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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x)^(sqrt(x))*(log(sin(x))/(2*sqrt(x))+sqrt(x)*cos(x)/sin(x))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
          ___ /                ___       \
        \/ x  |log(sin(x))   \/ x *cos(x)|
(sin(x))     *|----------- + ------------|
              |      ___        sin(x)   |
              \  2*\/ x                  /
(xcos⁡(x)sin⁡(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
sin(x)^(sqrt(x))*(log(sin(x))/((2*sqrt(x))) + (sqrt(x)*cos(x))/sin(x))
Simplificación general [src] 
               ___                                
        -1 + \/ x  /           log(sin(x))*sin(x)\
(sin(x))          *|x*cos(x) + ------------------|
                   \                   2         /
--------------------------------------------------
                        ___                       
                      \/ x
(xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x)2)sin⁡x−1(x)x\frac{\left(x \cos{\left(x \right)} + \frac{\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}}{2}\right) \sin^{\sqrt{x} - 1}{\left(x \right)}}{\sqrt{x}} 
sin(x)^(-1 + sqrt(x))*(x*cos(x) + log(sin(x))*sin(x)/2)/sqrt(x)
Respuesta numérica [src] 
sin(x)^(x^0.5)*(0.5*x^(-0.5)*log(sin(x)) + x^0.5*cos(x)/sin(x))
sin(x)^(x^0.5)*(0.5*x^(-0.5)*log(sin(x)) + x^0.5*cos(x)/sin(x))
Unión de expresiones racionales [src] 
          ___                                  
        \/ x                                   
(sin(x))     *(log(sin(x))*sin(x) + 2*x*cos(x))
-----------------------------------------------
                     ___                       
                 2*\/ x *sin(x)
(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))sin⁡x(x)2xsin⁡(x)\frac{\left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}} 
sin(x)^(sqrt(x))*(log(sin(x))*sin(x) + 2*x*cos(x))/(2*sqrt(x)*sin(x))
Combinatoria [src] 
          ___                                  
        \/ x                                   
(sin(x))     *(log(sin(x))*sin(x) + 2*x*cos(x))
-----------------------------------------------
                     ___                       
                 2*\/ x *sin(x)
(2xcos⁡(x)+log⁡(sin⁡(x))sin⁡(x))sin⁡x(x)2xsin⁡(x)\frac{\left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}} 
sin(x)^(sqrt(x))*(log(sin(x))*sin(x) + 2*x*cos(x))/(2*sqrt(x)*sin(x))
Denominador racional [src] 
               ___                                         ___       
        -1 + \/ x                                   -1 + \/ x        
(sin(x))          *log(sin(x))*sin(x) + 2*x*(sin(x))          *cos(x)
---------------------------------------------------------------------
                                   ___                               
                               2*\/ x
2xsin⁡x−1(x)cos⁡(x)+log⁡(sin⁡(x))sin⁡(x)sin⁡x−1(x)2x\frac{2 x \sin^{\sqrt{x} - 1}{\left(x \right)} \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x} - 1}{\left(x \right)}}{2 \sqrt{x}} 
(sin(x)^(-1 + sqrt(x))*log(sin(x))*sin(x) + 2*x*sin(x)^(-1 + sqrt(x))*cos(x))/(2*sqrt(x))
Potencias [src] 
                        ___ /   /   /   -I*x    I*x\ \             / I*x    -I*x\\
                      \/ x  |   |-I*\- e     + e   / |         ___ |e      e    ||
/   /   -I*x    I*x\ \      |log|--------------------|   2*I*\/ x *|---- + -----||
|-I*\- e     + e   / |      |   \         2          /             \ 2       2  /|
|--------------------|     *|------------------------- + ------------------------|
\         2          /      |             ___                    -I*x    I*x     |
                            \         2*\/ x                  - e     + e        /
(−i(eix−e−ix)2)x(2ix(eix2+e−ix2)eix−e−ix+log⁡(−i(eix−e−ix)2)2x)\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)^{\sqrt{x}} \left(\frac{2 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)}}{2 \sqrt{x}}\right) 
(-i*(-exp(-i*x) + exp(i*x))/2)^(sqrt(x))*(log(-i*(-exp(-i*x) + exp(i*x))/2)/(2*sqrt(x)) + 2*i*sqrt(x)*(exp(i*x)/2 + exp(-i*x)/2)/(-exp(-i*x) + exp(i*x)))
Abrimos la expresión [src] 
          ___                               ___       
        \/ x                  ___         \/ x        
(sin(x))     *log(sin(x))   \/ x *(sin(x))     *cos(x)
------------------------- + --------------------------
             ___                      sin(x)          
         2*\/ x
xsin⁡x(x)cos⁡(x)sin⁡(x)+log⁡(sin⁡(x))sin⁡x(x)2x\frac{\sqrt{x} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x}} 
sin(x)^(sqrt(x))*log(sin(x))/(2*sqrt(x)) + sqrt(x)*sin(x)^(sqrt(x))*cos(x)/sin(x)
Parte trigonométrica [src] 
               ___ /   /   /    pi\\               \
             \/ x  |log|cos|x - --||     ___       |
/   /    pi\\      |   \   \    2 //   \/ x *cos(x)|
|cos|x - --||     *|---------------- + ------------|
\   \    2 //      |        ___           /    pi\ |
                   |    2*\/ x         cos|x - --| |
                   \                      \    2 / /
(xcos⁡(x)cos⁡(x−π2)+log⁡(cos⁡(x−π2))2x)cos⁡x(x−π2)\left(\frac{\sqrt{x} \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}}{2 \sqrt{x}}\right) \cos^{\sqrt{x}}{\left(x - \frac{\pi}{2} \right)} 
              /  ___ /  1         /x\\              \
              |\/ x *|------ - tan|-||              |
              |      |   /x\      \2/|              |
          ___ |      |tan|-|         |              |
        \/ x  |      \   \2/         /   log(sin(x))|
(sin(x))     *|----------------------- + -----------|
              |           2                    ___  |
              \                            2*\/ x   /
(x(−tan⁡(x2)+1tan⁡(x2))2+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \frac{1}{\tan{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
          ___                             
        \/ x  /  ___          log(sin(x))\
(sin(x))     *|\/ x *cot(x) + -----------|
              |                     ___  |
              \                 2*\/ x   /
(xcot⁡(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\sqrt{x} \cot{\left(x \right)} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
                   /      /   /x   pi\         /x\  \                   \
                   |      |sec|- - --|      sec|-|  |                   |
                   |  ___ |   \2   2 /         \2/  |      /     1     \|
                   |\/ x *|----------- - -----------|   log|-----------||
               ___ |      |      /x\        /x   pi\|      |   /    pi\||
             \/ x  |      |   sec|-|     sec|- - --||      |sec|x - --|||
/     1     \      |      \      \2/        \2   2 //      \   \    2 //|
|-----------|     *|--------------------------------- + ----------------|
|   /    pi\|      |                2                           ___     |
|sec|x - --||      \                                        2*\/ x      /
\   \    2 //
(x(−sec⁡(x2)sec⁡(x2−π2)+sec⁡(x2−π2)sec⁡(x2))2+log⁡(1sec⁡(x−π2))2x)(1sec⁡(x−π2))x\left(\frac{\sqrt{x} \left(- \frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}} 
          ___ /  ___               \
        \/ x  |\/ x     log(sin(x))|
(sin(x))     *|------ + -----------|
              |tan(x)         ___  |
              \           2*\/ x   /
(xtan⁡(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x}}{\tan{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
          ___ /                ___         \
        \/ x  |log(sin(x))   \/ x *sin(2*x)|
(sin(x))     *|----------- + --------------|
              |      ___            2      |
              \  2*\/ x        2*sin (x)   /
(xsin⁡(2x)2sin⁡2(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
                   /                  /       /x\ \\
                   |                  |  2*cot|-| ||
               ___ |                  |       \2/ ||
             \/ x  |               log|-----------||
/       /x\ \      |                  |       2/x\||
|  2*cot|-| |      |                  |1 + cot |-|||
|       \2/ |      |  ___             \        \2//|
|-----------|     *|\/ x *cot(x) + ----------------|
|       2/x\|      |                       ___     |
|1 + cot |-||      \                   2*\/ x      /
\        \2//
(2cot⁡(x2)cot⁡2(x2)+1)x(xcot⁡(x)+log⁡(2cot⁡(x2)cot⁡2(x2)+1)2x)\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\sqrt{x} \cot{\left(x \right)} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
                   /   /       /x\ \                      \
                   |   |  2*tan|-| |                      |
               ___ |   |       \2/ |                      |
             \/ x  |log|-----------|                      |
/       /x\ \      |   |       2/x\|     ___ /       2/x\\|
|  2*tan|-| |      |   |1 + tan |-||   \/ x *|1 - tan |-|||
|       \2/ |      |   \        \2//         \        \2//|
|-----------|     *|---------------- + -------------------|
|       2/x\|      |        ___                   /x\     |
|1 + tan |-||      |    2*\/ x               2*tan|-|     |
\        \2//      \                              \2/     /
(2tan⁡(x2)tan⁡2(x2)+1)x(x(1−tan⁡2(x2))2tan⁡(x2)+log⁡(2tan⁡(x2)tan⁡2(x2)+1)2x)\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{2 \tan{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
                   /                               /       /x\ \\
                   |                               |  2*cot|-| ||
               ___ |  ___ /    1         /x\\      |       \2/ ||
             \/ x  |\/ x *|- ------ + cot|-||   log|-----------||
/       /x\ \      |      |     /x\      \2/|      |       2/x\||
|  2*cot|-| |      |      |  cot|-|         |      |1 + cot |-|||
|       \2/ |      |      \     \2/         /      \        \2//|
|-----------|     *|------------------------- + ----------------|
|       2/x\|      |            2                       ___     |
|1 + cot |-||      \                                2*\/ x      /
\        \2//
(2cot⁡(x2)cot⁡2(x2)+1)x(x(cot⁡(x2)−1cot⁡(x2))2+log⁡(2cot⁡(x2)cot⁡2(x2)+1)2x)\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\cot{\left(\frac{x}{2} \right)} - \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
              /                ___    /    pi\\
          ___ |              \/ x *sin|x + --||
        \/ x  |log(sin(x))            \    2 /|
(sin(x))     *|----------- + -----------------|
              |      ___           sin(x)     |
              \  2*\/ x                       /
(xsin⁡(x+π2)sin⁡(x)+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
                   /   /       /x\ \                       \
                   |   |  2*cot|-| |                       |
               ___ |   |       \2/ |                       |
             \/ x  |log|-----------|                       |
/       /x\ \      |   |       2/x\|     ___ /        2/x\\|
|  2*cot|-| |      |   |1 + cot |-||   \/ x *|-1 + cot |-|||
|       \2/ |      |   \        \2//         \         \2//|
|-----------|     *|---------------- + --------------------|
|       2/x\|      |        ___                   /x\      |
|1 + cot |-||      |    2*\/ x               2*cot|-|      |
\        \2//      \                              \2/      /
(2cot⁡(x2)cot⁡2(x2)+1)x(x(cot⁡2(x2)−1)2cot⁡(x2)+log⁡(2cot⁡(x2)cot⁡2(x2)+1)2x)\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{2 \cot{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
                   /                             /       /x\ \\
                   |                             |  2*tan|-| ||
               ___ |  ___ /  1         /x\\      |       \2/ ||
             \/ x  |\/ x *|------ - tan|-||   log|-----------||
/       /x\ \      |      |   /x\      \2/|      |       2/x\||
|  2*tan|-| |      |      |tan|-|         |      |1 + tan |-|||
|       \2/ |      |      \   \2/         /      \        \2//|
|-----------|     *|----------------------- + ----------------|
|       2/x\|      |           2                      ___     |
|1 + tan |-||      \                              2*\/ x      /
\        \2//
(2tan⁡(x2)tan⁡2(x2)+1)x(x(−tan⁡(x2)+1tan⁡(x2))2+log⁡(2tan⁡(x2)tan⁡2(x2)+1)2x)\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \frac{1}{\tan{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
              /      /                  2/x\\              \
              |      |             2*sin |-||              |
              |  ___ |  sin(x)           \2/|              |
          ___ |\/ x *|---------- - ---------|              |
        \/ x  |      \1 - cos(x)     sin(x) /   log(sin(x))|
(sin(x))     *|------------------------------ + -----------|
              |              2                        ___  |
              \                                   2*\/ x   /
(x(−2sin⁡2(x2)sin⁡(x)+sin⁡(x)1−cos⁡(x))2+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \left(- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + \frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
                   /   /     1     \                    \
                   |log|-----------|                    |
               ___ |   |   /    pi\|     ___    /    pi\|
             \/ x  |   |sec|x - --||   \/ x *sec|x - --||
/     1     \      |   \   \    2 //            \    2 /|
|-----------|     *|---------------- + -----------------|
|   /    pi\|      |        ___              sec(x)     |
|sec|x - --||      \    2*\/ x                          /
\   \    2 //
(xsec⁡(x−π2)sec⁡(x)+log⁡(1sec⁡(x−π2))2x)(1sec⁡(x−π2))x\left(\frac{\sqrt{x} \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}} 
                   /      /      /x\        /x   pi\\                   \
                   |      |   cos|-|     cos|- - --||                   |
                   |  ___ |      \2/        \2   2 /|                   |
                   |\/ x *|----------- - -----------|                   |
               ___ |      |   /x   pi\         /x\  |      /   /    pi\\|
             \/ x  |      |cos|- - --|      cos|-|  |   log|cos|x - --|||
/   /    pi\\      |      \   \2   2 /         \2/  /      \   \    2 //|
|cos|x - --||     *|--------------------------------- + ----------------|
\   \    2 //      |                2                           ___     |
                   \                                        2*\/ x      /
(x(cos⁡(x2)cos⁡(x2−π2)−cos⁡(x2−π2)cos⁡(x2))2+log⁡(cos⁡(x−π2))2x)cos⁡x(x−π2)\left(\frac{\sqrt{x} \left(\frac{\cos{\left(\frac{x}{2} \right)}}{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}}{2 \sqrt{x}}\right) \cos^{\sqrt{x}}{\left(x - \frac{\pi}{2} \right)} 
              /      /                 2/x\\              \
              |      |            2*sin |-||              |
              |  ___ |  sin(x)          \2/|              |
              |\/ x *|--------- - ---------|              |
              |      |     2/x\     sin(x) |              |
          ___ |      |2*sin |-|            |              |
        \/ x  |      \      \2/            /   log(sin(x))|
(sin(x))     *|----------------------------- + -----------|
              |              2                       ___  |
              \                                  2*\/ x   /
(x(−2sin⁡2(x2)sin⁡(x)+sin⁡(x)2sin⁡2(x2))2+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \left(- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
              /  ___ /     /x\      /x\\              \
          ___ |\/ x *|- tan|-| + cot|-||              |
        \/ x  |      \     \2/      \2//   log(sin(x))|
(sin(x))     *|------------------------- + -----------|
              |            2                     ___  |
              \                              2*\/ x   /
(x(−tan⁡(x2)+cot⁡(x2))2+log⁡(sin⁡(x))2x)sin⁡x(x)\left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \cot{\left(\frac{x}{2} \right)}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)} 
                   /            /       /x\ \\
                   |            |  2*tan|-| ||
               ___ |            |       \2/ ||
             \/ x  |         log|-----------||
/       /x\ \      |            |       2/x\||
|  2*tan|-| |      |  ___       |1 + tan |-|||
|       \2/ |      |\/ x        \        \2//|
|-----------|     *|------ + ----------------|
|       2/x\|      |tan(x)           ___     |
|1 + tan |-||      \             2*\/ x      /
\        \2//
(2tan⁡(x2)tan⁡2(x2)+1)x(xtan⁡(x)+log⁡(2tan⁡(x2)tan⁡2(x2)+1)2x)\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x}}{\tan{\left(x \right)}} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right) 
          ___ /   /  1   \               \
        \/ x  |log|------|     ___       |
/  1   \      |   \csc(x)/   \/ x *csc(x)|
|------|     *|----------- + ------------|
\csc(x)/      |      ___        sec(x)   |
              \  2*\/ x                  /
(xcsc⁡(x)sec⁡(x)+log⁡(1csc⁡(x))2x)(1csc⁡(x))x\left(\frac{\sqrt{x} \csc{\left(x \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}} 
          ___ /   /  1   \               \
        \/ x  |log|------|     ___       |
/  1   \      |   \csc(x)/   \/ x *csc(x)|
|------|     *|----------- + ------------|
\csc(x)/      |      ___        /pi    \ |
              |  2*\/ x      csc|-- - x| |
              \                 \2     / /
(xcsc⁡(x)csc⁡(−x+π2)+log⁡(1csc⁡(x))2x)(1csc⁡(x))x\left(\frac{\sqrt{x} \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}} 
              /      /      /x\        /pi   x\\              \
              |      |   csc|-|     csc|-- - -||              |
              |  ___ |      \2/        \2    2/|              |
              |\/ x *|----------- - -----------|              |
          ___ |      |   /pi   x\         /x\  |      /  1   \|
        \/ x  |      |csc|-- - -|      csc|-|  |   log|------||
/  1   \      |      \   \2    2/         \2/  /      \csc(x)/|
|------|     *|--------------------------------- + -----------|
\csc(x)/      |                2                         ___  |
              \                                      2*\/ x   /
(x(csc⁡(x2)csc⁡(−x2+π2)−csc⁡(−x2+π2)csc⁡(x2))2+log⁡(1csc⁡(x))2x)(1csc⁡(x))x\left(\frac{\sqrt{x} \left(\frac{\csc{\left(\frac{x}{2} \right)}}{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}} 
(1/csc(x))^(sqrt(x))*(sqrt(x)*(csc(x/2)/csc(pi/2 - x/2) - csc(pi/2 - x/2)/csc(x/2))/2 + log(1/csc(x))/(2*sqrt(x)))
Denominador común [src] 
          ___                                    ___       
        \/ x                                   \/ x        
(sin(x))     *log(sin(x))*sin(x) + 2*x*(sin(x))     *cos(x)
-----------------------------------------------------------
                           ___                             
                       2*\/ x *sin(x)
2xsin⁡x(x)cos⁡(x)+log⁡(sin⁡(x))sin⁡(x)sin⁡x(x)2xsin⁡(x)\frac{2 x \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}} 
(sin(x)^(sqrt(x))*log(sin(x))*sin(x) + 2*x*sin(x)^(sqrt(x))*cos(x))/(2*sqrt(x)*sin(x))
    © Sr Examen – Калькулятор