Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
¿cómo vas a descomponer esta expresión en fracciones?:
(s+3)/(5*s+15)
c^(k+5)*c^k/(c^2)^k
-2/((((x+1)^2/(1-x)^2)+1)*(1-x)^2)
(z+1)/(z+2)^3/(z-1)
Factorizar el polinomio:
y^3+y
y^3-6*y^2*x+12*y*x^2-8*x^3
z^3+5*z^2
y^3-3*y^2+6*y-8
Descomponer al cuadrado:
-y^4+8*y^2+2
y^4+8*y^2-3
-y^4-7*y^2-9
y^4+8*y^2-1
Expresiones idénticas
sin(x/ tres)^ tres /(uno +x^ dos)+sin(x/ tres)^ dos *atan(x)*cos(x/ tres)
seno de (x dividir por 3) al cubo dividir por (1 más x al cuadrado ) más seno de (x dividir por 3) al cuadrado multiplicar por arco tangente de gente de (x) multiplicar por coseno de (x dividir por 3)
seno de (x dividir por tres) en el grado tres dividir por (uno más x en el grado dos) más seno de (x dividir por tres) en el grado dos multiplicar por arco tangente de gente de (x) multiplicar por coseno de (x dividir por tres)
sin(x/3)3/(1+x2)+sin(x/3)2*atan(x)*cos(x/3)
sinx/33/1+x2+sinx/32*atanx*cosx/3
sin(x/3)³/(1+x²)+sin(x/3)²*atan(x)*cos(x/3)
sin(x/3) en el grado 3/(1+x en el grado 2)+sin(x/3) en el grado 2*atan(x)*cos(x/3)
sin(x/3)^3/(1+x^2)+sin(x/3)^2atan(x)cos(x/3)
sin(x/3)3/(1+x2)+sin(x/3)2atan(x)cos(x/3)
sinx/33/1+x2+sinx/32atanxcosx/3
sinx/3^3/1+x^2+sinx/3^2atanxcosx/3
sin(x dividir por 3)^3 dividir por (1+x^2)+sin(x dividir por 3)^2*atan(x)*cos(x dividir por 3)
Expresiones semejantes
sin(x/3)^3/(1-x^2)+sin(x/3)^2*atan(x)*cos(x/3)
sin(x/3)^3/(1+x^2)-sin(x/3)^2*atan(x)*cos(x/3)
sin(x/3)^3/(1+x^2)+sin(x/3)^2*arctan(x)*cos(x/3)
sin(x/3)^3/(1+x^2)+sin(x/3)^2*arctanx*cos(x/3)
Expresiones con funciones
Seno sin
sin(x)-cos(3*pi/(2-x))+cot(3*pi/(2+x))+cot(x)
sin(x)/(a*sqrt(1-cos(x)^((2/a)^2)))
sin(x)/4-1/(sin(x)*4)-cos(x)/4
sin(x)^(3)/(1+cos(x))+sin(x)^(3)/(1-x)
sin(x/2)^3/(2*(2+cos(x/2))^2)+cos(x/2)*sin(x/2)/(2+cos(x/2))
Seno sin
sin(x)-cos(3*pi/(2-x))+cot(3*pi/(2+x))+cot(x)
sin(x)/(a*sqrt(1-cos(x)^((2/a)^2)))
sin(x)/4-1/(sin(x)*4)-cos(x)/4
sin(x)^(3)/(1+cos(x))+sin(x)^(3)/(1-x)
sin(x/2)^3/(2*(2+cos(x/2))^2)+cos(x/2)*sin(x/2)/(2+cos(x/2))
Arcotangente arctan
atan(x)^log(acot(x))*(log(acot(x))/((1+x^2)*atan(x))-log(atan(x))/((1+x^2)*acot(x)))/2
atan((4*x-4)/(2*sqrt(6)))/sqrt(6)
atan(((6*sin(x))/(1+cos(x))+2)/(2*sqrt(5)))/sqrt(5)
atan(((4*sin(2*x))/(1+cos(2*x))+1)/sqrt(31))/sqrt(31)
atan(x/sqrt(2))/2^(3/2)-x/(4+2*x^2)
Coseno cos
cos(2*t)*x/(cos(t)+sin(x))-cos(t)
cos(x)*(-sin(x)-(cos(x)*sin(x)))/sqrt(1+cos(x)^(2))/(cos(x)+sqrt(1+cos(x)^(2)))
cos(x)/acos(x)+sin(x)/(sqrt(1-x^2)*acos(x)^2)
cos(x)/2+x/(1+x^2)-x*sin(x)/2+atan(x)
cos(x)^acot(x)*(-log(cos(x))/(1+x^2)-acot(x)*sin(x)/cos(x))

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x/3)^3/(1+x^2)+sin(x/3)^2*atan(x)*cos(x/3)

¿Cómo vas a descomponer esta sin(x/3)^3/(1+x^2)+sin(x/3)^2atan(x)cos(x/3) expresión en fracciones?

Solución

Ha introducido [src]

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} \cos{\left(\frac{x}{3} \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^3/(1 + x^2) + (sin(x/3)^2*atan(x))*cos(x/3)

Simplificación general [src]

   2/x\ //     2\            /x\      /x\\
sin |-|*|\1 + x /*atan(x)*cos|-| + sin|-||
    \3/ \                    \3/      \3//
------------------------------------------
                       2                  
                  1 + x

$$\frac{\left(\left(x^{2} + 1\right) \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \sin{\left(\frac{x}{3} \right)}\right) \sin^{2}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^2*((1 + x^2)*atan(x)*cos(x/3) + sin(x/3))/(1 + x^2)

Denominador racional [src]

   3/x\      2/x\ /     2\            /x\
sin |-| + sin |-|*\1 + x /*atan(x)*cos|-|
    \3/       \3/                     \3/
-----------------------------------------
                       2                 
                  1 + x

$$\frac{\left(x^{2} + 1\right) \sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

(sin(x/3)^3 + sin(x/3)^2*(1 + x^2)*atan(x)*cos(x/3))/(1 + x^2)

Combinatoria [src]

   2/x\ /           /x\    2            /x\      /x\\
sin |-|*|atan(x)*cos|-| + x *atan(x)*cos|-| + sin|-||
    \3/ \           \3/                 \3/      \3//
-----------------------------------------------------
                             2                       
                        1 + x

$$\frac{\left(x^{2} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \sin{\left(\frac{x}{3} \right)} + \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)}\right) \sin^{2}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^2*(atan(x)*cos(x/3) + x^2*atan(x)*cos(x/3) + sin(x/3))/(1 + x^2)

Unión de expresiones racionales [src]

   2/x\ //     2\            /x\      /x\\
sin |-|*|\1 + x /*atan(x)*cos|-| + sin|-||
    \3/ \                    \3/      \3//
------------------------------------------
                       2                  
                  1 + x

$$\frac{\left(\left(x^{2} + 1\right) \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \sin{\left(\frac{x}{3} \right)}\right) \sin^{2}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^2*((1 + x^2)*atan(x)*cos(x/3) + sin(x/3))/(1 + x^2)

Compilar la expresión [src]

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^3/(1 + x^2) + sin(x/3)^2*atan(x)*cos(x/3)

Abrimos la expresión [src]

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^3/(1 + x^2) + sin(x/3)^2*atan(x)*cos(x/3)

Parte trigonométrica [src]

       1              atan(x)    
---------------- + --------------
/     2\    3/x\      2/x\    /x\
\1 + x /*csc |-|   csc |-|*sec|-|
             \3/       \3/    \3/

$$\frac{\operatorname{atan}{\left(x \right)}}{\csc^{2}{\left(\frac{x}{3} \right)} \sec{\left(\frac{x}{3} \right)}} + \frac{1}{\left(x^{2} + 1\right) \csc^{3}{\left(\frac{x}{3} \right)}}$$

            3/x\               2/x\ /       2/x\\        
       8*tan |-|          4*tan |-|*|1 - tan |-||*atan(x)
             \6/                \6/ \        \6//        
----------------------- + -------------------------------
                      3                         3        
/     2\ /       2/x\\             /       2/x\\         
\1 + x /*|1 + tan |-||             |1 + tan |-||         
         \        \6//             \        \6//

$$\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \tan^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)}}{\left(\tan^{2}{\left(\frac{x}{6} \right)} + 1\right)^{3}} + \frac{8 \tan^{3}{\left(\frac{x}{6} \right)}}{\left(x^{2} + 1\right) \left(\tan^{2}{\left(\frac{x}{6} \right)} + 1\right)^{3}}$$

       1                 atan(x)      
---------------- + -------------------
/     2\    3/x\      2/x\    /pi   x\
\1 + x /*csc |-|   csc |-|*csc|-- - -|
             \3/       \3/    \2    3/

$$\frac{\operatorname{atan}{\left(x \right)}}{\csc^{2}{\left(\frac{x}{3} \right)} \csc{\left(- \frac{x}{3} + \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 1\right) \csc^{3}{\left(\frac{x}{3} \right)}}$$

               /x\                                                
-sin(x) + 3*sin|-|                                                
               \3/        2/x\    2/x\ /   2/x\      2/x\\        
------------------ + 4*cos |-|*sin |-|*|cos |-| - sin |-||*atan(x)
      /     2\             \6/     \6/ \    \6/       \6//        
    4*\1 + x /

$$4 \left(- \sin^{2}{\left(\frac{x}{6} \right)} + \cos^{2}{\left(\frac{x}{6} \right)}\right) \sin^{2}{\left(\frac{x}{6} \right)} \cos^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

               /x\                                                        
-sin(x) + 3*sin|-|                                                        
               \3/          2/x\    6/x \    12/x \ /        2/x\\        
------------------ + 256*cot |-|*cot |--|*sin  |--|*|-1 + cot |-||*atan(x)
      /     2\               \6/     \12/      \12/ \         \6//        
    4*\1 + x /

$$256 \left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right) \sin^{12}{\left(\frac{x}{12} \right)} \cot^{6}{\left(\frac{x}{12} \right)} \cot^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

               /x\                                                            
-sin(x) + 3*sin|-|                   6                                        
               \3/     /       2/x \\     12/x \    2/x\ /       2/x\\        
------------------ + 4*|1 - tan |--|| *cos  |--|*tan |-|*|1 - tan |-||*atan(x)
      /     2\         \        \12//       \12/     \6/ \        \6//        
    4*\1 + x /

$$4 \left(1 - \tan^{2}{\left(\frac{x}{12} \right)}\right)^{6} \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \cos^{12}{\left(\frac{x}{12} \right)} \tan^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

     /    pi\        /  pi   x\                            /           2/x\    \        
- cos|x - --| + 3*cos|- -- + -|                            |        cos |-|    |        
     \    2 /        \  2    3/        2/x\    4/  pi   x\ |            \6/    |        
------------------------------- + 4*cos |-|*cos |- -- + -|*|-1 + --------------|*atan(x)
             /     2\                   \6/     \  2    6/ |        2/  pi   x\|        
           4*\1 + x /                                      |     cos |- -- + -||        
                                                           \         \  2    6//

$$4 \left(\frac{\cos^{2}{\left(\frac{x}{6} \right)}}{\cos^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(\frac{x}{6} \right)} \cos^{4}{\left(\frac{x}{6} - \frac{\pi}{2} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \cos{\left(\frac{x}{3} - \frac{\pi}{2} \right)} - \cos{\left(x - \frac{\pi}{2} \right)}}{4 \left(x^{2} + 1\right)}$$

         /x\           /x\                                            
    2*cot|-|      6*cot|-|                     6                      
         \2/           \6/      /        2/x \\  /       1   \        
- ----------- + -----------   4*|-1 + cot |--|| *|1 - -------|*atan(x)
         2/x\          2/x\     \         \12//  |       2/x\|        
  1 + cot |-|   1 + cot |-|                      |    cot |-||        
          \2/           \6/                      \        \6//        
--------------------------- + ----------------------------------------
           /     2\                                 6                 
         4*\1 + x /                   /       2/x \\     2/x\         
                                      |1 + cot |--|| *cot |-|         
                                      \        \12//      \6/

$$\frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{6} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{12} \right)} - 1\right)^{6} \operatorname{atan}{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{12} \right)} + 1\right)^{6} \cot^{2}{\left(\frac{x}{6} \right)}} + \frac{- \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{6 \cot{\left(\frac{x}{6} \right)}}{\cot^{2}{\left(\frac{x}{6} \right)} + 1}}{4 \left(x^{2} + 1\right)}$$

                      /       2/pi   x\\        
                      |    csc |-- - -||        
    1        3        |        \2    6/|        
- ------ + ------   4*|1 - ------------|*atan(x)
  csc(x)      /x\     |         2/x\   |        
           csc|-|     |      csc |-|   |        
              \3/     \          \6/   /        
----------------- + ----------------------------
      /     2\             2/x\    4/pi   x\    
    4*\1 + x /          csc |-|*csc |-- - -|    
                            \6/     \2    6/

$$\frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{x}{6} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{6} \right)}}\right) \operatorname{atan}{\left(x \right)}}{\csc^{2}{\left(\frac{x}{6} \right)} \csc^{4}{\left(- \frac{x}{6} + \frac{\pi}{2} \right)}} + \frac{- \frac{1}{\csc{\left(x \right)}} + \frac{3}{\csc{\left(\frac{x}{3} \right)}}}{4 \left(x^{2} + 1\right)}$$

               /x\                                          
-sin(x) + 3*sin|-|                                          
               \3/        6/x\    2/x\ /       2/x\\        
------------------ + 4*cos |-|*tan |-|*|1 - tan |-||*atan(x)
      /     2\             \6/     \6/ \        \6//        
    4*\1 + x /

$$4 \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \cos^{6}{\left(\frac{x}{6} \right)} \tan^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

                                  /          2/x\    \        
                                  |       sec |-|    |        
       1              3           |           \6/    |        
- ----------- + -------------   4*|1 - --------------|*atan(x)
     /    pi\      /  pi   x\     |       2/  pi   x\|        
  sec|x - --|   sec|- -- + -|     |    sec |- -- + -||        
     \    2 /      \  2    3/     \        \  2    6//        
----------------------------- + ------------------------------
            /     2\                   4/x\    2/  pi   x\    
          4*\1 + x /                sec |-|*sec |- -- + -|    
                                        \6/     \  2    6/

$$\frac{4 \left(- \frac{\sec^{2}{\left(\frac{x}{6} \right)}}{\sec^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}} + 1\right) \operatorname{atan}{\left(x \right)}}{\sec^{4}{\left(\frac{x}{6} \right)} \sec^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}} + \frac{- \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{3}{\sec{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}}{4 \left(x^{2} + 1\right)}$$

               /x\                                                             
-sin(x) + 3*sin|-|                    6                                        
               \3/     /        2/x \\     12/x \    2/x\ /       2/x\\        
------------------ + 4*|-1 + cot |--|| *sin  |--|*tan |-|*|1 - tan |-||*atan(x)
      /     2\         \         \12//       \12/     \6/ \        \6//        
    4*\1 + x /

$$4 \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \left(\cot^{2}{\left(\frac{x}{12} \right)} - 1\right)^{6} \sin^{12}{\left(\frac{x}{12} \right)} \tan^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

   3/x\                              
sin |-|                              
    \3/      2/x\            /pi   x\
------- + sin |-|*atan(x)*sin|-- + -|
      2       \3/            \2    3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \sin{\left(\frac{x}{3} + \frac{\pi}{2} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

                                             /         4/x\\        
                                             |    4*sin |-||        
                           4/x\    6/pi   x\ |          \6/|        
                     16*sin |-|*sin |-- + -|*|1 - ---------|*atan(x)
               /x\          \6/     \2    6/ |        2/x\ |        
-sin(x) + 3*sin|-|                           |     sin |-| |        
               \3/                           \         \3/ /        
------------------ + -----------------------------------------------
      /     2\                              2/x\                    
    4*\1 + x /                           sin |-|                    
                                             \3/

$$\frac{16 \left(- \frac{4 \sin^{4}{\left(\frac{x}{6} \right)}}{\sin^{2}{\left(\frac{x}{3} \right)}} + 1\right) \sin^{4}{\left(\frac{x}{6} \right)} \sin^{6}{\left(\frac{x}{6} + \frac{\pi}{2} \right)} \operatorname{atan}{\left(x \right)}}{\sin^{2}{\left(\frac{x}{3} \right)}} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

         /x\           /x\                                               
    2*cot|-|      6*cot|-|                                               
         \2/           \6/                                               
- ----------- + -----------                                              
         2/x\          2/x\          2/x\    6/x \ /        2/x\\        
  1 + cot |-|   1 + cot |-|   256*cot |-|*cot |--|*|-1 + cot |-||*atan(x)
          \2/           \6/           \6/     \12/ \         \6//        
--------------------------- + -------------------------------------------
           /     2\                                       6              
         4*\1 + x /                         /       2/x \\               
                                            |1 + cot |--||               
                                            \        \12//

$$\frac{256 \left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right) \cot^{6}{\left(\frac{x}{12} \right)} \cot^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{12} \right)} + 1\right)^{6}} + \frac{- \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{6 \cot{\left(\frac{x}{6} \right)}}{\cot^{2}{\left(\frac{x}{6} \right)} + 1}}{4 \left(x^{2} + 1\right)}$$

           1                     atan(x)       
----------------------- + ---------------------
/     2\    3/  pi   x\      /x\    2/  pi   x\
\1 + x /*sec |- -- + -|   sec|-|*sec |- -- + -|
             \  2    3/      \3/     \  2    3/

$$\frac{\operatorname{atan}{\left(x \right)}}{\sec{\left(\frac{x}{3} \right)} \sec^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}} + \frac{1}{\left(x^{2} + 1\right) \sec^{3}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}$$

         /x\           /x\                                       
    2*tan|-|      6*tan|-|                                       
         \2/           \6/           6/x \ /        1   \        
- ----------- + -----------   256*tan |--|*|-1 + -------|*atan(x)
         2/x\          2/x\           \12/ |        2/x\|        
  1 + tan |-|   1 + tan |-|                |     tan |-||        
          \2/           \6/                \         \6//        
--------------------------- + -----------------------------------
           /     2\                               6              
         4*\1 + x /                 /       2/x \\     2/x\      
                                    |1 + tan |--|| *tan |-|      
                                    \        \12//      \6/

$$\frac{256 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{6} \right)}}\right) \tan^{6}{\left(\frac{x}{12} \right)} \operatorname{atan}{\left(x \right)}}{\left(\tan^{2}{\left(\frac{x}{12} \right)} + 1\right)^{6} \tan^{2}{\left(\frac{x}{6} \right)}} + \frac{- \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{6 \tan{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} + 1}}{4 \left(x^{2} + 1\right)}$$

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

               /x\                   /         2/x\ \        
-sin(x) + 3*sin|-|                   |      sin |-| |        
               \3/      2/x\    2/x\ |          \3/ |        
------------------ + sin |-|*sin |-|*|-1 + ---------|*atan(x)
      /     2\           \3/     \6/ |          4/x\|        
    4*\1 + x /                       |     4*sin |-||        
                                     \           \6//

$$\left(-1 + \frac{\sin^{2}{\left(\frac{x}{3} \right)}}{4 \sin^{4}{\left(\frac{x}{6} \right)}}\right) \sin^{2}{\left(\frac{x}{6} \right)} \sin^{2}{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

               /x\                                           
-sin(x) + 3*sin|-|                                           
               \3/        2/x\    6/x\ /        2/x\\        
------------------ + 4*cot |-|*sin |-|*|-1 + cot |-||*atan(x)
      /     2\             \6/     \6/ \         \6//        
    4*\1 + x /

$$4 \left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right) \sin^{6}{\left(\frac{x}{6} \right)} \cot^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

               /x\                                          
-sin(x) + 3*sin|-|                                          
               \3/        4/x\    2/x\ /       2/x\\        
------------------ + 4*cos |-|*sin |-|*|1 - tan |-||*atan(x)
      /     2\             \6/     \6/ \        \6//        
    4*\1 + x /

$$4 \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \sin^{2}{\left(\frac{x}{6} \right)} \cos^{4}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

                            12/x \    6/x \ /        1   \        
                     256*cos  |--|*tan |--|*|-1 + -------|*atan(x)
               /x\            \12/     \12/ |        2/x\|        
-sin(x) + 3*sin|-|                          |     tan |-||        
               \3/                          \         \6//        
------------------ + ---------------------------------------------
      /     2\                             2/x\                   
    4*\1 + x /                          tan |-|                   
                                            \6/

$$\frac{256 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{6} \right)}}\right) \cos^{12}{\left(\frac{x}{12} \right)} \tan^{6}{\left(\frac{x}{12} \right)} \operatorname{atan}{\left(x \right)}}{\tan^{2}{\left(\frac{x}{6} \right)}} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

                                  /        2/  pi   x\\        
                                  |     sec |- -- + -||        
       1              3           |         \  2    6/|        
- ----------- + -------------   4*|-1 + --------------|*atan(x)
     /    pi\      /  pi   x\     |           2/x\    |        
  sec|x - --|   sec|- -- + -|     |        sec |-|    |        
     \    2 /      \  2    3/     \            \6/    /        
----------------------------- + -------------------------------
            /     2\                    2/x\    4/  pi   x\    
          4*\1 + x /                 sec |-|*sec |- -- + -|    
                                         \6/     \  2    6/

$$\frac{4 \left(-1 + \frac{\sec^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{6} \right)}}\right) \operatorname{atan}{\left(x \right)}}{\sec^{2}{\left(\frac{x}{6} \right)} \sec^{4}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}} + \frac{- \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{3}{\sec{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}}{4 \left(x^{2} + 1\right)}$$

     /    pi\        /  pi   x\                            /       2/  pi   x\\        
- cos|x - --| + 3*cos|- -- + -|                            |    cos |- -- + -||        
     \    2 /        \  2    3/        4/x\    2/  pi   x\ |        \  2    6/|        
------------------------------- + 4*cos |-|*cos |- -- + -|*|1 - --------------|*atan(x)
             /     2\                   \6/     \  2    6/ |          2/x\    |        
           4*\1 + x /                                      |       cos |-|    |        
                                                           \           \6/    /

$$4 \left(1 - \frac{\cos^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{6} \right)}}\right) \cos^{4}{\left(\frac{x}{6} \right)} \cos^{2}{\left(\frac{x}{6} - \frac{\pi}{2} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \cos{\left(\frac{x}{3} - \frac{\pi}{2} \right)} - \cos{\left(x - \frac{\pi}{2} \right)}}{4 \left(x^{2} + 1\right)}$$

   3/  pi   x\                                
cos |- -- + -|                                
    \  2    3/      2/  pi   x\            /x\
-------------- + cos |- -- + -|*atan(x)*cos|-|
         2           \  2    3/            \3/
    1 + x

$$\cos{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)} \operatorname{atan}{\left(x \right)} + \frac{\cos^{3}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}{x^{2} + 1}$$

               /x\                                           
-sin(x) + 3*sin|-|                                           
               \3/        2/x\    4/x\ /        1   \        
------------------ + 4*cos |-|*sin |-|*|-1 + -------|*atan(x)
      /     2\             \6/     \6/ |        2/x\|        
    4*\1 + x /                         |     tan |-||        
                                       \         \6//

$$4 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{6} \right)}}\right) \sin^{4}{\left(\frac{x}{6} \right)} \cos^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

/                        4/x\ \                          /x\
|                     sin |-| |           -sin(x) + 3*sin|-|
|     2/x\    2/x\        \3/ |                          \3/
|- sin |-|*sin |-| + ---------|*atan(x) + ------------------
|      \3/     \6/        2/x\|                 /     2\    
|                    4*sin |-||               4*\1 + x /    
\                          \6//

$$\left(- \sin^{2}{\left(\frac{x}{6} \right)} \sin^{2}{\left(\frac{x}{3} \right)} + \frac{\sin^{4}{\left(\frac{x}{3} \right)}}{4 \sin^{2}{\left(\frac{x}{6} \right)}}\right) \operatorname{atan}{\left(x \right)} + \frac{3 \sin{\left(\frac{x}{3} \right)} - \sin{\left(x \right)}}{4 \left(x^{2} + 1\right)}$$

         /x\           /x\                                                   
    2*tan|-|      6*tan|-|                                                   
         \2/           \6/                                                   
- ----------- + -----------                   6                              
         2/x\          2/x\     /       2/x \\     2/x\ /       2/x\\        
  1 + tan |-|   1 + tan |-|   4*|1 - tan |--|| *tan |-|*|1 - tan |-||*atan(x)
          \2/           \6/     \        \12//      \6/ \        \6//        
--------------------------- + -----------------------------------------------
           /     2\                                         6                
         4*\1 + x /                           /       2/x \\                 
                                              |1 + tan |--||                 
                                              \        \12//

$$\frac{4 \left(1 - \tan^{2}{\left(\frac{x}{12} \right)}\right)^{6} \left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right) \tan^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)}}{\left(\tan^{2}{\left(\frac{x}{12} \right)} + 1\right)^{6}} + \frac{- \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{6 \tan{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} + 1}}{4 \left(x^{2} + 1\right)}$$

            3/x\               2/x\ /        2/x\\        
       8*cot |-|          4*cot |-|*|-1 + cot |-||*atan(x)
             \6/                \6/ \         \6//        
----------------------- + --------------------------------
                      3                         3         
/     2\ /       2/x\\             /       2/x\\          
\1 + x /*|1 + cot |-||             |1 + cot |-||          
         \        \6//             \        \6//

$$\frac{4 \left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right) \cot^{2}{\left(\frac{x}{6} \right)} \operatorname{atan}{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{6} \right)} + 1\right)^{3}} + \frac{8 \cot^{3}{\left(\frac{x}{6} \right)}}{\left(x^{2} + 1\right) \left(\cot^{2}{\left(\frac{x}{6} \right)} + 1\right)^{3}}$$

                      /          2/x\   \        
                      |       csc |-|   |        
    1        3        |           \6/   |        
- ------ + ------   4*|-1 + ------------|*atan(x)
  csc(x)      /x\     |        2/pi   x\|        
           csc|-|     |     csc |-- - -||        
              \3/     \         \2    6//        
----------------- + -----------------------------
      /     2\              4/x\    2/pi   x\    
    4*\1 + x /           csc |-|*csc |-- - -|    
                             \6/     \2    6/

$$\frac{4 \left(\frac{\csc^{2}{\left(\frac{x}{6} \right)}}{\csc^{2}{\left(- \frac{x}{6} + \frac{\pi}{2} \right)}} - 1\right) \operatorname{atan}{\left(x \right)}}{\csc^{4}{\left(\frac{x}{6} \right)} \csc^{2}{\left(- \frac{x}{6} + \frac{\pi}{2} \right)}} + \frac{- \frac{1}{\csc{\left(x \right)}} + \frac{3}{\csc{\left(\frac{x}{3} \right)}}}{4 \left(x^{2} + 1\right)}$$

(-1/csc(x) + 3/csc(x/3))/(4*(1 + x^2)) + 4*(-1 + csc(x/6)^2/csc(pi/2 - x/6)^2)*atan(x)/(csc(x/6)^4*csc(pi/2 - x/6)^2)

Respuesta numérica [src]

sin(x/3)^3/(1.0 + x^2) + sin(x/3)^2*atan(x)*cos(x/3)

sin(x/3)^3/(1.0 + x^2) + sin(x/3)^2*atan(x)*cos(x/3)

Potencias [src]

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

                   2 / -I*x     I*x\                               
  /   -I*x     I*x\  | -----    ---|                              3
  |   -----    ---|  |   3       3 |             /   -I*x     I*x\ 
  |     3       3 |  |e        e   |             |   -----    ---| 
  \- e      + e   / *|------ + ----|*atan(x)     |     3       3 | 
                     \  2       2  /           I*\- e      + e   / 
- ------------------------------------------ + --------------------
                      4                               /     2\     
                                                    8*\1 + x /

$$- \frac{\left(\frac{e^{\frac{i x}{3}}}{2} + \frac{e^{- \frac{i x}{3}}}{2}\right) \left(e^{\frac{i x}{3}} - e^{- \frac{i x}{3}}\right)^{2} \operatorname{atan}{\left(x \right)}}{4} + \frac{i \left(e^{\frac{i x}{3}} - e^{- \frac{i x}{3}}\right)^{3}}{8 \left(x^{2} + 1\right)}$$

-(-exp(-i*x/3) + exp(i*x/3))^2*(exp(-i*x/3)/2 + exp(i*x/3)/2)*atan(x)/4 + i*(-exp(-i*x/3) + exp(i*x/3))^3/(8*(1 + x^2))

Denominador común [src]

   3/x\                         
sin |-|                         
    \3/      2/x\            /x\
------- + sin |-|*atan(x)*cos|-|
      2       \3/            \3/
 1 + x

$$\sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(\frac{x}{3} \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{x^{2} + 1}$$

sin(x/3)^3/(1 + x^2) + sin(x/3)^2*atan(x)*cos(x/3)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta sin(x/3)^3/(1+x^2)+sin(x/3)^2*atan(x)*cos(x/3) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta sin(x/3)^3/(1+x^2)+sin(x/3)^2atan(x)cos(x/3) expresión en fracciones?