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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)^(sqrt(x))*(-3/(2*sqrt(x))+(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))^3/8-3*(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))*(4*sqrt(x)+log(sin(x))/x^(3/2)-4*cos(x)/(sqrt(x)*sin(x))+4*sqrt(x)*cos(x)^2/sin(x)^2)/8+3*log(sin(x))/(8*x^(5/2))+2*sqrt(x)*cos(x)^3/sin(x)^3+2*sqrt(x)*cos(x)/sin(x)-3*cos(x)^2/(2*sqrt(x)*sin(x)^2)-3*cos(x)/(4*x^(3/2)*sin(x)))

¿Cómo vas a descomponer esta sin(x)^(sqrt(x))*(-3/(2*sqrt(x))+(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))^3/8-3*(log(sin(x))/sqrt(x)+2*sqrt(x)*cos(x)/sin(x))*(4*sqrt(x)+log(sin(x))/x^(3/2)-4*cos(x)/(sqrt(x)*sin(x))+4*sqrt(x)*cos(x)^2/sin(x)^2)/8+3*log(sin(x))/(8*x^(5/2))+2*sqrt(x)*cos(x)^3/sin(x)^3+2*sqrt(x)*cos(x)/sin(x)-3*cos(x)^2/(2*sqrt(x)*sin(x)^2)-3*cos(x)/(4*x^(3/2)*sin(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
              /                                          3                                                                                                                                                                                 \
              |            /                  ___       \      /                  ___       \ /                                           ___    2   \                                                                                     |
              |            |log(sin(x))   2*\/ x *cos(x)|      |log(sin(x))   2*\/ x *cos(x)| |    ___   log(sin(x))     4*cos(x)     4*\/ x *cos (x)|                                                                                     |
              |            |----------- + --------------|    3*|----------- + --------------|*|4*\/ x  + ----------- - ------------ + ---------------|                                                                                     |
          ___ |            |     ___          sin(x)    |      |     ___          sin(x)    | |               3/2        ___                 2       |                       ___    3          ___                  2                      |
        \/ x  |     3      \   \/ x                     /      \   \/ x                     / \              x         \/ x *sin(x)       sin (x)    /   3*log(sin(x))   2*\/ x *cos (x)   2*\/ x *cos(x)      3*cos (x)         3*cos(x)  |
(sin(x))     *|- ------- + ------------------------------- - ----------------------------------------------------------------------------------------- + ------------- + --------------- + -------------- - --------------- - -------------|
              |      ___                  8                                                              8                                                      5/2             3              sin(x)           ___    2         3/2       |
              \  2*\/ x                                                                                                                                      8*x             sin (x)                        2*\/ x *sin (x)   4*x   *sin(x)/
(((2xcos⁡(x)sin⁡(x)+(2xcos⁡3(x)sin⁡3(x)+((−3(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)(4xcos⁡2(x)sin⁡2(x)+((4x+log⁡(sin⁡(x))x32)−4cos⁡(x)xsin⁡(x)))8+((2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)38−32x))+3log⁡(sin⁡(x))8x52)))−3cos⁡2(x)2xsin⁡2(x))−3cos⁡(x)4x32sin⁡(x))sin⁡x(x)\left(\left(\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \left(\frac{2 \sqrt{x} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \left(\left(- \frac{3 \left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(\frac{4 \sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \left(\left(4 \sqrt{x} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{\frac{3}{2}}}\right) - \frac{4 \cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}}\right)\right)}{8} + \left(\frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{3}{2 \sqrt{x}}\right)\right) + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right)\right)\right) - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}}\right) - \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
sin(x)^(sqrt(x))*(-3*1/(2*sqrt(x)) + (log(sin(x))/sqrt(x) + ((2*sqrt(x))*cos(x))/sin(x))^3/8 - (3*(log(sin(x))/sqrt(x) + ((2*sqrt(x))*cos(x))/sin(x)))*(4*sqrt(x) + log(sin(x))/x^(3/2) - 4*cos(x)/(sqrt(x)*sin(x)) + ((4*sqrt(x))*cos(x)^2)/sin(x)^2)/8 + (3*log(sin(x)))/((8*x^(5/2))) + ((2*sqrt(x))*cos(x)^3)/sin(x)^3 + ((2*sqrt(x))*cos(x))/sin(x) - 3*cos(x)^2/((2*sqrt(x))*sin(x)^2) - 3*cos(x)/((4*x^(3/2))*sin(x)))
Simplificación general [src] 
               ___ /                                                                                                                                                                                               7                                   /   2                                                    \\
        -3 + \/ x  | 15/2                                  3       17/2    3          19/2    3          17/2    2                15/2    2                13/2    3                      19/2    2             3*x *(log(sin(x))*sin(x) + 2*x*cos(x))*\8*x  - cos(2*x)*log(sin(x)) - 4*x*sin(2*x) + log(sin(x))/|
(sin(x))          *|x    *(log(sin(x))*sin(x) + 2*x*cos(x))  - 12*x    *sin (x) + 16*x    *cos (x) - 12*x    *cos (x)*sin(x) - 6*x    *sin (x)*cos(x) + 3*x    *sin (x)*log(sin(x)) + 16*x    *sin (x)*cos(x) - -------------------------------------------------------------------------------------------------|
                   \                                                                                                                                                                                                                                            2                                                /
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                                                                                                                                                          9                                                                                                                                                       
                                                                                                                                                       8*x
(16x192sin⁡2(x)cos⁡(x)+16x192cos⁡3(x)−12x172sin⁡3(x)−12x172sin⁡(x)cos⁡2(x)+x152(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))3−6x152sin⁡2(x)cos⁡(x)+3x132log⁡(sin⁡(x))sin⁡3(x)−3x7(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))(8x2−4xsin⁡(2x)−log⁡(sin⁡(x))cos⁡(2x)+log⁡(sin⁡(x)))2)sin⁡x−3(x)8x9\frac{\left(16 x^{\frac{19}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 16 x^{\frac{19}{2}} \cos^{3}{\left(x \right)} - 12 x^{\frac{17}{2}} \sin^{3}{\left(x \right)} - 12 x^{\frac{17}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + x^{\frac{15}{2}} \left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{3} - 6 x^{\frac{15}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 x^{\frac{13}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)} - \frac{3 x^{7} \left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \left(8 x^{2} - 4 x \sin{\left(2 x \right)} - \log{\left(\sin{\left(x \right)} \right)} \cos{\left(2 x \right)} + \log{\left(\sin{\left(x \right)} \right)}\right)}{2}\right) \sin^{\sqrt{x} - 3}{\left(x \right)}}{8 x^{9}} 
sin(x)^(-3 + sqrt(x))*(x^(15/2)*(log(sin(x))*sin(x) + 2*x*cos(x))^3 - 12*x^(17/2)*sin(x)^3 + 16*x^(19/2)*cos(x)^3 - 12*x^(17/2)*cos(x)^2*sin(x) - 6*x^(15/2)*sin(x)^2*cos(x) + 3*x^(13/2)*sin(x)^3*log(sin(x)) + 16*x^(19/2)*sin(x)^2*cos(x) - 3*x^7*(log(sin(x))*sin(x) + 2*x*cos(x))*(8*x^2 - cos(2*x)*log(sin(x)) - 4*x*sin(2*x) + log(sin(x)))/2)/(8*x^9)
Respuesta numérica [src] 
sin(x)^(x^0.5)*(1.0*(0.5*x^(-0.5)*log(sin(x)) + x^0.5*cos(x)/sin(x))^3 - 1.5*x^(-0.5) + 0.375*x^(-2.5)*log(sin(x)) - 0.375*(x^(-0.5)*log(sin(x)) + 2.0*x^0.5*cos(x)/sin(x))*(4.0*x^0.5 + x^(-1.5)*log(sin(x)) + 4.0*x^0.5*cos(x)^2/sin(x)^2 - 4.0*x^(-0.5)*cos(x)/sin(x)) + 2.0*x^0.5*cos(x)^3/sin(x)^3 + 2.0*x^0.5*cos(x)/sin(x) - 0.75*x^(-1.5)*cos(x)/sin(x) - 1.5*x^(-0.5)*cos(x)^2/sin(x)^2)
sin(x)^(x^0.5)*(1.0*(0.5*x^(-0.5)*log(sin(x)) + x^0.5*cos(x)/sin(x))^3 - 1.5*x^(-0.5) + 0.375*x^(-2.5)*log(sin(x)) - 0.375*(x^(-0.5)*log(sin(x)) + 2.0*x^0.5*cos(x)/sin(x))*(4.0*x^0.5 + x^(-1.5)*log(sin(x)) + 4.0*x^0.5*cos(x)^2/sin(x)^2 - 4.0*x^(-0.5)*cos(x)/sin(x)) + 2.0*x^0.5*cos(x)^3/sin(x)^3 + 2.0*x^0.5*cos(x)/sin(x) - 0.75*x^(-1.5)*cos(x)/sin(x) - 1.5*x^(-0.5)*cos(x)^2/sin(x)^2)
Denominador común [src] 
              ___                                            ___                             ___                              ___                            ___                                        ___                           ___                                     ___                                    ___                                                   ___                             ___                                     ___                                   ___                                     ___                                             ___                                                             ___                                  ___                   
            \/ x                      19/2    3            \/ x       21/2    3            \/ x        17/2    3            \/ x        10    3            \/ x     15/2    3            3            \/ x        9    2            \/ x               19/2    2            \/ x              13/2    3            \/ x                   7    2            3            \/ x       15/2    2            \/ x               17/2    2            \/ x               10    2            \/ x               19/2    2            \/ x                          8    2            \/ x                          17/2    2            2            \/ x               9    2            \/ x                    
  3*(sin(x))     *log(sin(x))   - 16*x    *cos (x)*(sin(x))      - 8*x    *cos (x)*(sin(x))      + 12*x    *sin (x)*(sin(x))      + 24*x  *cos (x)*(sin(x))      - x    *log (sin(x))*sin (x)*(sin(x))      - 24*x *cos (x)*(sin(x))     *sin(x) - 16*x    *sin (x)*(sin(x))     *cos(x) - 3*x    *sin (x)*(sin(x))     *log(sin(x)) + 3*x *log (sin(x))*sin (x)*(sin(x))      + 6*x    *sin (x)*(sin(x))     *cos(x) + 12*x    *cos (x)*(sin(x))     *sin(x) + 24*x  *sin (x)*(sin(x))     *cos(x) - 12*x    *cos (x)*(sin(x))     *log(sin(x))*sin(x) - 6*x *sin (x)*(sin(x))     *cos(x)*log(sin(x)) - 6*x    *log (sin(x))*sin (x)*(sin(x))     *cos(x) + 12*x *cos (x)*(sin(x))     *log(sin(x))*sin(x)
- --------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
               2                                                                                                                                                                                                                                                                                                                                                   9    3                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                8*x *sin (x)
−3log⁡(sin⁡(x))sin⁡x(x)2−−8x212sin⁡x(x)cos⁡3(x)−12x192log⁡(sin⁡(x))sin⁡(x)sin⁡x(x)cos⁡2(x)−16x192sin⁡2(x)sin⁡x(x)cos⁡(x)−16x192sin⁡x(x)cos⁡3(x)−6x172log⁡(sin⁡(x))2sin⁡2(x)sin⁡x(x)cos⁡(x)+12x172sin⁡3(x)sin⁡x(x)+12x172sin⁡(x)sin⁡x(x)cos⁡2(x)−x152log⁡(sin⁡(x))3sin⁡3(x)sin⁡x(x)+6x152sin⁡2(x)sin⁡x(x)cos⁡(x)−3x132log⁡(sin⁡(x))sin⁡3(x)sin⁡x(x)+24x10sin⁡2(x)sin⁡x(x)cos⁡(x)+24x10sin⁡x(x)cos⁡3(x)+12x9log⁡(sin⁡(x))sin⁡(x)sin⁡x(x)cos⁡2(x)−24x9sin⁡(x)sin⁡x(x)cos⁡2(x)−6x8log⁡(sin⁡(x))sin⁡2(x)sin⁡x(x)cos⁡(x)+3x7log⁡(sin⁡(x))2sin⁡3(x)sin⁡x(x)8x9sin⁡3(x)- \frac{3 \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2} - \frac{- 8 x^{\frac{21}{2}} \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)} - 12 x^{\frac{19}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)} - 16 x^{\frac{19}{2}} \sin^{2}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} - 16 x^{\frac{19}{2}} \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)} - 6 x^{\frac{17}{2}} \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{2}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} + 12 x^{\frac{17}{2}} \sin^{3}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} + 12 x^{\frac{17}{2}} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)} - x^{\frac{15}{2}} \log{\left(\sin{\left(x \right)} \right)}^{3} \sin^{3}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} + 6 x^{\frac{15}{2}} \sin^{2}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} - 3 x^{\frac{13}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} + 24 x^{10} \sin^{2}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} + 24 x^{10} \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)} + 12 x^{9} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)} - 24 x^{9} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)} - 6 x^{8} \log{\left(\sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} + 3 x^{7} \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{3}{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{9} \sin^{3}{\left(x \right)}} 
-3*sin(x)^(sqrt(x))*log(sin(x))/2 - (-16*x^(19/2)*cos(x)^3*sin(x)^(sqrt(x)) - 8*x^(21/2)*cos(x)^3*sin(x)^(sqrt(x)) + 12*x^(17/2)*sin(x)^3*sin(x)^(sqrt(x)) + 24*x^10*cos(x)^3*sin(x)^(sqrt(x)) - x^(15/2)*log(sin(x))^3*sin(x)^3*sin(x)^(sqrt(x)) - 24*x^9*cos(x)^2*sin(x)^(sqrt(x))*sin(x) - 16*x^(19/2)*sin(x)^2*sin(x)^(sqrt(x))*cos(x) - 3*x^(13/2)*sin(x)^3*sin(x)^(sqrt(x))*log(sin(x)) + 3*x^7*log(sin(x))^2*sin(x)^3*sin(x)^(sqrt(x)) + 6*x^(15/2)*sin(x)^2*sin(x)^(sqrt(x))*cos(x) + 12*x^(17/2)*cos(x)^2*sin(x)^(sqrt(x))*sin(x) + 24*x^10*sin(x)^2*sin(x)^(sqrt(x))*cos(x) - 12*x^(19/2)*cos(x)^2*sin(x)^(sqrt(x))*log(sin(x))*sin(x) - 6*x^8*sin(x)^2*sin(x)^(sqrt(x))*cos(x)*log(sin(x)) - 6*x^(17/2)*log(sin(x))^2*sin(x)^2*sin(x)^(sqrt(x))*cos(x) + 12*x^9*cos(x)^2*sin(x)^(sqrt(x))*log(sin(x))*sin(x))/(8*x^9*sin(x)^3)
Denominador racional [src] 
          ___                                                                                                                                                                                                                                                                                                                                                                                                                                                 
        \/ x  /        15/2    13                3/2 /        7    2       11          ___    2    //   3    /   5/2 /   5/2    4    /      3/2    3          ___                                  3\       2    3    /   2    /     3/2            ___ /   2              \       \      5/2    2          \                                    \        9/2    7               \         15/2    3       7   \                15/2    10          \\       \
(sin(x))     *\- 6144*x    *sin  (x)*cos(x) + 4*x   *\- 3072*x *cos (x)*sin  (x) + 2*\/ x *sin (x)*\\sin (x)*\8*x   *\8*x   *sin (x)*\- 24*x   *sin (x) + 2*\/ x *(log(sin(x))*sin(x) + 2*x*cos(x)) / - 16*x *sin (x)*\sin (x)*\- 4*x   *cos(x) + \/ x *\4*x  + log(sin(x))/*sin(x)/ + 4*x   *cos (x)*sin(x)/*(3*log(sin(x))*sin(x) + 6*x*cos(x))/ + 384*x   *sin (x)*log(sin(x))/ + 2048*x    *cos (x)*sin (x)/*sin(x) + 2048*x    *sin  (x)*cos(x)//*sin(x)/
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                                                                                                                                                                                                                             9    14                                                                                                                                                                                                                          
                                                                                                                                                                                                                       8192*x *sin  (x)
(−6144x152sin⁡13(x)cos⁡(x)+4x32(2x(2048x152sin⁡10(x)cos⁡(x)+(2048x152sin⁡7(x)cos⁡3(x)+(384x92log⁡(sin⁡(x))sin⁡7(x)+8x52(8x52(−24x32sin⁡3(x)+2x(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))3)sin⁡4(x)−16x2(6xcos⁡(x)+3log⁡(sin⁡(x))sin⁡(x))(4x52sin⁡(x)cos⁡2(x)+(−4x32cos⁡(x)+x(4x2+log⁡(sin⁡(x)))sin⁡(x))sin⁡2(x))sin⁡3(x)))sin⁡3(x))sin⁡(x))sin⁡2(x)−3072x7sin⁡11(x)cos⁡2(x))sin⁡(x))sin⁡x(x)8192x9sin⁡14(x)\frac{\left(- 6144 x^{\frac{15}{2}} \sin^{13}{\left(x \right)} \cos{\left(x \right)} + 4 x^{\frac{3}{2}} \left(2 \sqrt{x} \left(2048 x^{\frac{15}{2}} \sin^{10}{\left(x \right)} \cos{\left(x \right)} + \left(2048 x^{\frac{15}{2}} \sin^{7}{\left(x \right)} \cos^{3}{\left(x \right)} + \left(384 x^{\frac{9}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin^{7}{\left(x \right)} + 8 x^{\frac{5}{2}} \left(8 x^{\frac{5}{2}} \left(- 24 x^{\frac{3}{2}} \sin^{3}{\left(x \right)} + 2 \sqrt{x} \left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{3}\right) \sin^{4}{\left(x \right)} - 16 x^{2} \left(6 x \cos{\left(x \right)} + 3 \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \left(4 x^{\frac{5}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \left(- 4 x^{\frac{3}{2}} \cos{\left(x \right)} + \sqrt{x} \left(4 x^{2} + \log{\left(\sin{\left(x \right)} \right)}\right) \sin{\left(x \right)}\right) \sin^{2}{\left(x \right)}\right) \sin^{3}{\left(x \right)}\right)\right) \sin^{3}{\left(x \right)}\right) \sin{\left(x \right)}\right) \sin^{2}{\left(x \right)} - 3072 x^{7} \sin^{11}{\left(x \right)} \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{8192 x^{9} \sin^{14}{\left(x \right)}} 
sin(x)^(sqrt(x))*(-6144*x^(15/2)*sin(x)^13*cos(x) + 4*x^(3/2)*(-3072*x^7*cos(x)^2*sin(x)^11 + 2*sqrt(x)*sin(x)^2*((sin(x)^3*(8*x^(5/2)*(8*x^(5/2)*sin(x)^4*(-24*x^(3/2)*sin(x)^3 + 2*sqrt(x)*(log(sin(x))*sin(x) + 2*x*cos(x))^3) - 16*x^2*sin(x)^3*(sin(x)^2*(-4*x^(3/2)*cos(x) + sqrt(x)*(4*x^2 + log(sin(x)))*sin(x)) + 4*x^(5/2)*cos(x)^2*sin(x))*(3*log(sin(x))*sin(x) + 6*x*cos(x))) + 384*x^(9/2)*sin(x)^7*log(sin(x))) + 2048*x^(15/2)*cos(x)^3*sin(x)^7)*sin(x) + 2048*x^(15/2)*sin(x)^10*cos(x)))*sin(x))/(8192*x^9*sin(x)^14)
Potencias [src] 
                            /                                                                                                                                /                                                             2                         \                                                                                                                                          \
                            |                                                                  3   /     /   /   -I*x    I*x\ \              / I*x    -I*x\\ |             /   /   -I*x    I*x\ \            / I*x    -I*x\                          |                                                                                                                                          |
                            |            /   /   /   -I*x    I*x\ \             / I*x    -I*x\\    |     |-I*\- e     + e   / |          ___ |e      e    || |             |-I*\- e     + e   / |        ___ |e      e    |                          |                                                                                                                                          |
                            |            |   |-I*\- e     + e   / |         ___ |e      e    ||    |3*log|--------------------|   12*I*\/ x *|---- + -----|| |          log|--------------------|   16*\/ x *|---- + -----|        /   I*x      -I*x\|                                                                                                                                          |
                            |            |log|--------------------|   4*I*\/ x *|---- + -----||    |     \         2          /              \ 2       2  /| |    ___      \         2          /            \ 2       2  /    2*I*\2*e    + 2*e    /|                                                    2                               3                                                     |
                        ___ |            |   \         2          /             \ 2       2  /|    |--------------------------- + -------------------------|*|4*\/ x  + ------------------------- - ------------------------ - ----------------------|        /   /   -I*x    I*x\ \        / I*x    -I*x\                  / I*x    -I*x\              / I*x    -I*x\       /   I*x      -I*x\ |
                      \/ x  |            |------------------------- + ------------------------|    |             ___                       -I*x    I*x     | |                      3/2                                2         ___ /   -I*x    I*x\|        |-I*\- e     + e   / |        |e      e    |              ___ |e      e    |          ___ |e      e    |       |3*e      3*e    | |
/   /   -I*x    I*x\ \      |            |            ___                     -I*x    I*x     |    \           \/ x                     - e     + e        / |                     x                   /   -I*x    I*x\        \/ x *\- e     + e   /|   3*log|--------------------|      6*|---- + -----|       16*I*\/ x *|---- + -----|    4*I*\/ x *|---- + -----|     I*|------ + -------| |
|-I*\- e     + e   / |      |     3      \          \/ x                   - e     + e        /                                                              \                                         \- e     + e   /                              /        \         2          /        \ 2       2  /                  \ 2       2  /              \ 2       2  /       \  2         2   / |
|--------------------|     *|- ------- + ------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------- + ----------------------- - -------------------------- + ------------------------ - -----------------------|
\         2          /      |      ___                              8                                                                                                       8                                                                                          5/2                                   2                       3                -I*x    I*x           3/2 /   -I*x    I*x\|
                            |  2*\/ x                                                                                                                                                                                                                               8*x                  ___ /   -I*x    I*x\        /   -I*x    I*x\              - e     + e           2*x   *\- e     + e   /|
                            \                                                                                                                                                                                                                                                          \/ x *\- e     + e   /        \- e     + e   /                                                           /
(−i(eix−e−ix)2)x(−16ix(eix2+e−ix2)3(eix−e−ix)3+4ix(eix2+e−ix2)eix−e−ix+(4ix(eix2+e−ix2)eix−e−ix+log⁡(−i(eix−e−ix)2)x)38−(12ix(eix2+e−ix2)eix−e−ix+3log⁡(−i(eix−e−ix)2)x)(−16x(eix2+e−ix2)2(eix−e−ix)2+4x−2i(2eix+2e−ix)x(eix−e−ix)+log⁡(−i(eix−e−ix)2)x32)8+6(eix2+e−ix2)2x(eix−e−ix)2−32x−i(3eix2+3e−ix2)2x32(eix−e−ix)+3log⁡(−i(eix−e−ix)2)8x52)\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)^{\sqrt{x}} \left(- \frac{16 i \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{3}}{\left(e^{i x} - e^{- i x}\right)^{3}} + \frac{4 i \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{e^{i x} - e^{- i x}} + \frac{\left(\frac{4 i \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{e^{i x} - e^{- i x}} + \frac{\log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{\left(\frac{12 i \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{e^{i x} - e^{- i x}} + \frac{3 \log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{\sqrt{x}}\right) \left(- \frac{16 \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\left(e^{i x} - e^{- i x}\right)^{2}} + 4 \sqrt{x} - \frac{2 i \left(2 e^{i x} + 2 e^{- i x}\right)}{\sqrt{x} \left(e^{i x} - e^{- i x}\right)} + \frac{\log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{x^{\frac{3}{2}}}\right)}{8} + \frac{6 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\sqrt{x} \left(e^{i x} - e^{- i x}\right)^{2}} - \frac{3}{2 \sqrt{x}} - \frac{i \left(\frac{3 e^{i x}}{2} + \frac{3 e^{- i x}}{2}\right)}{2 x^{\frac{3}{2}} \left(e^{i x} - e^{- i x}\right)} + \frac{3 \log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{8 x^{\frac{5}{2}}}\right) 
              /                                          3                                                                                                                                                                                 \
              |            /                  ___       \    /                    ___       \ /                                           ___    2   \                                                                                     |
              |            |log(sin(x))   2*\/ x *cos(x)|    |3*log(sin(x))   6*\/ x *cos(x)| |    ___   log(sin(x))     4*cos(x)     4*\/ x *cos (x)|                                                                                     |
              |            |----------- + --------------|    |------------- + --------------|*|4*\/ x  + ----------- - ------------ + ---------------|                                                                                     |
          ___ |            |     ___          sin(x)    |    |      ___           sin(x)    | |               3/2        ___                 2       |                       ___    3          ___                  2                      |
        \/ x  |     3      \   \/ x                     /    \    \/ x                      / \              x         \/ x *sin(x)       sin (x)    /   3*log(sin(x))   2*\/ x *cos (x)   2*\/ x *cos(x)      3*cos (x)         3*cos(x)  |
(sin(x))     *|- ------- + ------------------------------- - ----------------------------------------------------------------------------------------- + ------------- + --------------- + -------------- - --------------- - -------------|
              |      ___                  8                                                              8                                                      5/2             3              sin(x)           ___    2         3/2       |
              \  2*\/ x                                                                                                                                      8*x             sin (x)                        2*\/ x *sin (x)   4*x   *sin(x)/
(2xcos⁡(x)sin⁡(x)+2xcos⁡3(x)sin⁡3(x)+(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)38−(6xcos⁡(x)sin⁡(x)+3log⁡(sin⁡(x))x)(4x+4xcos⁡2(x)sin⁡2(x)−4cos⁡(x)xsin⁡(x)+log⁡(sin⁡(x))x32)8−32x−3cos⁡2(x)2xsin⁡2(x)−3cos⁡(x)4x32sin⁡(x)+3log⁡(sin⁡(x))8x52)sin⁡x(x)\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \sqrt{x} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{\left(\frac{6 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(4 \sqrt{x} + \frac{4 \sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{3}{2 \sqrt{x}} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
sin(x)^(sqrt(x))*(-3/(2*sqrt(x)) + (log(sin(x))/sqrt(x) + 2*sqrt(x)*cos(x)/sin(x))^3/8 - (3*log(sin(x))/sqrt(x) + 6*sqrt(x)*cos(x)/sin(x))*(4*sqrt(x) + log(sin(x))/x^(3/2) - 4*cos(x)/(sqrt(x)*sin(x)) + 4*sqrt(x)*cos(x)^2/sin(x)^2)/8 + 3*log(sin(x))/(8*x^(5/2)) + 2*sqrt(x)*cos(x)^3/sin(x)^3 + 2*sqrt(x)*cos(x)/sin(x) - 3*cos(x)^2/(2*sqrt(x)*sin(x)^2) - 3*cos(x)/(4*x^(3/2)*sin(x)))
Unión de expresiones racionales [src] 
          ___                                                                                                                                                                                                                                                                                     
        \/ x  / 2 /                                 3           3   \       4    3          3    2                2    2                3/2 ///   2              \                    \             2    2   \                                            3                      4    2          \
(sin(x))     *\x *\(log(sin(x))*sin(x) + 2*x*cos(x))  - 12*x*sin (x)/ + 16*x *cos (x) - 12*x *cos (x)*sin(x) - 6*x *sin (x)*cos(x) - 3*x   *\\\4*x  + log(sin(x))/*sin(x) - 4*x*cos(x)/*sin(x) + 4*x *cos (x)/*(log(sin(x))*sin(x) + 2*x*cos(x)) + 3*x*sin (x)*log(sin(x)) + 16*x *sin (x)*cos(x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                             7/2    3                                                                                                                                             
                                                                                                                                          8*x   *sin (x)
(−3x32(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))(4x2cos⁡2(x)+(−4xcos⁡(x)+(4x2+log⁡(sin⁡(x)))sin⁡(x))sin⁡(x))+16x4sin⁡2(x)cos⁡(x)+16x4cos⁡3(x)−12x3sin⁡(x)cos⁡2(x)+x2(−12xsin⁡3(x)+(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))3)−6x2sin⁡2(x)cos⁡(x)+3xlog⁡(sin⁡(x))sin⁡3(x))sin⁡x(x)8x72sin⁡3(x)\frac{\left(- 3 x^{\frac{3}{2}} \left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \left(4 x^{2} \cos^{2}{\left(x \right)} + \left(- 4 x \cos{\left(x \right)} + \left(4 x^{2} + \log{\left(\sin{\left(x \right)} \right)}\right) \sin{\left(x \right)}\right) \sin{\left(x \right)}\right) + 16 x^{4} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 16 x^{4} \cos^{3}{\left(x \right)} - 12 x^{3} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + x^{2} \left(- 12 x \sin^{3}{\left(x \right)} + \left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right)^{3}\right) - 6 x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 x \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{\frac{7}{2}} \sin^{3}{\left(x \right)}} 
sin(x)^(sqrt(x))*(x^2*((log(sin(x))*sin(x) + 2*x*cos(x))^3 - 12*x*sin(x)^3) + 16*x^4*cos(x)^3 - 12*x^3*cos(x)^2*sin(x) - 6*x^2*sin(x)^2*cos(x) - 3*x^(3/2)*(((4*x^2 + log(sin(x)))*sin(x) - 4*x*cos(x))*sin(x) + 4*x^2*cos(x)^2)*(log(sin(x))*sin(x) + 2*x*cos(x)) + 3*x*sin(x)^3*log(sin(x)) + 16*x^4*sin(x)^2*cos(x))/(8*x^(7/2)*sin(x)^3)
Compilar la expresión [src] 
              /                                          3                                                                                                                                                                                 \
              |            /                  ___       \    /                    ___       \ /                                           ___    2   \                                                                                     |
              |            |log(sin(x))   2*\/ x *cos(x)|    |3*log(sin(x))   6*\/ x *cos(x)| |    ___   log(sin(x))     4*cos(x)     4*\/ x *cos (x)|                                                                                     |
              |            |----------- + --------------|    |------------- + --------------|*|4*\/ x  + ----------- - ------------ + ---------------|                                                                                     |
          ___ |            |     ___          sin(x)    |    |      ___           sin(x)    | |               3/2        ___                 2       |                       ___    3          ___                  2                      |
        \/ x  |     3      \   \/ x                     /    \    \/ x                      / \              x         \/ x *sin(x)       sin (x)    /   3*log(sin(x))   2*\/ x *cos (x)   2*\/ x *cos(x)      3*cos (x)         3*cos(x)  |
(sin(x))     *|- ------- + ------------------------------- - ----------------------------------------------------------------------------------------- + ------------- + --------------- + -------------- - --------------- - -------------|
              |      ___                  8                                                              8                                                      5/2             3              sin(x)           ___    2         3/2       |
              \  2*\/ x                                                                                                                                      8*x             sin (x)                        2*\/ x *sin (x)   4*x   *sin(x)/
(2xcos⁡(x)sin⁡(x)+2xcos⁡3(x)sin⁡3(x)+(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)38−(6xcos⁡(x)sin⁡(x)+3log⁡(sin⁡(x))x)(4x+4xcos⁡2(x)sin⁡2(x)−4cos⁡(x)xsin⁡(x)+log⁡(sin⁡(x))x32)8−32x−3cos⁡2(x)2xsin⁡2(x)−3cos⁡(x)4x32sin⁡(x)+3log⁡(sin⁡(x))8x52)sin⁡x(x)\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \sqrt{x} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{\left(\frac{6 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(4 \sqrt{x} + \frac{4 \sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{3}{2 \sqrt{x}} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
sin(x)^(sqrt(x))*(-3/(2*sqrt(x)) + (log(sin(x))/sqrt(x) + 2*sqrt(x)*cos(x)/sin(x))^3/8 - (3*log(sin(x))/sqrt(x) + 6*sqrt(x)*cos(x)/sin(x))*(4*sqrt(x) + log(sin(x))/x^(3/2) - 4*cos(x)/(sqrt(x)*sin(x)) + 4*sqrt(x)*cos(x)^2/sin(x)^2)/8 + 3*log(sin(x))/(8*x^(5/2)) + 2*sqrt(x)*cos(x)^3/sin(x)^3 + 2*sqrt(x)*cos(x)/sin(x) - 3*cos(x)^2/(2*sqrt(x)*sin(x)^2) - 3*cos(x)/(4*x^(3/2)*sin(x)))
Abrimos la expresión [src] 
              /                                          3                                                                                                                                                                                 \
              |            /                  ___       \                                         /                  ___       \ /              ___    2                                \                                                  |
              |            |log(sin(x))   2*\/ x *cos(x)|                                         |log(sin(x))   2*\/ x *cos(x)| |    ___   4*\/ x *cos (x)   log(sin(x))     4*cos(x)  |                                                  |
              |            |----------- + --------------|                                       3*|----------- + --------------|*|4*\/ x  + --------------- + ----------- - ------------|                                                  |
          ___ |            |     ___          sin(x)    |        ___    3          ___            |     ___          sin(x)    | |                 2               3/2        ___       |                           2                      |
        \/ x  |     3      \   \/ x                     /    2*\/ x *cos (x)   2*\/ x *cos(x)     \   \/ x                     / \              sin (x)           x         \/ x *sin(x)/   3*log(sin(x))      3*cos (x)         3*cos(x)  |
(sin(x))     *|- ------- + ------------------------------- + --------------- + -------------- - ----------------------------------------------------------------------------------------- + ------------- - --------------- - -------------|
              |      ___                  8                         3              sin(x)                                                   8                                                      5/2          ___    2         3/2       |
              \  2*\/ x                                          sin (x)                                                                                                                        8*x         2*\/ x *sin (x)   4*x   *sin(x)/
(2xcos⁡(x)sin⁡(x)+2xcos⁡3(x)sin⁡3(x)+(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)38−3(2xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))x)(4x+4xcos⁡2(x)sin⁡2(x)+log⁡(sin⁡(x))x32−4cos⁡(x)xsin⁡(x))8−32x−3cos⁡2(x)2xsin⁡2(x)−3cos⁡(x)4x32sin⁡(x)+3log⁡(sin⁡(x))8x52)sin⁡x(x)\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \sqrt{x} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{\left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{3 \left(\frac{2 \sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{x}}\right) \left(4 \sqrt{x} + \frac{4 \sqrt{x} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{x^{\frac{3}{2}}} - \frac{4 \cos{\left(x \right)}}{\sqrt{x} \sin{\left(x \right)}}\right)}{8} - \frac{3}{2 \sqrt{x}} - \frac{3 \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
              ___               ___                                   ___                            ___                          ___               ___                                      ___                         ___                 ___                                    ___                     ___                              ___                       ___                           ___                                    ___                           ___                                               ___       
            \/ x              \/ x                     2            \/ x         2                 \/ x       3                 \/ x              \/ x                 3/2    3            \/ x           3            \/ x                \/ x               ___    3            \/ x        ___         \/ x                2            \/ x         2            \/ x                          \/ x               ___    2            \/ x                          \/ x                            2                 \/ x        
  3*(sin(x))        3*(sin(x))     *log(sin(x))   3*cos (x)*(sin(x))        3*log (sin(x))*(sin(x))        log (sin(x))*(sin(x))        3*(sin(x))     *log(sin(x))   x   *cos (x)*(sin(x))        3*x*cos (x)*(sin(x))        3*x*(sin(x))     *cos(x)   2*\/ x *cos (x)*(sin(x))        2*\/ x *(sin(x))     *cos(x)   3*cos (x)*(sin(x))        3*cos (x)*(sin(x))     *log(sin(x))   3*(sin(x))     *cos(x)   3*\/ x *cos (x)*(sin(x))     *log(sin(x))   3*(sin(x))     *cos(x)*log(sin(x))   3*log (sin(x))*(sin(x))     *cos(x)
- --------------- - --------------------------- + ----------------------- - ---------------------------- + -------------------------- + --------------------------- + -------------------------- - ------------------------- - ------------------------ + ----------------------------- + ---------------------------- - ----------------------- - ----------------------------------- - ---------------------- + ----------------------------------------- + ---------------------------------- + -----------------------------------
          ___                    2                           2                             2                            3/2                           5/2                         3                            3                        sin(x)                          3                            sin(x)                      ___    2                            2                          3/2                                    2                                  4*x*sin(x)                              ___                 
      2*\/ x                                              sin (x)                       8*x                          8*x                           8*x                         sin (x)                      sin (x)                                                  sin (x)                                                 2*\/ x *sin (x)                    2*sin (x)                    4*x   *sin(x)                        2*sin (x)                                                                   4*\/ x *sin(x)
x32sin⁡x(x)cos⁡3(x)sin⁡3(x)+3xlog⁡(sin⁡(x))sin⁡x(x)cos⁡2(x)2sin⁡2(x)+2xsin⁡x(x)cos⁡(x)sin⁡(x)+2xsin⁡x(x)cos⁡3(x)sin⁡3(x)−3xsin⁡x(x)cos⁡(x)sin⁡(x)−3xsin⁡x(x)cos⁡3(x)sin⁡3(x)−3log⁡(sin⁡(x))sin⁡x(x)2−3log⁡(sin⁡(x))sin⁡x(x)cos⁡2(x)2sin⁡2(x)+3sin⁡x(x)cos⁡2(x)sin⁡2(x)+3log⁡(sin⁡(x))sin⁡x(x)cos⁡(x)4xsin⁡(x)−3log⁡(sin⁡(x))2sin⁡x(x)8x2+3log⁡(sin⁡(x))2sin⁡x(x)cos⁡(x)4xsin⁡(x)−3sin⁡x(x)2x−3sin⁡x(x)cos⁡2(x)2xsin⁡2(x)+log⁡(sin⁡(x))3sin⁡x(x)8x32−3sin⁡x(x)cos⁡(x)4x32sin⁡(x)+3log⁡(sin⁡(x))sin⁡x(x)8x52\frac{x^{\frac{3}{2}} \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{3 \sqrt{x} \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{2 \sqrt{x} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \sqrt{x} \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3 x \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 x \sin^{\sqrt{x}}{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{3 \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2} - \frac{3 \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{3 \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{4 x \sin{\left(x \right)}} - \frac{3 \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{2}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{4 \sqrt{x} \sin{\left(x \right)}} - \frac{3 \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x}} - \frac{3 \sin^{\sqrt{x}}{\left(x \right)} \cos^{2}{\left(x \right)}}{2 \sqrt{x} \sin^{2}{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}^{3} \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{\frac{3}{2}}} - \frac{3 \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{4 x^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{\frac{5}{2}}} 
-3*sin(x)^(sqrt(x))/(2*sqrt(x)) - 3*sin(x)^(sqrt(x))*log(sin(x))/2 + 3*cos(x)^2*sin(x)^(sqrt(x))/sin(x)^2 - 3*log(sin(x))^2*sin(x)^(sqrt(x))/(8*x^2) + log(sin(x))^3*sin(x)^(sqrt(x))/(8*x^(3/2)) + 3*sin(x)^(sqrt(x))*log(sin(x))/(8*x^(5/2)) + x^(3/2)*cos(x)^3*sin(x)^(sqrt(x))/sin(x)^3 - 3*x*cos(x)^3*sin(x)^(sqrt(x))/sin(x)^3 - 3*x*sin(x)^(sqrt(x))*cos(x)/sin(x) + 2*sqrt(x)*cos(x)^3*sin(x)^(sqrt(x))/sin(x)^3 + 2*sqrt(x)*sin(x)^(sqrt(x))*cos(x)/sin(x) - 3*cos(x)^2*sin(x)^(sqrt(x))/(2*sqrt(x)*sin(x)^2) - 3*cos(x)^2*sin(x)^(sqrt(x))*log(sin(x))/(2*sin(x)^2) - 3*sin(x)^(sqrt(x))*cos(x)/(4*x^(3/2)*sin(x)) + 3*sqrt(x)*cos(x)^2*sin(x)^(sqrt(x))*log(sin(x))/(2*sin(x)^2) + 3*sin(x)^(sqrt(x))*cos(x)*log(sin(x))/(4*x*sin(x)) + 3*log(sin(x))^2*sin(x)^(sqrt(x))*cos(x)/(4*sqrt(x)*sin(x))
Combinatoria [src] 
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        \/ x  /      11/2    3          4    3         6    3          5    3       3    3            3          11/2    2                 4    2                 9/2    3                     3    2                5/2    2            3         2    3                      5    2                 9/2    2                 9/2    2                            4    2            2                7/2    2                             5    2                      \
(sin(x))     *\- 24*x    *cos (x) - 12*x *sin (x) + 8*x *cos (x) + 16*x *cos (x) + x *log (sin(x))*sin (x) - 24*x    *sin (x)*cos(x) - 12*x *cos (x)*sin(x) - 12*x   *sin (x)*log(sin(x)) - 6*x *sin (x)*cos(x) - 3*x   *log (sin(x))*sin (x) + 3*x *sin (x)*log(sin(x)) + 16*x *sin (x)*cos(x) + 24*x   *cos (x)*sin(x) - 12*x   *cos (x)*log(sin(x))*sin(x) + 6*x *log (sin(x))*sin (x)*cos(x) + 6*x   *sin (x)*cos(x)*log(sin(x)) + 12*x *cos (x)*log(sin(x))*sin(x)/
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                                                                                                                                                                                                                             8*x   *sin (x)
(−24x112sin⁡2(x)cos⁡(x)−24x112cos⁡3(x)−12x92log⁡(sin⁡(x))sin⁡3(x)−12x92log⁡(sin⁡(x))sin⁡(x)cos⁡2(x)+24x92sin⁡(x)cos⁡2(x)+6x72log⁡(sin⁡(x))sin⁡2(x)cos⁡(x)−3x52log⁡(sin⁡(x))2sin⁡3(x)+8x6cos⁡3(x)+12x5log⁡(sin⁡(x))sin⁡(x)cos⁡2(x)+16x5sin⁡2(x)cos⁡(x)+16x5cos⁡3(x)+6x4log⁡(sin⁡(x))2sin⁡2(x)cos⁡(x)−12x4sin⁡3(x)−12x4sin⁡(x)cos⁡2(x)+x3log⁡(sin⁡(x))3sin⁡3(x)−6x3sin⁡2(x)cos⁡(x)+3x2log⁡(sin⁡(x))sin⁡3(x))sin⁡x(x)8x92sin⁡3(x)\frac{\left(- 24 x^{\frac{11}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 24 x^{\frac{11}{2}} \cos^{3}{\left(x \right)} - 12 x^{\frac{9}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)} - 12 x^{\frac{9}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 24 x^{\frac{9}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 6 x^{\frac{7}{2}} \log{\left(\sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 3 x^{\frac{5}{2}} \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{3}{\left(x \right)} + 8 x^{6} \cos^{3}{\left(x \right)} + 12 x^{5} \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 16 x^{5} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 16 x^{5} \cos^{3}{\left(x \right)} + 6 x^{4} \log{\left(\sin{\left(x \right)} \right)}^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - 12 x^{4} \sin^{3}{\left(x \right)} - 12 x^{4} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + x^{3} \log{\left(\sin{\left(x \right)} \right)}^{3} \sin^{3}{\left(x \right)} - 6 x^{3} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 x^{2} \log{\left(\sin{\left(x \right)} \right)} \sin^{3}{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{8 x^{\frac{9}{2}} \sin^{3}{\left(x \right)}} 
sin(x)^(sqrt(x))*(-24*x^(11/2)*cos(x)^3 - 12*x^4*sin(x)^3 + 8*x^6*cos(x)^3 + 16*x^5*cos(x)^3 + x^3*log(sin(x))^3*sin(x)^3 - 24*x^(11/2)*sin(x)^2*cos(x) - 12*x^4*cos(x)^2*sin(x) - 12*x^(9/2)*sin(x)^3*log(sin(x)) - 6*x^3*sin(x)^2*cos(x) - 3*x^(5/2)*log(sin(x))^2*sin(x)^3 + 3*x^2*sin(x)^3*log(sin(x)) + 16*x^5*sin(x)^2*cos(x) + 24*x^(9/2)*cos(x)^2*sin(x) - 12*x^(9/2)*cos(x)^2*log(sin(x))*sin(x) + 6*x^4*log(sin(x))^2*sin(x)^2*cos(x) + 6*x^(7/2)*sin(x)^2*cos(x)*log(sin(x)) + 12*x^5*cos(x)^2*log(sin(x))*sin(x))/(8*x^(9/2)*sin(x)^3)
    © Sr Examen – Калькулятор