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¿cómo vas a descomponer esta expresión en fracciones?:
(y+z+y*z/x)*(x+y+x*y/z+x+z+x*z/y)/(2*(x+y+z)+y*z/x+x*y/z+x*z/y)
(a-2)/(a^2*x-a^2-4*x+4)
1/(3,94436∙〖10〗^(-7))
1/(a*x-1)
Factorizar el polinomio:
y^5-y^3-y+1
y^3+y^3
y^3+8
y^3-y^2-y-2
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4+8*y^2-13
-y^4+9*y^2-13
Expresiones idénticas
sin(x)^(sqrt(x))*(log(sin(x))/(dos *sqrt(x))+sqrt(x)*cos(x)/sin(x))
seno de (x) en el grado ( raíz cuadrada de (x)) multiplicar por ( logaritmo de ( seno de (x)) dividir por (2 multiplicar por raíz cuadrada de (x)) más raíz cuadrada de (x) multiplicar por coseno de (x) dividir por seno de (x))
seno de (x) en el grado ( raíz cuadrada de (x)) multiplicar por ( logaritmo de ( seno de (x)) dividir por (dos multiplicar por raíz cuadrada de (x)) más raíz cuadrada de (x) multiplicar por coseno de (x) dividir por seno de (x))
sin(x)^(√(x))*(log(sin(x))/(2*√(x))+√(x)*cos(x)/sin(x))
sin(x)(sqrt(x))*(log(sin(x))/(2*sqrt(x))+sqrt(x)*cos(x)/sin(x))
sinxsqrtx*logsinx/2*sqrtx+sqrtx*cosx/sinx
sin(x)^(sqrt(x))(log(sin(x))/(2sqrt(x))+sqrt(x)cos(x)/sin(x))
sin(x)(sqrt(x))(log(sin(x))/(2sqrt(x))+sqrt(x)cos(x)/sin(x))
sinxsqrtxlogsinx/2sqrtx+sqrtxcosx/sinx
sinx^sqrtxlogsinx/2sqrtx+sqrtxcosx/sinx
sin(x)^(sqrt(x))*(log(sin(x)) dividir por (2*sqrt(x))+sqrt(x)*cos(x) dividir por sin(x))
Expresiones semejantes
sin(x)^(sqrt(x))*(log(sin(x))/(2*sqrt(x))-sqrt(x)*cos(x)/sin(x))
sinx^(sqrt(x))*(log(sinx)/(2*sqrt(x))+sqrt(x)*cosx/sinx)
Expresiones con funciones
Seno sin
sin^2a/(1-cosa)
sin(x)/(x-sin(x))+(-1+cos(x))*(2-cos(x))/(x-sin(x))^2
sin(x)/(tg(pi/4-x/2)*(1+sin(x)))
sin(x)/(a*sqrt(1-cos(x)^2/(a^2)))
sin(x)^(3)/(1+cos(x))+sin(x)^(3)/(1*cos(x))
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(1-x^2)/(1-x^2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x)/(x-16)-sqrt(x)/((4-sqrt(x))^2)*(m^2-8*m+16)/4*sqrt(m)
Logaritmo log
log(x^2+1)/2-log(x)+atan(x)/2+(x-2)/(2+2*x^2)
log(x^4-x^2+5)/4+atan((2*x^2-1)/sqrt(19))/(2*sqrt(19))
log(x)*((5*x-a)/(6*x+a))
log(x^2+3*x-1)/2-(3*log((2*x-sqrt(13)+3)/(2*x+sqrt(13)+3)))/(2*sqrt(13))
log(x+1)/4+(3*log(x-1))/4+3/(2+2*x)
Seno sin
sin^2a/(1-cosa)
sin(x)/(x-sin(x))+(-1+cos(x))*(2-cos(x))/(x-sin(x))^2
sin(x)/(tg(pi/4-x/2)*(1+sin(x)))
sin(x)/(a*sqrt(1-cos(x)^2/(a^2)))
sin(x)^(3)/(1+cos(x))+sin(x)^(3)/(1*cos(x))
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(1-x^2)/(1-x^2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x)/(x-16)-sqrt(x)/((4-sqrt(x))^2)*(m^2-8*m+16)/4*sqrt(m)
Raíz cuadrada sqrt
Sqrt(2b+2*sqrt(b^2-4))/(sqrt(b^2-4)+b+2)
sqrt(1-x^2)/(1-x^2)
sqrt(x/(x-a^2))/((2*x^2-2*a^2)/a^2)
sqrt(x)/(-(x^7))
sqrt(x)/(x-16)-sqrt(x)/((4-sqrt(x))^2)*(m^2-8*m+16)/4*sqrt(m)
Coseno cos
cos(2*x)*x/(cos(x)+sin(x))-cos(x)
cos(10*a)/(sin(5*a)-cos(5*a))
cos(x)/(x^2+cos(x))+(-2*x+sin(x))*sin(x)/(x^2+cos(x))^2
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
cos(x)*exp(sqrt(sin(x)))/(2*sqrt(sin(x)))
Seno sin
sin^2a/(1-cosa)
sin(x)/(x-sin(x))+(-1+cos(x))*(2-cos(x))/(x-sin(x))^2
sin(x)/(tg(pi/4-x/2)*(1+sin(x)))
sin(x)/(a*sqrt(1-cos(x)^2/(a^2)))
sin(x)^(3)/(1+cos(x))+sin(x)^(3)/(1*cos(x))

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))/(2sqrt(x))+sqrt(x)*cos(x)/sin(x)) expresión en fracciones?

Solución

Ha introducido [src]

          ___ /                ___       \
        \/ x  |log(sin(x))   \/ x *cos(x)|
(sin(x))     *|----------- + ------------|
              |      ___        sin(x)   |
              \  2*\/ 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

$$\frac{\left(x \cos{\left(x \right)} + \frac{\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}}{2}\right) \sin^{\sqrt{x} - 1}{\left(x \right)}}{\sqrt{x}}$$

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)

$$\frac{\left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}}$$

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)

$$\frac{\left(2 x \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)}\right) \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}}$$

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

$$\frac{2 x \sin^{\sqrt{x} - 1}{\left(x \right)} \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x} - 1}{\left(x \right)}}{2 \sqrt{x}}$$

(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        /

$$\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2}\right)^{\sqrt{x}} \left(\frac{2 i \sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{e^{i x} - e^{- i x}} + \frac{\log{\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}}{2 \sqrt{x}}\right)$$

(-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

$$\frac{\sqrt{x} \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x}}$$

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 / /

$$\left(\frac{\sqrt{x} \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}}{2 \sqrt{x}}\right) \cos^{\sqrt{x}}{\left(x - \frac{\pi}{2} \right)}$$

              /  ___ /  1         /x\\              \
              |\/ x *|------ - tan|-||              |
              |      |   /x\      \2/|              |
          ___ |      |tan|-|         |              |
        \/ x  |      \   \2/         /   log(sin(x))|
(sin(x))     *|----------------------- + -----------|
              |           2                    ___  |
              \                            2*\/ x   /

$$\left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \frac{1}{\tan{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

          ___                             
        \/ x  /  ___          log(sin(x))\
(sin(x))     *|\/ x *cot(x) + -----------|
              |                     ___  |
              \                 2*\/ x   /

$$\left(\sqrt{x} \cot{\left(x \right)} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

                   /      /   /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 //

$$\left(\frac{\sqrt{x} \left(- \frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + \frac{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}}$$

          ___ /  ___               \
        \/ x  |\/ x     log(sin(x))|
(sin(x))     *|------ + -----------|
              |tan(x)         ___  |
              \           2*\/ x   /

$$\left(\frac{\sqrt{x}}{\tan{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

          ___ /                ___         \
        \/ x  |log(sin(x))   \/ x *sin(2*x)|
(sin(x))     *|----------- + --------------|
              |      ___            2      |
              \  2*\/ x        2*sin (x)   /

$$\left(\frac{\sqrt{x} \sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

                   /                  /       /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//

$$\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\sqrt{x} \cot{\left(x \right)} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

                   /   /       /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/     /

$$\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{2 \tan{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

                   /                               /       /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//

$$\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\cot{\left(\frac{x}{2} \right)} - \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

              /                ___    /    pi\\
          ___ |              \/ x *sin|x + --||
        \/ x  |log(sin(x))            \    2 /|
(sin(x))     *|----------- + -----------------|
              |      ___           sin(x)     |
              \  2*\/ x                       /

$$\left(\frac{\sqrt{x} \sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

                   /   /       /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/      /

$$\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{2 \cot{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

                   /                             /       /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//

$$\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \frac{1}{\tan{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

              /      /                  2/x\\              \
              |      |             2*sin |-||              |
              |  ___ |  sin(x)           \2/|              |
          ___ |\/ x *|---------- - ---------|              |
        \/ x  |      \1 - cos(x)     sin(x) /   log(sin(x))|
(sin(x))     *|------------------------------ + -----------|
              |              2                        ___  |
              \                                   2*\/ x   /

$$\left(\frac{\sqrt{x} \left(- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + \frac{\sin{\left(x \right)}}{1 - \cos{\left(x \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

                   /   /     1     \                    \
                   |log|-----------|                    |
               ___ |   |   /    pi\|     ___    /    pi\|
             \/ x  |   |sec|x - --||   \/ x *sec|x - --||
/     1     \      |   \   \    2 //            \    2 /|
|-----------|     *|---------------- + -----------------|
|   /    pi\|      |        ___              sec(x)     |
|sec|x - --||      \    2*\/ x                          /
\   \    2 //

$$\left(\frac{\sqrt{x} \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sqrt{x}}$$

                   /      /      /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      /

$$\left(\frac{\sqrt{x} \left(\frac{\cos{\left(\frac{x}{2} \right)}}{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}}{2 \sqrt{x}}\right) \cos^{\sqrt{x}}{\left(x - \frac{\pi}{2} \right)}$$

              /      /                 2/x\\              \
              |      |            2*sin |-||              |
              |  ___ |  sin(x)          \2/|              |
              |\/ x *|--------- - ---------|              |
              |      |     2/x\     sin(x) |              |
          ___ |      |2*sin |-|            |              |
        \/ x  |      \      \2/            /   log(sin(x))|
(sin(x))     *|----------------------------- + -----------|
              |              2                       ___  |
              \                                  2*\/ x   /

$$\left(\frac{\sqrt{x} \left(- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

              /  ___ /     /x\      /x\\              \
          ___ |\/ x *|- tan|-| + cot|-||              |
        \/ x  |      \     \2/      \2//   log(sin(x))|
(sin(x))     *|------------------------- + -----------|
              |            2                     ___  |
              \                              2*\/ x   /

$$\left(\frac{\sqrt{x} \left(- \tan{\left(\frac{x}{2} \right)} + \cot{\left(\frac{x}{2} \right)}\right)}{2} + \frac{\log{\left(\sin{\left(x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(x \right)}$$

                   /            /       /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//

$$\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{\sqrt{x}} \left(\frac{\sqrt{x}}{\tan{\left(x \right)}} + \frac{\log{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}}{2 \sqrt{x}}\right)$$

          ___ /   /  1   \               \
        \/ x  |log|------|     ___       |
/  1   \      |   \csc(x)/   \/ x *csc(x)|
|------|     *|----------- + ------------|
\csc(x)/      |      ___        sec(x)   |
              \  2*\/ x                  /

$$\left(\frac{\sqrt{x} \csc{\left(x \right)}}{\sec{\left(x \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}}$$

          ___ /   /  1   \               \
        \/ x  |log|------|     ___       |
/  1   \      |   \csc(x)/   \/ x *csc(x)|
|------|     *|----------- + ------------|
\csc(x)/      |      ___        /pi    \ |
              |  2*\/ x      csc|-- - x| |
              \                 \2     / /

$$\left(\frac{\sqrt{x} \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}}$$

              /      /      /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   /

$$\left(\frac{\sqrt{x} \left(\frac{\csc{\left(\frac{x}{2} \right)}}{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right)}{2} + \frac{\log{\left(\frac{1}{\csc{\left(x \right)}} \right)}}{2 \sqrt{x}}\right) \left(\frac{1}{\csc{\left(x \right)}}\right)^{\sqrt{x}}$$

(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)

$$\frac{2 x \sin^{\sqrt{x}}{\left(x \right)} \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} \sin^{\sqrt{x}}{\left(x \right)}}{2 \sqrt{x} \sin{\left(x \right)}}$$

(sin(x)^(sqrt(x))*log(sin(x))*sin(x) + 2*x*sin(x)^(sqrt(x))*cos(x))/(2*sqrt(x)*sin(x))

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

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