Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
 cos(x)        x        2*sin(x)*sin(2*x)       /x\
-------- + ---------- + ----------------- + atan|-|
cos(2*x)     /     2\          2                \2/
             |    x |       cos (2*x)              
           2*|1 + --|                              
             \    4 /
(2sin⁡(x)sin⁡(2x)cos⁡2(2x)+(x2(x24+1)+cos⁡(x)cos⁡(2x)))+atan⁡(x2)\left(\frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \left(\frac{x}{2 \left(\frac{x^{2}}{4} + 1\right)} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}}\right)\right) + \operatorname{atan}{\left(\frac{x}{2} \right)} 
cos(x)/cos(2*x) + x/((2*(1 + x^2/4))) + ((2*sin(x))*sin(2*x))/cos(2*x)^2 + atan(x/2)
Simplificación general [src] 
       2           2      /     2\     /x\   /     2\                   /       2\                
2*x*cos (2*x) + cos (2*x)*\4 + x /*atan|-| + \4 + x /*cos(x)*cos(2*x) + \8 + 2*x /*sin(x)*sin(2*x)
                                       \2/                                                        
--------------------------------------------------------------------------------------------------
                                        /     2\    2                                             
                                        \4 + x /*cos (2*x)
2xcos⁡2(2x)+(x2+4)cos⁡(x)cos⁡(2x)+(x2+4)cos⁡2(2x)atan⁡(x2)+(2x2+8)sin⁡(x)sin⁡(2x)(x2+4)cos⁡2(2x)\frac{2 x \cos^{2}{\left(2 x \right)} + \left(x^{2} + 4\right) \cos{\left(x \right)} \cos{\left(2 x \right)} + \left(x^{2} + 4\right) \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\frac{x}{2} \right)} + \left(2 x^{2} + 8\right) \sin{\left(x \right)} \sin{\left(2 x \right)}}{\left(x^{2} + 4\right) \cos^{2}{\left(2 x \right)}} 
(2*x*cos(2*x)^2 + cos(2*x)^2*(4 + x^2)*atan(x/2) + (4 + x^2)*cos(x)*cos(2*x) + (8 + 2*x^2)*sin(x)*sin(2*x))/((4 + x^2)*cos(2*x)^2)
Unión de expresiones racionales [src] 
//     2\                      \               2      /     2\     /x\     /     2\                
\\4 + x /*cos(x) + 2*x*cos(2*x)/*cos(2*x) + cos (2*x)*\4 + x /*atan|-| + 2*\4 + x /*sin(x)*sin(2*x)
                                                                   \2/                             
---------------------------------------------------------------------------------------------------
                                         /     2\    2                                             
                                         \4 + x /*cos (2*x)
2(x2+4)sin⁡(x)sin⁡(2x)+(x2+4)cos⁡2(2x)atan⁡(x2)+(2xcos⁡(2x)+(x2+4)cos⁡(x))cos⁡(2x)(x2+4)cos⁡2(2x)\frac{2 \left(x^{2} + 4\right) \sin{\left(x \right)} \sin{\left(2 x \right)} + \left(x^{2} + 4\right) \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\frac{x}{2} \right)} + \left(2 x \cos{\left(2 x \right)} + \left(x^{2} + 4\right) \cos{\left(x \right)}\right) \cos{\left(2 x \right)}}{\left(x^{2} + 4\right) \cos^{2}{\left(2 x \right)}} 
(((4 + x^2)*cos(x) + 2*x*cos(2*x))*cos(2*x) + cos(2*x)^2*(4 + x^2)*atan(x/2) + 2*(4 + x^2)*sin(x)*sin(2*x))/((4 + x^2)*cos(2*x)^2)
Denominador común [src] 
       2                                                 2                      2                          
2*x*cos (2*x) + 4*cos(x)*cos(2*x) + 8*sin(x)*sin(2*x) + x *cos(x)*cos(2*x) + 2*x *sin(x)*sin(2*x)       /x\
------------------------------------------------------------------------------------------------- + atan|-|
                                         2         2    2                                               \2/
                                    4*cos (2*x) + x *cos (2*x)
atan⁡(x2)+2x2sin⁡(x)sin⁡(2x)+x2cos⁡(x)cos⁡(2x)+2xcos⁡2(2x)+8sin⁡(x)sin⁡(2x)+4cos⁡(x)cos⁡(2x)x2cos⁡2(2x)+4cos⁡2(2x)\operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{2 x^{2} \sin{\left(x \right)} \sin{\left(2 x \right)} + x^{2} \cos{\left(x \right)} \cos{\left(2 x \right)} + 2 x \cos^{2}{\left(2 x \right)} + 8 \sin{\left(x \right)} \sin{\left(2 x \right)} + 4 \cos{\left(x \right)} \cos{\left(2 x \right)}}{x^{2} \cos^{2}{\left(2 x \right)} + 4 \cos^{2}{\left(2 x \right)}} 
(2*x*cos(2*x)^2 + 4*cos(x)*cos(2*x) + 8*sin(x)*sin(2*x) + x^2*cos(x)*cos(2*x) + 2*x^2*sin(x)*sin(2*x))/(4*cos(2*x)^2 + x^2*cos(2*x)^2) + atan(x/2)
Abrimos la expresión [src] 
2*sin(x)*sin(2*x)    cos(x)        x            /x\
----------------- + -------- + ---------- + atan|-|
       2            cos(2*x)     /     2\       \2/
    cos (2*x)                    |    x |          
                               2*|1 + --|          
                                 \    4 /
x2(x24+1)+2sin⁡(x)sin⁡(2x)cos⁡2(2x)+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{2 \left(\frac{x^{2}}{4} + 1\right)} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
                                    2                        
  x          cos(x)            4*sin (x)*cos(x)           /x\
------ + -------------- + ------------------------- + atan|-|
     2             2               2           4          \2/
    x    -1 + 2*cos (x)   1 - 4*cos (x) + 4*cos (x)          
2 + --                                                       
    2
xx22+2+atan⁡(x2)+4sin⁡2(x)cos⁡(x)4cos⁡4(x)−4cos⁡2(x)+1+cos⁡(x)2cos⁡2(x)−1\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{4 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{4 \cos^{4}{\left(x \right)} - 4 \cos^{2}{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 1} 
x/(2 + x^2/2) + cos(x)/(-1 + 2*cos(x)^2) + 4*sin(x)^2*cos(x)/(1 - 4*cos(x)^2 + 4*cos(x)^4) + atan(x/2)
Compilar la expresión [src] 
  x       cos(x)    2*sin(x)*sin(2*x)       /x\
------ + -------- + ----------------- + atan|-|
     2   cos(2*x)          2                \2/
    x                   cos (2*x)              
2 + --                                         
    2
xx22+2+2sin⁡(x)sin⁡(2x)cos⁡2(2x)+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
x/(2 + x^2/2) + cos(x)/cos(2*x) + 2*sin(x)*sin(2*x)/cos(2*x)^2 + atan(x/2)
Denominador racional [src] 
   2      //       2\                      \      3      /       2\     /x\     /       2\                         
cos (2*x)*\\8 + 2*x /*cos(x) + 4*x*cos(2*x)/ + cos (2*x)*\8 + 2*x /*atan|-| + 2*\8 + 2*x /*cos(2*x)*sin(x)*sin(2*x)
                                                                        \2/                                        
-------------------------------------------------------------------------------------------------------------------
                                                /       2\    3                                                    
                                                \8 + 2*x /*cos (2*x)
2(2x2+8)sin⁡(x)sin⁡(2x)cos⁡(2x)+(2x2+8)cos⁡3(2x)atan⁡(x2)+(4xcos⁡(2x)+(2x2+8)cos⁡(x))cos⁡2(2x)(2x2+8)cos⁡3(2x)\frac{2 \left(2 x^{2} + 8\right) \sin{\left(x \right)} \sin{\left(2 x \right)} \cos{\left(2 x \right)} + \left(2 x^{2} + 8\right) \cos^{3}{\left(2 x \right)} \operatorname{atan}{\left(\frac{x}{2} \right)} + \left(4 x \cos{\left(2 x \right)} + \left(2 x^{2} + 8\right) \cos{\left(x \right)}\right) \cos^{2}{\left(2 x \right)}}{\left(2 x^{2} + 8\right) \cos^{3}{\left(2 x \right)}} 
(cos(2*x)^2*((8 + 2*x^2)*cos(x) + 4*x*cos(2*x)) + cos(2*x)^3*(8 + 2*x^2)*atan(x/2) + 2*(8 + 2*x^2)*cos(2*x)*sin(x)*sin(2*x))/((8 + 2*x^2)*cos(2*x)^3)
Respuesta numérica [src] 
x/(2.0 + 0.5*x^2) + cos(x)/cos(2*x) + 2.0*sin(x)*sin(2*x)/cos(2*x)^2 + atan(x/2)
x/(2.0 + 0.5*x^2) + cos(x)/cos(2*x) + 2.0*sin(x)*sin(2*x)/cos(2*x)^2 + atan(x/2)
Parte trigonométrica [src] 
    x         cos(x)    -cos(3*x) + cos(x)       /x\
---------- + -------- + ------------------ + atan|-|
  /     2\   cos(2*x)          2                 \2/
  |    x |                  cos (2*x)               
2*|1 + --|                                          
  \    4 /
x2(x24+1)+cos⁡(x)−cos⁡(3x)cos⁡2(2x)+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{2 \left(\frac{x^{2}}{4} + 1\right)} + \frac{\cos{\left(x \right)} - \cos{\left(3 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
         /       2   \ /        2/x\\     /       2   \           /x\          
         \1 + cot (x)/*|-1 + cot |-||   8*\1 + cot (x)/*cot(x)*cot|-|          
  x                    \         \2//                             \2/       /x\
------ + ---------------------------- + ----------------------------- + atan|-|
     2   /       2/x\\ /        2   \                               2       \2/
    x    |1 + cot |-||*\-1 + cot (x)/   /       2/x\\ /        2   \           
2 + --   \        \2//                  |1 + cot |-||*\-1 + cot (x)/           
    2                                   \        \2//
xx22+2+(cot⁡2(x2)−1)(cot⁡2(x)+1)(cot⁡2(x2)+1)(cot⁡2(x)−1)+atan⁡(x2)+8(cot⁡2(x)+1)cot⁡(x2)cot⁡(x)(cot⁡2(x2)+1)(cot⁡2(x)−1)2\frac{x}{\frac{x^{2}}{2} + 2} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} - 1\right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)} \cot{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} - 1\right)^{2}} 
                                2                      
  x      sec(2*x)          2*sec (2*x)              /x\
------ + -------- + ------------------------- + atan|-|
     2    sec(x)       /    pi\    /      pi\       \2/
    x               sec|x - --|*sec|2*x - --|          
2 + --                 \    2 /    \      2 /          
    2
xx22+2+atan⁡(x2)+2sec⁡2(2x)sec⁡(x−π2)sec⁡(2x−π2)+sec⁡(2x)sec⁡(x)\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{2 \sec^{2}{\left(2 x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sec{\left(2 x \right)}}{\sec{\left(x \right)}} 
                      /  1         1    \          
                    2*|------ - --------|          
  x      sec(2*x)     \sec(x)   sec(3*x)/       /x\
------ + -------- + --------------------- + atan|-|
     2    sec(x)                1               \2/
    x                    1 + --------              
2 + --                       sec(4*x)              
    2
xx22+2+atan⁡(x2)+sec⁡(2x)sec⁡(x)+2(−1sec⁡(3x)+1sec⁡(x))1+1sec⁡(4x)\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{\sec{\left(2 x \right)}}{\sec{\left(x \right)}} + \frac{2 \left(- \frac{1}{\sec{\left(3 x \right)}} + \frac{1}{\sec{\left(x \right)}}\right)}{1 + \frac{1}{\sec{\left(4 x \right)}}} 
            /pi      \        2/pi      \          
         csc|-- - 2*x|   2*csc |-- - 2*x|          
  x         \2       /         \2       /       /x\
------ + ------------- + ---------------- + atan|-|
     2       /pi    \    csc(x)*csc(2*x)        \2/
    x     csc|-- - x|                              
2 + --       \2     /                              
    2
xx22+2+atan⁡(x2)+csc⁡(−2x+π2)csc⁡(−x+π2)+2csc⁡2(−2x+π2)csc⁡(x)csc⁡(2x)\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2 \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)} \csc{\left(2 x \right)}} 
           /       2/x\          2/3*x\\                                        
           |1 - tan |-|   1 - tan |---||                                        
           |        \2/           \ 2 /|                                        
         2*|----------- - -------------|                                        
           |       2/x\          2/3*x\|   /       2   \ /       2/x\\          
           |1 + tan |-|   1 + tan |---||   \1 + tan (x)/*|1 - tan |-||          
  x        \        \2/           \ 2 //                 \        \2//       /x\
------ + ------------------------------- + --------------------------- + atan|-|
     2                     2               /       2/x\\ /       2   \       \2/
    x               1 - tan (2*x)          |1 + tan |-||*\1 - tan (x)/          
2 + --          1 + -------------          \        \2//                        
    2                      2                                                    
                    1 + tan (2*x)
xx22+2+(1−tan⁡2(x2))(tan⁡2(x)+1)(1−tan⁡2(x))(tan⁡2(x2)+1)+2(1−tan⁡2(x2)tan⁡2(x2)+1−1−tan⁡2(3x2)tan⁡2(3x2)+1)1−tan⁡2(2x)tan⁡2(2x)+1+1+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{2 \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{1 - \tan^{2}{\left(\frac{3 x}{2} \right)}}{\tan^{2}{\left(\frac{3 x}{2} \right)} + 1}\right)}{\frac{1 - \tan^{2}{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1} + 1} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
             /    pi\                               
          sin|x + --|                               
  x          \    2 /    2*sin(x)*sin(2*x)       /x\
------ + ------------- + ----------------- + atan|-|
     2      /pi      \        2/pi      \        \2/
    x    sin|-- + 2*x|     sin |-- + 2*x|           
2 + --      \2       /         \2       /           
    2
xx22+2+2sin⁡(x)sin⁡(2x)sin⁡2(2x+π2)+sin⁡(x+π2)sin⁡(2x+π2)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x + \frac{\pi}{2} \right)}} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
                         /    pi\    /      pi\          
                    2*cos|x - --|*cos|2*x - --|          
  x       cos(x)         \    2 /    \      2 /       /x\
------ + -------- + --------------------------- + atan|-|
     2   cos(2*x)               2                     \2/
    x                        cos (2*x)                   
2 + --                                                   
    2
xx22+2+cos⁡(x)cos⁡(2x)+atan⁡(x2)+2cos⁡(x−π2)cos⁡(2x−π2)cos⁡2(2x)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{2 \cos{\left(x - \frac{\pi}{2} \right)} \cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}} 
                           2                 
  x      sec(2*x)     2*sec (2*x)         /x\
------ + -------- + --------------- + atan|-|
     2    sec(x)    csc(x)*csc(2*x)       \2/
    x                                        
2 + --                                       
    2
xx22+2+atan⁡(x2)+sec⁡(2x)sec⁡(x)+2sec⁡2(2x)csc⁡(x)csc⁡(2x)\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{\sec{\left(2 x \right)}}{\sec{\left(x \right)}} + \frac{2 \sec^{2}{\left(2 x \right)}}{\csc{\left(x \right)} \csc{\left(2 x \right)}} 
           /        2/x\           2/3*x\\                                         
           |-1 + cot |-|   -1 + cot |---||                                         
           |         \2/            \ 2 /|                                         
         2*|------------ - --------------|                                         
           |       2/x\           2/3*x\ |   /       2   \ /        2/x\\          
           |1 + cot |-|    1 + cot |---| |   \1 + cot (x)/*|-1 + cot |-||          
  x        \        \2/            \ 2 / /                 \         \2//       /x\
------ + --------------------------------- + ---------------------------- + atan|-|
     2                       2               /       2/x\\ /        2   \       \2/
    x                -1 + cot (2*x)          |1 + cot |-||*\-1 + cot (x)/          
2 + --           1 + --------------          \        \2//                         
    2                       2                                                      
                     1 + cot (2*x)
xx22+2+2(cot⁡2(x2)−1cot⁡2(x2)+1−cot⁡2(3x2)−1cot⁡2(3x2)+1)cot⁡2(2x)−1cot⁡2(2x)+1+1+(cot⁡2(x2)−1)(cot⁡2(x)+1)(cot⁡2(x2)+1)(cot⁡2(x)−1)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\cot^{2}{\left(\frac{3 x}{2} \right)} - 1}{\cot^{2}{\left(\frac{3 x}{2} \right)} + 1}\right)}{\frac{\cot^{2}{\left(2 x \right)} - 1}{\cot^{2}{\left(2 x \right)} + 1} + 1} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} - 1\right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
  x       cos(x)    2*sin(x)*sin(2*x)       /x\
------ + -------- + ----------------- + atan|-|
     2   cos(2*x)          2                \2/
    x                   cos (2*x)              
2 + --                                         
    2
xx22+2+2sin⁡(x)sin⁡(2x)cos⁡2(2x)+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
             /    pi\      /     /pi      \      /    pi\\          
          sin|x + --|    2*|- sin|-- + 3*x| + sin|x + --||          
  x          \    2 /      \     \2       /      \    2 //       /x\
------ + ------------- + --------------------------------- + atan|-|
     2      /pi      \                  /pi      \               \2/
    x    sin|-- + 2*x|           1 + sin|-- + 4*x|                  
2 + --      \2       /                  \2       /                  
    2
xx22+2+2(sin⁡(x+π2)−sin⁡(3x+π2))sin⁡(4x+π2)+1+sin⁡(x+π2)sin⁡(2x+π2)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \left(\sin{\left(x + \frac{\pi}{2} \right)} - \sin{\left(3 x + \frac{\pi}{2} \right)}\right)}{\sin{\left(4 x + \frac{\pi}{2} \right)} + 1} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
  x       cos(x)    2*(-cos(3*x) + cos(x))       /x\
------ + -------- + ---------------------- + atan|-|
     2   cos(2*x)        1 + cos(4*x)            \2/
    x                                               
2 + --                                              
    2
xx22+2+2(cos⁡(x)−cos⁡(3x))cos⁡(4x)+1+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \left(\cos{\left(x \right)} - \cos{\left(3 x \right)}\right)}{\cos{\left(4 x \right)} + 1} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
                           /     1              1      \          
                         2*|----------- - -------------|          
            /pi      \     |   /pi    \      /pi      \|          
         csc|-- - 2*x|     |csc|-- - x|   csc|-- - 3*x||          
  x         \2       /     \   \2     /      \2       //       /x\
------ + ------------- + ------------------------------- + atan|-|
     2       /pi    \                     1                    \2/
    x     csc|-- - x|           1 + -------------                 
2 + --       \2     /                  /pi      \                 
    2                               csc|-- - 4*x|                 
                                       \2       /
xx22+2+atan⁡(x2)+csc⁡(−2x+π2)csc⁡(−x+π2)+2(1csc⁡(−x+π2)−1csc⁡(−3x+π2))1+1csc⁡(−4x+π2)\frac{x}{\frac{x^{2}}{2} + 2} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{2 \left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- 3 x + \frac{\pi}{2} \right)}}\right)}{1 + \frac{1}{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}} 
         /       2   \ /       2/x\\     /       2   \           /x\          
         \1 + tan (x)/*|1 - tan |-||   8*\1 + tan (x)/*tan(x)*tan|-|          
  x                    \        \2//                             \2/       /x\
------ + --------------------------- + ----------------------------- + atan|-|
     2   /       2/x\\ /       2   \                               2       \2/
    x    |1 + tan |-||*\1 - tan (x)/    /       2/x\\ /       2   \           
2 + --   \        \2//                  |1 + tan |-||*\1 - tan (x)/           
    2                                   \        \2//
xx22+2+(1−tan⁡2(x2))(tan⁡2(x)+1)(1−tan⁡2(x))(tan⁡2(x2)+1)+atan⁡(x2)+8(tan⁡2(x)+1)tan⁡(x2)tan⁡(x)(1−tan⁡2(x))2(tan⁡2(x2)+1)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
  x                             2                            /x\
------ + cos(x)*sec(2*x) + 2*sec (2*x)*sin(x)*sin(2*x) + atan|-|
     2                                                       \2/
    x                                                           
2 + --                                                          
    2
xx22+2+2sin⁡(x)sin⁡(2x)sec⁡2(2x)+cos⁡(x)sec⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + 2 \sin{\left(x \right)} \sin{\left(2 x \right)} \sec^{2}{\left(2 x \right)} + \cos{\left(x \right)} \sec{\left(2 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
  x                        2*(-cos(3*x) + cos(x))       /x\
------ + cos(x)*sec(2*x) + ---------------------- + atan|-|
     2                          1 + cos(4*x)            \2/
    x                                                      
2 + --                                                     
    2
xx22+2+2(cos⁡(x)−cos⁡(3x))cos⁡(4x)+1+cos⁡(x)sec⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \left(\cos{\left(x \right)} - \cos{\left(3 x \right)}\right)}{\cos{\left(4 x \right)} + 1} + \cos{\left(x \right)} \sec{\left(2 x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
x/(2 + x^2/2) + cos(x)*sec(2*x) + 2*(-cos(3*x) + cos(x))/(1 + cos(4*x)) + atan(x/2)
Potencias [src] 
            I*x    -I*x                                                    
           e      e                                                        
           ---- + -----     /   -I*x    I*x\ /   -2*I*x    2*I*x\          
  x         2       2       \- e     + e   /*\- e       + e     /       /x\
------ + ---------------- - ------------------------------------- + atan|-|
     2    -2*I*x    2*I*x                               2               \2/
    x    e         e                  / -2*I*x    2*I*x\                   
2 + --   ------- + ------             |e         e     |                   
    2       2        2              2*|------- + ------|                   
                                      \   2        2   /
xx22+2+eix2+e−ix2e2ix2+e−2ix2−(eix−e−ix)(e2ix−e−2ix)2(e2ix2+e−2ix2)2+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}} - \frac{\left(e^{i x} - e^{- i x}\right) \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)^{2}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
  x       cos(x)    2*sin(x)*sin(2*x)       /x\
------ + -------- + ----------------- + atan|-|
     2   cos(2*x)          2                \2/
    x                   cos (2*x)              
2 + --                                         
    2
xx22+2+2sin⁡(x)sin⁡(2x)cos⁡2(2x)+cos⁡(x)cos⁡(2x)+atan⁡(x2)\frac{x}{\frac{x^{2}}{2} + 2} + \frac{2 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{\cos{\left(x \right)}}{\cos{\left(2 x \right)}} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
x/(2 + x^2/2) + cos(x)/cos(2*x) + 2*sin(x)*sin(2*x)/cos(2*x)^2 + atan(x/2)
Combinatoria [src] 
       2             2          /x\                                            2    2          /x\    2                      2                
2*x*cos (2*x) + 4*cos (2*x)*atan|-| + 4*cos(x)*cos(2*x) + 8*sin(x)*sin(2*x) + x *cos (2*x)*atan|-| + x *cos(x)*cos(2*x) + 2*x *sin(x)*sin(2*x)
                                \2/                                                            \2/                                            
----------------------------------------------------------------------------------------------------------------------------------------------
                                                              /     2\    2                                                                   
                                                              \4 + x /*cos (2*x)
2x2sin⁡(x)sin⁡(2x)+x2cos⁡(x)cos⁡(2x)+x2cos⁡2(2x)atan⁡(x2)+2xcos⁡2(2x)+8sin⁡(x)sin⁡(2x)+4cos⁡(x)cos⁡(2x)+4cos⁡2(2x)atan⁡(x2)(x2+4)cos⁡2(2x)\frac{2 x^{2} \sin{\left(x \right)} \sin{\left(2 x \right)} + x^{2} \cos{\left(x \right)} \cos{\left(2 x \right)} + x^{2} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\frac{x}{2} \right)} + 2 x \cos^{2}{\left(2 x \right)} + 8 \sin{\left(x \right)} \sin{\left(2 x \right)} + 4 \cos{\left(x \right)} \cos{\left(2 x \right)} + 4 \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\frac{x}{2} \right)}}{\left(x^{2} + 4\right) \cos^{2}{\left(2 x \right)}} 
(2*x*cos(2*x)^2 + 4*cos(2*x)^2*atan(x/2) + 4*cos(x)*cos(2*x) + 8*sin(x)*sin(2*x) + x^2*cos(2*x)^2*atan(x/2) + x^2*cos(x)*cos(2*x) + 2*x^2*sin(x)*sin(2*x))/((4 + x^2)*cos(2*x)^2)
    © Sr Examen – Калькулятор