cot⁡(x2)cot⁡2(x2)+14(cot⁡2(x)−1cot⁡2(x)+1)34(cot⁡2(x)−1cot⁡2(x)+1+(−cot⁡2(x2)−1cot⁡2(x2)+1+1)2+2(cot⁡2(x2)−1)cot⁡2(x2)+1−1)\frac{- \frac{2 \cot{\left(\frac{3 x}{2} \right)}}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1} + \frac{6 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}{4 \left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \left(\sqrt{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} + \left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{2} + \frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right)} 
            1                            1               
- --------------------- + -------------------------------
      __________                      5/4                
     /    1                 /   1    \                   
  4 /  -------- *csc(x)   2*|--------|   *csc(2*x)*sec(x)
  \/   sec(2*x)             \sec(2*x)/                   
---------------------------------------------------------
                              1                          
                1 + ----------------------               
                        __________                       
                       /    1         2                  
                      /  -------- *sec (x)               
                    \/   sec(2*x)
−11sec⁡(2x)4csc⁡(x)+12(1sec⁡(2x))54csc⁡(2x)sec⁡(x)1+11sec⁡(2x)sec⁡2(x)\frac{- \frac{1}{\sqrt[4]{\frac{1}{\sec{\left(2 x \right)}}} \csc{\left(x \right)}} + \frac{1}{2 \left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{5}{4}} \csc{\left(2 x \right)} \sec{\left(x \right)}}}{1 + \frac{1}{\sqrt{\frac{1}{\sec{\left(2 x \right)}}} \sec^{2}{\left(x \right)}}} 
                                     1         3                                    
                                - -------- + ------                                 
                                  csc(3*x)   csc(x)                                 
------------------------------------------------------------------------------------
                 3/4 /           _______________                    2              \
  /      1      \    |          /       1          /         1     \         2     |
4*|-------------|   *|-1 +     /  -------------  + |1 - -----------|  + -----------|
  |   /pi      \|    |        /      /pi      \    |       /pi    \|       /pi    \|
  |csc|-- - 2*x||    |       /    csc|-- - 2*x|    |    csc|-- - x||    csc|-- - x||
  \   \2       //    \     \/        \2       /    \       \2     //       \2     //
−1csc⁡(3x)+3csc⁡(x)4((1−1csc⁡(−x+π2))2+1csc⁡(−2x+π2)−1+2csc⁡(−x+π2))(1csc⁡(−2x+π2))34\frac{- \frac{1}{\csc{\left(3 x \right)}} + \frac{3}{\csc{\left(x \right)}}}{4 \left(\left(1 - \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{2} + \sqrt{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} - 1 + \frac{2}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \left(\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right)^{\frac{3}{4}}} 
                    /x\                           /       2/x\\                   
               2*tan|-|                           |1 - tan |-||*tan(x)            
                    \2/                           \        \2//                   
- --------------------------------- + --------------------------------------------
        _____________                              5/4                            
       /        2                     /       2   \                               
      /  1 - tan (x)  /       2/x\\   |1 - tan (x)|    /       2   \ /       2/x\\
     /   ----------- *|1 + tan |-||   |-----------|   *\1 + tan (x)/*|1 + tan |-||
  4 /           2     \        \2//   |       2   |                  \        \2//
  \/     1 + tan (x)                  \1 + tan (x)/                               
----------------------------------------------------------------------------------
                                                 2                                
                                    /       2/x\\                                 
                                    |1 - tan |-||                                 
                                    \        \2//                                 
                      1 + ----------------------------------                      
                                _____________                                     
                               /        2                  2                      
                              /  1 - tan (x)  /       2/x\\                       
                             /   ----------- *|1 + tan |-||                       
                            /           2     \        \2//                       
                          \/     1 + tan (x)
−2tan⁡(x2)1−tan⁡2(x)tan⁡2(x)+14(tan⁡2(x2)+1)+(1−tan⁡2(x2))tan⁡(x)(1−tan⁡2(x)tan⁡2(x)+1)54(tan⁡2(x2)+1)(tan⁡2(x)+1)1+(1−tan⁡2(x2))21−tan⁡2(x)tan⁡2(x)+1(tan⁡2(x2)+1)2\frac{- \frac{2 \tan{\left(\frac{x}{2} \right)}}{\sqrt[4]{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{\frac{5}{4}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}}{1 + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\sqrt{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} 
                               -sin(3*x) + 3*sin(x)                               
----------------------------------------------------------------------------------
  /                      2       _______________                \                 
  |     /       /    pi\\       /    /pi      \         /    pi\|    3/4/pi      \
4*|-1 + |1 - sin|x + --||  +   /  sin|-- + 2*x|  + 2*sin|x + --||*sin   |-- + 2*x|
  \     \       \    2 //    \/      \2       /         \    2 //       \2       /
3sin⁡(x)−sin⁡(3x)4((1−sin⁡(x+π2))2+2sin⁡(x+π2)+sin⁡(2x+π2)−1)sin⁡34(2x+π2)\frac{3 \sin{\left(x \right)} - \sin{\left(3 x \right)}}{4 \left(\left(1 - \sin{\left(x + \frac{\pi}{2} \right)}\right)^{2} + 2 \sin{\left(x + \frac{\pi}{2} \right)} + \sqrt{\sin{\left(2 x + \frac{\pi}{2} \right)}} - 1\right) \sin^{\frac{3}{4}}{\left(2 x + \frac{\pi}{2} \right)}} 
                    /x\                            /        2/x\\                   
               2*cot|-|                            |-1 + cot |-||*cot(x)            
                    \2/                            \         \2//                   
- ---------------------------------- + ---------------------------------------------
        ______________                               5/4                            
       /         2                     /        2   \                               
      /  -1 + cot (x)  /       2/x\\   |-1 + cot (x)|    /       2   \ /       2/x\\
     /   ------------ *|1 + cot |-||   |------------|   *\1 + cot (x)/*|1 + cot |-||
  4 /           2      \        \2//   |       2    |                  \        \2//
  \/     1 + cot (x)                   \1 + cot (x) /                               
------------------------------------------------------------------------------------
                                                  2                                 
                                    /        2/x\\                                  
                                    |-1 + cot |-||                                  
                                    \         \2//                                  
                      1 + -----------------------------------                       
                                ______________                                      
                               /         2                  2                       
                              /  -1 + cot (x)  /       2/x\\                        
                             /   ------------ *|1 + cot |-||                        
                            /           2      \        \2//                        
                          \/     1 + cot (x)
−2cot⁡(x2)cot⁡2(x)−1cot⁡2(x)+14(cot⁡2(x2)+1)+(cot⁡2(x2)−1)cot⁡(x)(cot⁡2(x)−1cot⁡2(x)+1)54(cot⁡2(x2)+1)(cot⁡2(x)+1)1+(cot⁡2(x2)−1)2cot⁡2(x)−1cot⁡2(x)+1(cot⁡2(x2)+1)2\frac{- \frac{2 \cot{\left(\frac{x}{2} \right)}}{\sqrt[4]{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}\right)^{\frac{5}{4}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}}{1 + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\sqrt{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} 
                  3/    pi\               
               cos |x - --|               
                   \    2 /               
------------------------------------------
                    5/4 /         2      \
/         2/    pi\\    |      cos (x)   |
|1 - 2*cos |x - --||   *|1 + ------------|
\          \    2 //    |      __________|
                        \    \/ cos(2*x) /
cos⁡3(x−π2)(1−2cos⁡2(x−π2))54(cos⁡2(x)cos⁡(2x)+1)\frac{\cos^{3}{\left(x - \frac{\pi}{2} \right)}}{\left(1 - 2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}\right)^{\frac{5}{4}} \left(\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1\right)} 
                                    /    pi\
                        sin(2*x)*sin|x + --|
         sin(x)                     \    2 /
- ------------------- + --------------------
      _______________         5/4/pi      \ 
     /    /pi      \     2*sin   |-- + 2*x| 
  4 /  sin|-- + 2*x|             \2       / 
  \/      \2       /                        
--------------------------------------------
                     2/    pi\              
                  sin |x + --|              
                      \    2 /              
          1 + -------------------           
                  _______________           
                 /    /pi      \            
                /  sin|-- + 2*x|            
              \/      \2       /
−sin⁡(x)sin⁡(2x+π2)4+sin⁡(2x)sin⁡(x+π2)2sin⁡54(2x+π2)sin⁡2(x+π2)sin⁡(2x+π2)+1\frac{- \frac{\sin{\left(x \right)}}{\sqrt[4]{\sin{\left(2 x + \frac{\pi}{2} \right)}}} + \frac{\sin{\left(2 x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{2 \sin^{\frac{5}{4}}{\left(2 x + \frac{\pi}{2} \right)}}}{\frac{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}{\sqrt{\sin{\left(2 x + \frac{\pi}{2} \right)}}} + 1} 
                                    /3*x\           /x\                             
                               2*tan|---|      6*tan|-|                             
                                    \ 2 /           \2/                             
                           - ------------- + -----------                            
                                    2/3*x\          2/x\                            
                             1 + tan |---|   1 + tan |-|                            
                                     \ 2 /           \2/                            
------------------------------------------------------------------------------------
                   /                                            2                  \
               3/4 |           _____________   /           2/x\\      /       2/x\\|
  /       2   \    |          /        2       |    1 - tan |-||    2*|1 - tan |-|||
  |1 - tan (x)|    |         /  1 - tan (x)    |            \2/|      \        \2//|
4*|-----------|   *|-1 +    /   -----------  + |1 - -----------|  + ---------------|
  |       2   |    |       /           2       |           2/x\|             2/x\  |
  \1 + tan (x)/    |     \/     1 + tan (x)    |    1 + tan |-||      1 + tan |-|  |
                   \                           \            \2//              \2/  /
−2tan⁡(3x2)tan⁡2(3x2)+1+6tan⁡(x2)tan⁡2(x2)+14(1−tan⁡2(x)tan⁡2(x)+1)34(1−tan⁡2(x)tan⁡2(x)+1+2(1−tan⁡2(x2))tan⁡2(x2)+1+(−1−tan⁡2(x2)tan⁡2(x2)+1+1)2−1)\frac{- \frac{2 \tan{\left(\frac{3 x}{2} \right)}}{\tan^{2}{\left(\frac{3 x}{2} \right)} + 1} + \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{4 \left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right)^{\frac{3}{4}} \left(\sqrt{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} + \frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \left(- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{2} - 1\right)} 
               1                                     1                    
- ---------------------------- + -----------------------------------------
        _______________                           5/4                     
       /       1                   /      1      \                /pi    \
      /  ------------- *csc(x)   2*|-------------|   *csc(2*x)*csc|-- - x|
     /      /pi      \             |   /pi      \|                \2     /
  4 /    csc|-- - 2*x|             |csc|-- - 2*x||                        
  \/        \2       /             \   \2       //                        
--------------------------------------------------------------------------
                                      1                                   
                  1 + ----------------------------------                  
                            _______________                               
                           /       1           2/pi    \                  
                          /  ------------- *csc |-- - x|                  
                         /      /pi      \      \2     /                  
                        /    csc|-- - 2*x|                                
                      \/        \2       /
−11csc⁡(−2x+π2)4csc⁡(x)+12(1csc⁡(−2x+π2))54csc⁡(2x)csc⁡(−x+π2)1+11csc⁡(−2x+π2)csc⁡2(−x+π2)\frac{- \frac{1}{\sqrt[4]{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc{\left(x \right)}} + \frac{1}{2 \left(\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right)^{\frac{5}{4}} \csc{\left(2 x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}}{1 + \frac{1}{\sqrt{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}} 
                    -sin(3*x) + 3*sin(x)                    
------------------------------------------------------------
  /                 2     __________           \    3/4     
4*\-1 + (1 - cos(x))  + \/ cos(2*x)  + 2*cos(x)/*cos   (2*x)
3sin⁡(x)−sin⁡(3x)4((1−cos⁡(x))2+2cos⁡(x)+cos⁡(2x)−1)cos⁡34(2x)\frac{3 \sin{\left(x \right)} - \sin{\left(3 x \right)}}{4 \left(\left(1 - \cos{\left(x \right)}\right)^{2} + 2 \cos{\left(x \right)} + \sqrt{\cos{\left(2 x \right)}} - 1\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
     sin(x)      cos(x)*sin(2*x)
- ------------ + ---------------
  4 __________         5/4      
  \/ cos(2*x)     2*cos   (2*x) 
--------------------------------
                 2              
              cos (x)           
        1 + ------------        
              __________        
            \/ cos(2*x)
−sin⁡(x)cos⁡(2x)4+sin⁡(2x)cos⁡(x)2cos⁡54(2x)cos⁡2(x)cos⁡(2x)+1\frac{- \frac{\sin{\left(x \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}} + \frac{\sin{\left(2 x \right)} \cos{\left(x \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
                        1              3                      
                - ------------- + -----------                 
                     /      pi\      /    pi\                 
                  sec|3*x - --|   sec|x - --|                 
                     \      2 /      \    2 /                 
--------------------------------------------------------------
            3/4 /         __________               2         \
  /   1    \    |        /    1        /      1   \      2   |
4*|--------|   *|-1 +   /  --------  + |1 - ------|  + ------|
  \sec(2*x)/    \     \/   sec(2*x)    \    sec(x)/    sec(x)/
−1sec⁡(3x−π2)+3sec⁡(x−π2)4((1−1sec⁡(x))2+1sec⁡(2x)−1+2sec⁡(x))(1sec⁡(2x))34\frac{- \frac{1}{\sec{\left(3 x - \frac{\pi}{2} \right)}} + \frac{3}{\sec{\left(x - \frac{\pi}{2} \right)}}}{4 \left(\left(1 - \frac{1}{\sec{\left(x \right)}}\right)^{2} + \sqrt{\frac{1}{\sec{\left(2 x \right)}}} - 1 + \frac{2}{\sec{\left(x \right)}}\right) \left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{3}{4}}} 
     /    pi\              /      pi\
  cos|x - --|    cos(x)*cos|2*x - --|
     \    2 /              \      2 /
- ------------ + --------------------
  4 __________           5/4         
  \/ cos(2*x)       2*cos   (2*x)    
-------------------------------------
                    2                
                 cos (x)             
           1 + ------------          
                 __________          
               \/ cos(2*x)
cos⁡(x)cos⁡(2x−π2)2cos⁡54(2x)−cos⁡(x−π2)cos⁡(2x)4cos⁡2(x)cos⁡(2x)+1\frac{\frac{\cos{\left(x \right)} \cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \cos^{\frac{5}{4}}{\left(2 x \right)}} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\sqrt[4]{\cos{\left(2 x \right)}}}}{\frac{\cos^{2}{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)}}} + 1} 
                                1                                
-----------------------------------------------------------------
             5/4                                                 
/       2   \    /                    1                 \    3   
|1 - -------|   *|1 + ----------------------------------|*csc (x)
|       2   |    |          _______________             |        
\    csc (x)/    |         /       1           2/pi    \|        
                 |        /  ------------- *csc |-- - x||        
                 |       /      /pi      \      \2     /|        
                 |      /    csc|-- - 2*x|              |        
                 \    \/        \2       /              /
1(1+11csc⁡(−2x+π2)csc⁡2(−x+π2))(1−2csc⁡2(x))54csc⁡3(x)\frac{1}{\left(1 + \frac{1}{\sqrt{\frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}\right) \left(1 - \frac{2}{\csc^{2}{\left(x \right)}}\right)^{\frac{5}{4}} \csc^{3}{\left(x \right)}} 
                   /      pi\        /    pi\               
              - cos|3*x - --| + 3*cos|x - --|               
                   \      2 /        \    2 /               
------------------------------------------------------------
  /                 2     __________           \    3/4     
4*\-1 + (1 - cos(x))  + \/ cos(2*x)  + 2*cos(x)/*cos   (2*x)
3cos⁡(x−π2)−cos⁡(3x−π2)4((1−cos⁡(x))2+2cos⁡(x)+cos⁡(2x)−1)cos⁡34(2x)\frac{3 \cos{\left(x - \frac{\pi}{2} \right)} - \cos{\left(3 x - \frac{\pi}{2} \right)}}{4 \left(\left(1 - \cos{\left(x \right)}\right)^{2} + 2 \cos{\left(x \right)} + \sqrt{\cos{\left(2 x \right)}} - 1\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
                                        3/x\                                   
                                   8*tan |-|                                   
                                         \2/                                   
-------------------------------------------------------------------------------
                                   5/4 /                           2          \
               /           2/x\   \    |              /       2/x\\           |
             3 |      8*tan |-|   |    |              |1 - tan |-||           |
/       2/x\\  |            \2/   |    |              \        \2//           |
|1 + tan |-|| *|1 - --------------|   *|1 + ----------------------------------|
\        \2//  |                 2|    |          _____________               |
               |    /       2/x\\ |    |         /        2                  2|
               |    |1 + tan |-|| |    |        /  1 - tan (x)  /       2/x\\ |
               \    \        \2// /    |       /   ----------- *|1 + tan |-|| |
                                       |      /           2     \        \2// |
                                       \    \/     1 + tan (x)                /
8tan⁡3(x2)(1−8tan⁡2(x2)(tan⁡2(x2)+1)2)54(1+(1−tan⁡2(x2))21−tan⁡2(x)tan⁡2(x)+1(tan⁡2(x2)+1)2)(tan⁡2(x2)+1)3\frac{8 \tan^{3}{\left(\frac{x}{2} \right)}}{\left(1 - \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right)^{\frac{5}{4}} \left(1 + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\sqrt{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{3}} 
                     3                      
                  sin (x)                   
--------------------------------------------
                   /           2/    pi\   \
               5/4 |        sin |x + --|   |
/         2   \    |            \    2 /   |
\1 - 2*sin (x)/   *|1 + -------------------|
                   |        _______________|
                   |       /    /pi      \ |
                   |      /  sin|-- + 2*x| |
                   \    \/      \2       / /
sin⁡3(x)(1−2sin⁡2(x))54(sin⁡2(x+π2)sin⁡(2x+π2)+1)\frac{\sin^{3}{\left(x \right)}}{\left(1 - 2 \sin^{2}{\left(x \right)}\right)^{\frac{5}{4}} \left(\frac{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}{\sqrt{\sin{\left(2 x + \frac{\pi}{2} \right)}}} + 1\right)} 
                               1                               
---------------------------------------------------------------
                  5/4                                          
/         2      \    /              1           \    3/    pi\
|1 - ------------|   *|1 + ----------------------|*sec |x - --|
|       2/    pi\|    |        __________        |     \    2 /
|    sec |x - --||    |       /    1         2   |             
\        \    2 //    |      /  -------- *sec (x)|             
                      \    \/   sec(2*x)         /
1(1+11sec⁡(2x)sec⁡2(x))(1−2sec⁡2(x−π2))54sec⁡3(x−π2)\frac{1}{\left(1 + \frac{1}{\sqrt{\frac{1}{\sec{\left(2 x \right)}}} \sec^{2}{\left(x \right)}}\right) \left(1 - \frac{2}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}\right)^{\frac{5}{4}} \sec^{3}{\left(x - \frac{\pi}{2} \right)}} 
            -sin(3*x) + 3*sin(x)           
-------------------------------------------
  /1     __________   cos(2*x)\    3/4     
4*|- + \/ cos(2*x)  + --------|*cos   (2*x)
  \2                     2    /
3sin⁡(x)−sin⁡(3x)4(cos⁡(2x)+cos⁡(2x)2+12)cos⁡34(2x)\frac{3 \sin{\left(x \right)} - \sin{\left(3 x \right)}}{4 \left(\sqrt{\cos{\left(2 x \right)}} + \frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2}\right) \cos^{\frac{3}{4}}{\left(2 x \right)}} 
              1                                 1                  
- -------------------------- + ------------------------------------
      __________                           5/4                     
     /    1         /    pi\     /   1    \              /      pi\
  4 /  -------- *sec|x - --|   2*|--------|   *sec(x)*sec|2*x - --|
  \/   sec(2*x)     \    2 /     \sec(2*x)/              \      2 /
-------------------------------------------------------------------
                                   1                               
                     1 + ----------------------                    
                             __________                            
                            /    1         2                       
                           /  -------- *sec (x)                    
                         \/   sec(2*x)
−11sec⁡(2x)4sec⁡(x−π2)+12(1sec⁡(2x))54sec⁡(x)sec⁡(2x−π2)1+11sec⁡(2x)sec⁡2(x)\frac{- \frac{1}{\sqrt[4]{\frac{1}{\sec{\left(2 x \right)}}} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{2 \left(\frac{1}{\sec{\left(2 x \right)}}\right)^{\frac{5}{4}} \sec{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}}{1 + \frac{1}{\sqrt{\frac{1}{\sec{\left(2 x \right)}}} \sec^{2}{\left(x \right)}}} 
(-1/((1/sec(2*x))^(1/4)*sec(x - pi/2)) + 1/(2*(1/sec(2*x))^(5/4)*sec(x)*sec(2*x - pi/2)))/(1 + 1/(sqrt(1/sec(2*x))*sec(x)^2))
    © Sr Examen – Калькулятор