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Simplificación de expresiones/ Descomposición en fracciones simples/ sin((x+6)/3)^3/6-1/((x+4)*log(2))/(x+4)-cos((x+6)/3)^2*sin((x+6)/3)/3

¿Cómo vas a descomponer esta sin((x+6)/3)^3/6-1/((x+4)*log(2))/(x+4)-cos((x+6)/3)^2*sin((x+6)/3)/3 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   3/x + 6\                               2/x + 6\    /x + 6\
sin |-----|                            cos |-----|*sin|-----|
    \  3  /             1                  \  3  /    \  3  /
----------- - ---------------------- - ----------------------
     6        (x + 4)*log(2)*(x + 4)             3
−sin⁡(x+63)cos⁡2(x+63)3+(sin⁡3(x+63)6−1(x+4)log⁡(2)(x+4))- \frac{\sin{\left(\frac{x + 6}{3} \right)} \cos^{2}{\left(\frac{x + 6}{3} \right)}}{3} + \left(\frac{\sin^{3}{\left(\frac{x + 6}{3} \right)}}{6} - \frac{1}{\left(x + 4\right) \log{\left(2 \right)} \left(x + 4\right)}\right) 
sin((x + 6)/3)^3/6 - 1/(((x + 4)*log(2))*(x + 4)) - cos((x + 6)/3)^2*sin((x + 6)/3)/3
Simplificación general [src] 
                  /    x\                  
               sin|2 + -|                  
  sin(6 + x)      \    3/          1       
- ---------- + ---------- - ---------------
      8            24              2       
                            (4 + x) *log(2)
sin⁡(x3+2)24−sin⁡(x+6)8−1(x+4)2log⁡(2)\frac{\sin{\left(\frac{x}{3} + 2 \right)}}{24} - \frac{\sin{\left(x + 6 \right)}}{8} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}} 
-sin(6 + x)/8 + sin(2 + x/3)/24 - 1/((4 + x)^2*log(2))
Respuesta numérica [src] 
0.166666666666667*sin((x + 6)/3)^3 - 1/((4.0 + x)*(2.77258872223978 + 0.693147180559945*x)) - 0.333333333333333*cos((x + 6)/3)^2*sin((x + 6)/3)
0.166666666666667*sin((x + 6)/3)^3 - 1/((4.0 + x)*(2.77258872223978 + 0.693147180559945*x)) - 0.333333333333333*cos((x + 6)/3)^2*sin((x + 6)/3)
Combinatoria [src] 
 /          3/    x\           2    3/    x\                 3/    x\                2/    x\           /    x\      2    2/    x\           /    x\           2/    x\           /    x\\ 
-|6 - 16*sin |2 + -|*log(2) - x *sin |2 + -|*log(2) - 8*x*sin |2 + -|*log(2) + 32*cos |2 + -|*log(2)*sin|2 + -| + 2*x *cos |2 + -|*log(2)*sin|2 + -| + 16*x*cos |2 + -|*log(2)*sin|2 + -|| 
 \           \    3/                 \    3/                  \    3/                 \    3/           \    3/            \    3/           \    3/            \    3/           \    3// 
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              2                                                                                            
                                                                                     6*(4 + x) *log(2)
−−x2log⁡(2)sin⁡3(x3+2)+2x2log⁡(2)sin⁡(x3+2)cos⁡2(x3+2)−8xlog⁡(2)sin⁡3(x3+2)+16xlog⁡(2)sin⁡(x3+2)cos⁡2(x3+2)−16log⁡(2)sin⁡3(x3+2)+32log⁡(2)sin⁡(x3+2)cos⁡2(x3+2)+66(x+4)2log⁡(2)- \frac{- x^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 2 x^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 8 x \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 16 x \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 16 \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 32 \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} + 6}{6 \left(x + 4\right)^{2} \log{\left(2 \right)}} 
-(6 - 16*sin(2 + x/3)^3*log(2) - x^2*sin(2 + x/3)^3*log(2) - 8*x*sin(2 + x/3)^3*log(2) + 32*cos(2 + x/3)^2*log(2)*sin(2 + x/3) + 2*x^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3) + 16*x*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(6*(4 + x)^2*log(2))
Unión de expresiones racionales [src] 
            2    3/    x\                   2    2/    x\           /    x\
-6 + (4 + x) *sin |2 + -|*log(2) - 2*(4 + x) *cos |2 + -|*log(2)*sin|2 + -|
                  \    3/                         \    3/           \    3/
---------------------------------------------------------------------------
                                      2                                    
                             6*(4 + x) *log(2)
(x+4)2log⁡(2)sin⁡3(x3+2)−2(x+4)2log⁡(2)sin⁡(x3+2)cos⁡2(x3+2)−66(x+4)2log⁡(2)\frac{\left(x + 4\right)^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} - 2 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 6}{6 \left(x + 4\right)^{2} \log{\left(2 \right)}} 
(-6 + (4 + x)^2*sin(2 + x/3)^3*log(2) - 2*(4 + x)^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(6*(4 + x)^2*log(2))
Abrimos la expresión [src] 
   3/x + 6\                        2/x + 6\    /x + 6\
sin |-----|                     cos |-----|*sin|-----|
    \  3  /          1              \  3  /    \  3  /
----------- - --------------- - ----------------------
     6               2                    3           
              (x + 4) *log(2)
−sin⁡(x+63)cos⁡2(x+63)3+sin⁡3(x+63)6−1(x+4)2log⁡(2)- \frac{\sin{\left(\frac{x + 6}{3} \right)} \cos^{2}{\left(\frac{x + 6}{3} \right)}}{3} + \frac{\sin^{3}{\left(\frac{x + 6}{3} \right)}}{6} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}} 
                                          3/x\                                            2/x\    /x\        6       3/x\                                                              4       2       3/x\        5       3/x\               6       2/x\    /x\        3/x\                      2       2       3/x\        3       3/x\    3           3       3/x\                3       2/x\    /x\                2       2/x\    2       /x\        3       3       2/x\    /x\        2/x\           /x\                4       2/x\    2       /x\         5       2/x\    /x\       
                                       sin |-|                                         cos |-|*sin|-|   4*cos (1)*sin |-|                                                         8*cos (1)*sin (1)*sin |-|   8*cos (1)*cos |-|*sin(1)   8*cos (1)*cos |-|*sin|-|   2*cos |-|*cos(1)*sin(1)   4*cos (1)*sin (1)*sin |-|   4*cos (1)*cos |-|*sin (1)   8*cos (1)*cos |-|*sin(1)   28*cos (1)*sin |-|*cos|-|*sin(1)   14*cos (1)*cos |-|*sin (1)*sin|-|   8*cos (1)*sin (1)*sin |-|*cos|-|   7*sin |-|*cos(1)*cos|-|*sin(1)   28*cos (1)*cos |-|*sin (1)*sin|-|   28*cos (1)*sin |-|*cos|-|*sin(1)
                  1                        \3/      2       3/x\        4       3/x\       \3/    \3/                 \3/        2       2/x\    /x\        4       2/x\    /x\                         \3/                 \3/                        \3/    \3/         \3/                                       \3/                 \3/                         \3/                         \3/    \3/                         \3/            \3/                         \3/    \3/         \3/           \3/                         \3/            \3/                  \3/    \3/       
- ---------------------------------- - ------- + cos (1)*sin |-| - 2*cos (1)*sin |-| + -------------- + ----------------- - 2*cos (1)*cos |-|*sin|-| + 4*cos (1)*cos |-|*sin|-| - ------------------------- - ------------------------ - ------------------------ - ----------------------- + ------------------------- + ------------------------- + ------------------------ - -------------------------------- - --------------------------------- - -------------------------------- + ------------------------------ + --------------------------------- + --------------------------------
               2                          6                  \3/                 \3/         3                  3                         \3/    \3/                 \3/    \3/               3                          3                          3                          3                          3                           3                          3                              3                                   3                                  3                                 3                                  3                                  3                
  16*log(2) + x *log(2) + 8*x*log(2)
−2sin⁡3(x3)cos⁡4(1)−sin⁡3(x3)6−8sin⁡2(1)sin⁡3(x3)cos⁡4(1)3+4sin⁡3(x3)cos⁡6(1)3+4sin⁡2(1)sin⁡3(x3)cos⁡2(1)3+sin⁡3(x3)cos⁡2(1)−28sin⁡(1)sin⁡2(x3)cos⁡3(1)cos⁡(x3)3−8sin⁡3(1)sin⁡2(x3)cos⁡3(1)cos⁡(x3)3+28sin⁡(1)sin⁡2(x3)cos⁡5(1)cos⁡(x3)3+7sin⁡(1)sin⁡2(x3)cos⁡(1)cos⁡(x3)3−14sin⁡2(1)sin⁡(x3)cos⁡2(1)cos⁡2(x3)3−2sin⁡(x3)cos⁡2(1)cos⁡2(x3)−8sin⁡(x3)cos⁡6(1)cos⁡2(x3)3+sin⁡(x3)cos⁡2(x3)3+4sin⁡(x3)cos⁡4(1)cos⁡2(x3)+28sin⁡2(1)sin⁡(x3)cos⁡4(1)cos⁡2(x3)3−2sin⁡(1)cos⁡(1)cos⁡3(x3)3−8sin⁡(1)cos⁡5(1)cos⁡3(x3)3+4sin⁡3(1)cos⁡3(1)cos⁡3(x3)3+8sin⁡(1)cos⁡3(1)cos⁡3(x3)3−1x2log⁡(2)+8xlog⁡(2)+16log⁡(2)- 2 \sin^{3}{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} - \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{6} - \frac{8 \sin^{2}{\left(1 \right)} \sin^{3}{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)}}{3} + \frac{4 \sin^{3}{\left(\frac{x}{3} \right)} \cos^{6}{\left(1 \right)}}{3} + \frac{4 \sin^{2}{\left(1 \right)} \sin^{3}{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)}}{3} + \sin^{3}{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} - \frac{28 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{3}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} - \frac{8 \sin^{3}{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{3}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} + \frac{28 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{5}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} + \frac{7 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} - \frac{14 \sin^{2}{\left(1 \right)} \sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} - 2 \sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)} - \frac{8 \sin{\left(\frac{x}{3} \right)} \cos^{6}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} + \frac{\sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} + 4 \sin{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)} + \frac{28 \sin^{2}{\left(1 \right)} \sin{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} - \frac{2 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} - \frac{8 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} + \frac{4 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} + \frac{8 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} - \frac{1}{x^{2} \log{\left(2 \right)} + 8 x \log{\left(2 \right)} + 16 \log{\left(2 \right)}} 
-1/(16*log(2) + x^2*log(2) + 8*x*log(2)) - sin(x/3)^3/6 + cos(1)^2*sin(x/3)^3 - 2*cos(1)^4*sin(x/3)^3 + cos(x/3)^2*sin(x/3)/3 + 4*cos(1)^6*sin(x/3)^3/3 - 2*cos(1)^2*cos(x/3)^2*sin(x/3) + 4*cos(1)^4*cos(x/3)^2*sin(x/3) - 8*cos(1)^4*sin(1)^2*sin(x/3)^3/3 - 8*cos(1)^5*cos(x/3)^3*sin(1)/3 - 8*cos(1)^6*cos(x/3)^2*sin(x/3)/3 - 2*cos(x/3)^3*cos(1)*sin(1)/3 + 4*cos(1)^2*sin(1)^2*sin(x/3)^3/3 + 4*cos(1)^3*cos(x/3)^3*sin(1)^3/3 + 8*cos(1)^3*cos(x/3)^3*sin(1)/3 - 28*cos(1)^3*sin(x/3)^2*cos(x/3)*sin(1)/3 - 14*cos(1)^2*cos(x/3)^2*sin(1)^2*sin(x/3)/3 - 8*cos(1)^3*sin(1)^3*sin(x/3)^2*cos(x/3)/3 + 7*sin(x/3)^2*cos(1)*cos(x/3)*sin(1)/3 + 28*cos(1)^4*cos(x/3)^2*sin(1)^2*sin(x/3)/3 + 28*cos(1)^5*sin(x/3)^2*cos(x/3)*sin(1)/3
Compilar la expresión [src] 
   3/x + 6\                        2/x + 6\    /x + 6\
sin |-----|                     cos |-----|*sin|-----|
    \  3  /          1              \  3  /    \  3  /
----------- - --------------- - ----------------------
     6               2                    3           
              (4 + x) *log(2)
sin⁡3(x+63)6−sin⁡(x+63)cos⁡2(x+63)3−1(x+4)2log⁡(2)\frac{\sin^{3}{\left(\frac{x + 6}{3} \right)}}{6} - \frac{\sin{\left(\frac{x + 6}{3} \right)} \cos^{2}{\left(\frac{x + 6}{3} \right)}}{3} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}} 
sin((x + 6)/3)^3/6 - 1/((4 + x)^2*log(2)) - cos((x + 6)/3)^2*sin((x + 6)/3)/3
Denominador común [src] 
                                          3/    x\      2/    x\    /    x\
                                       sin |2 + -|   cos |2 + -|*sin|2 + -|
                  1                        \    3/       \    3/    \    3/
- ---------------------------------- + ----------- - ----------------------
               2                            6                  3           
  16*log(2) + x *log(2) + 8*x*log(2)
sin⁡3(x3+2)6−sin⁡(x3+2)cos⁡2(x3+2)3−1x2log⁡(2)+8xlog⁡(2)+16log⁡(2)\frac{\sin^{3}{\left(\frac{x}{3} + 2 \right)}}{6} - \frac{\sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)}}{3} - \frac{1}{x^{2} \log{\left(2 \right)} + 8 x \log{\left(2 \right)} + 16 \log{\left(2 \right)}} 
-1/(16*log(2) + x^2*log(2) + 8*x*log(2)) + sin(2 + x/3)^3/6 - cos(2 + x/3)^2*sin(2 + x/3)/3
Potencias [src] 
                                                                                  2                             
                                                        /   /     x\      /    x\\                              
                                                  3     | I*|-2 - -|    I*|2 + -||  /     /     x\      /    x\\
                      /     /     x\      /    x\\      |   \     3/      \    3/|  |   I*|-2 - -|    I*|2 + -||
                      |   I*|-2 - -|    I*|2 + -||      |e             e         |  |     \     3/      \    3/|
                      |     \     3/      \    3/|    I*|----------- + ----------| *\- e           + e         /
         1          I*\- e           + e         /      \     2            2     /                              
- --------------- + ------------------------------- + ----------------------------------------------------------
         2                         48                                             6                             
  (4 + x) *log(2)
i(−ei(−x3−2)+ei(x3+2))348+i(−ei(−x3−2)+ei(x3+2))(ei(−x3−2)2+ei(x3+2)2)26−1(x+4)2log⁡(2)\frac{i \left(- e^{i \left(- \frac{x}{3} - 2\right)} + e^{i \left(\frac{x}{3} + 2\right)}\right)^{3}}{48} + \frac{i \left(- e^{i \left(- \frac{x}{3} - 2\right)} + e^{i \left(\frac{x}{3} + 2\right)}\right) \left(\frac{e^{i \left(- \frac{x}{3} - 2\right)}}{2} + \frac{e^{i \left(\frac{x}{3} + 2\right)}}{2}\right)^{2}}{6} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}} 
   3/    x\                        2/    x\    /    x\
sin |2 + -|                     cos |2 + -|*sin|2 + -|
    \    3/          1              \    3/    \    3/
----------- - --------------- - ----------------------
     6               2                    3           
              (4 + x) *log(2)
sin⁡3(x3+2)6−sin⁡(x3+2)cos⁡2(x3+2)3−1(x+4)2log⁡(2)\frac{\sin^{3}{\left(\frac{x}{3} + 2 \right)}}{6} - \frac{\sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)}}{3} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}} 
sin(2 + x/3)^3/6 - 1/((4 + x)^2*log(2)) - cos(2 + x/3)^2*sin(2 + x/3)/3
Denominador racional [src] 
               2    3/    x\                   2    2/    x\           /    x\
-18 + 3*(4 + x) *sin |2 + -|*log(2) - 6*(4 + x) *cos |2 + -|*log(2)*sin|2 + -|
                     \    3/                         \    3/           \    3/
------------------------------------------------------------------------------
                                        2                                     
                              18*(4 + x) *log(2)
3(x+4)2log⁡(2)sin⁡3(x3+2)−6(x+4)2log⁡(2)sin⁡(x3+2)cos⁡2(x3+2)−1818(x+4)2log⁡(2)\frac{3 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} - 6 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 18}{18 \left(x + 4\right)^{2} \log{\left(2 \right)}} 
(-18 + 3*(4 + x)^2*sin(2 + x/3)^3*log(2) - 6*(4 + x)^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(18*(4 + x)^2*log(2))
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