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¿cómo vas a descomponer esta expresión en fracciones?:
45*x*y^2/(75*y^2)
(z^2-m^2)/(z^2*m+z*m^2)-5/z
((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z))
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
Factorizar el polinomio:
y^7-2*y^5
-y^6+1
y*x^2+i*y^3/3
y^8-1
Descomponer al cuadrado:
y^4-9*y^2+10
y^4-9*y^2-15
y^4-9*y^2+4
y^4-9*y^2+2
Expresiones idénticas
tan(x)^(dos *(uno -x)^(dos / tres))*(- cuatro *log(tan(x))/(tres *(uno -x)^(uno / tres))+ dos *(uno -x)^(dos / tres)*(uno +tan(x)^ dos)/tan(x))
tangente de (x) en el grado (2 multiplicar por (1 menos x) en el grado (2 dividir por 3)) multiplicar por ( menos 4 multiplicar por logaritmo de ( tangente de (x)) dividir por (3 multiplicar por (1 menos x) en el grado (1 dividir por 3)) más 2 multiplicar por (1 menos x) en el grado (2 dividir por 3) multiplicar por (1 más tangente de (x) al cuadrado ) dividir por tangente de (x))
tangente de (x) en el grado (dos multiplicar por (uno menos x) en el grado (dos dividir por tres)) multiplicar por ( menos cuatro multiplicar por logaritmo de ( tangente de (x)) dividir por (tres multiplicar por (uno menos x) en el grado (uno dividir por tres)) más dos multiplicar por (uno menos x) en el grado (dos dividir por tres) multiplicar por (uno más tangente de (x) en el grado dos) dividir por tangente de (x))
tan(x)(2*(1-x)(2/3))*(-4*log(tan(x))/(3*(1-x)(1/3))+2*(1-x)(2/3)*(1+tan(x)2)/tan(x))
tanx2*1-x2/3*-4*logtanx/3*1-x1/3+2*1-x2/3*1+tanx2/tanx
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)²)/tan(x))
tan(x) en el grado (2*(1-x) en el grado (2/3))*(-4*log(tan(x))/(3*(1-x) en el grado (1/3))+2*(1-x) en el grado (2/3)*(1+tan(x) en el grado 2)/tan(x))
tan(x)^(2(1-x)^(2/3))(-4log(tan(x))/(3(1-x)^(1/3))+2(1-x)^(2/3)(1+tan(x)^2)/tan(x))
tan(x)(2(1-x)(2/3))(-4log(tan(x))/(3(1-x)(1/3))+2(1-x)(2/3)(1+tan(x)2)/tan(x))
tanx21-x2/3-4logtanx/31-x1/3+21-x2/31+tanx2/tanx
tanx^21-x^2/3-4logtanx/31-x^1/3+21-x^2/31+tanx^2/tanx
tan(x)^(2*(1-x)^(2 dividir por 3))*(-4*log(tan(x)) dividir por (3*(1-x)^(1 dividir por 3))+2*(1-x)^(2 dividir por 3)*(1+tan(x)^2) dividir por tan(x))
Expresiones semejantes
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))-2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1+x)^(2/3)*(1+tan(x)^2)/tan(x))
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1-tan(x)^2)/tan(x))
tan(x)^(2*(1-x)^(2/3))*(4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
tan(x)^(2*(1+x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1+x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
Expresiones con funciones
Tangente tan
tan(x)/x^2+x^(4/5)*(-1-cot(x)^2)-(1+tan(x)^2)/x+4*cot(x)/(5*x^(1/5))
tan(x)/(2*tan(x)^2+2)+x/2
tan(atan((2-1)/(2^3-1))+atan((3-1)/(3^3-1)))
tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))
tan((pi/2)-x)^(2)-(1-sin(2*x))/(1+sin(2*x))
Logaritmo log
log(y)/(2*x)
log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)
log(x+a)/(2*a)-log(x-a)/(2*a)
log(x^2+2)/9-atan(x/sqrt(2))/(9*sqrt(2))-(2*log(x-1))/9-1/(3*x-3)
log((sqrt(1-a^2/x^2)-1)/(sqrt(1-a^2/x^2)+1))
Tangente tan
tan(x)/x^2+x^(4/5)*(-1-cot(x)^2)-(1+tan(x)^2)/x+4*cot(x)/(5*x^(1/5))
tan(x)/(2*tan(x)^2+2)+x/2
tan(atan((2-1)/(2^3-1))+atan((3-1)/(3^3-1)))
tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))
tan((pi/2)-x)^(2)-(1-sin(2*x))/(1+sin(2*x))
Tangente tan
tan(x)/x^2+x^(4/5)*(-1-cot(x)^2)-(1+tan(x)^2)/x+4*cot(x)/(5*x^(1/5))
tan(x)/(2*tan(x)^2+2)+x/2
tan(atan((2-1)/(2^3-1))+atan((3-1)/(3^3-1)))
tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))
tan((pi/2)-x)^(2)-(1-sin(2*x))/(1+sin(2*x))
Tangente tan
tan(x)/x^2+x^(4/5)*(-1-cot(x)^2)-(1+tan(x)^2)/x+4*cot(x)/(5*x^(1/5))
tan(x)/(2*tan(x)^2+2)+x/2
tan(atan((2-1)/(2^3-1))+atan((3-1)/(3^3-1)))
tan(t)^atan(t)*((log(tan(t))/(1+t^2)+(1+tan(t)^2)*atan(t)/tan(t))^2+2*(1+tan(t)^2)*atan(t)-(1+tan(t)^2)^2*atan(t)/tan(t)^2-2*t*log(tan(t))/(1+t^2)^2+2*(1+tan(t)^2)/((1+t^2)*tan(t)))
tan((pi/2)-x)^(2)-(1-sin(2*x))/(1+sin(2*x))

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

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

Solución

Ha introducido [src]

                 2/3 /                          2/3 /       2   \\
        2*(1 - x)    |-4*log(tan(x))   2*(1 - x)   *\1 + tan (x)/|
(tan(x))            *|-------------- + --------------------------|
                     |   3 _______               tan(x)          |
                     \ 3*\/ 1 - x                                /

$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \frac{\left(-1\right) 4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

tan(x)^(2*(1 - x)^(2/3))*((-4*log(tan(x)))/((3*(1 - x)^(1/3))) + ((2*(1 - x)^(2/3))*(1 + tan(x)^2))/tan(x))

Simplificación general [src]

                        2/3                                 
          -1 + 2*(1 - x)    /3 - 3*x                       \
2*(tan(x))                 *|------- - 2*log(tan(x))*tan(x)|
                            |   2                          |
                            \cos (x)                       /
------------------------------------------------------------
                          3 _______                         
                        3*\/ 1 - x

$$\frac{2 \left(\frac{3 - 3 x}{\cos^{2}{\left(x \right)}} - 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}} - 1}{\left(x \right)}}{3 \sqrt[3]{1 - x}}$$

2*tan(x)^(-1 + 2*(1 - x)^(2/3))*((3 - 3*x)/cos(x)^2 - 2*log(tan(x))*tan(x))/(3*(1 - x)^(1/3))

Respuesta numérica [src]

tan(x)^(2.0*(1.0 - x)^0.666666666666667)*(-1.33333333333333*(1.0 - x)^(-0.333333333333333)*log(tan(x)) + 2.0*(1.0 - x)^0.666666666666667*(1.0 + tan(x)^2)/tan(x))

tan(x)^(2.0*(1.0 - x)^0.666666666666667)*(-1.33333333333333*(1.0 - x)^(-0.333333333333333)*log(tan(x)) + 2.0*(1.0 - x)^0.666666666666667*(1.0 + tan(x)^2)/tan(x))

Unión de expresiones racionales [src]

                   2/3                                                  
          2*(1 - x)    /                          /       2   \        \
2*(tan(x))            *\-2*log(tan(x))*tan(x) + 3*\1 + tan (x)/*(1 - x)/
------------------------------------------------------------------------
                             3 _______                                  
                           3*\/ 1 - x *tan(x)

$$\frac{2 \left(3 \left(1 - x\right) \left(\tan^{2}{\left(x \right)} + 1\right) - 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$

2*tan(x)^(2*(1 - x)^(2/3))*(-2*log(tan(x))*tan(x) + 3*(1 + tan(x)^2)*(1 - x))/(3*(1 - x)^(1/3)*tan(x))

Potencias [src]

                 2/3 /                           2/3 /       2   \\
        2*(1 - x)    |  4*log(tan(x))   2*(1 - x)   *\1 + tan (x)/|
(tan(x))            *|- ------------- + --------------------------|
                     |     3 _______              tan(x)          |
                     \   3*\/ 1 - x                               /

$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

       /       2/3\                                               
       \(1 - x)   / /                         2/3 /         2   \\
   2                |  4*log(tan(x))   (1 - x)   *\2 + 2*tan (x)/|
tan (x)            *|- ------------- + --------------------------|
                    |     3 _______              tan(x)          |
                    \   3*\/ 1 - x                               /

$$\left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(2 \tan^{2}{\left(x \right)} + 2\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\tan^{2}{\left(x \right)}\right)^{\left(1 - x\right)^{\frac{2}{3}}}$$

                                 /                                             /                    2\               \
                                 |                                             |    /   I*x    -I*x\ |               |
                                 |       /  /   I*x    -I*x\\              2/3 |    \- e    + e    / | / I*x    -I*x\|
                             2/3 |       |I*\- e    + e    /|   2*I*(1 - x)   *|1 - -----------------|*\e    + e    /|
                    2*(1 - x)    |  4*log|------------------|                  |                   2 |               |
/  /   I*x    -I*x\\             |       |    I*x    -I*x   |                  |     / I*x    -I*x\  |               |
|I*\- e    + e    /|             |       \   e    + e       /                  \     \e    + e    /  /               |
|------------------|            *|- ------------------------- - -----------------------------------------------------|
|    I*x    -I*x   |             |           3 _______                                 I*x    -I*x                   |
\   e    + e       /             \         3*\/ 1 - x                               - e    + e                       /

$$\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(- \frac{2 i \left(1 - x\right)^{\frac{2}{3}} \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1\right) \left(e^{i x} + e^{- i x}\right)}{- e^{i x} + e^{- i x}} - \frac{4 \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                 2/3 /                         2/3 /         2   \\
        2*(1 - x)    |  4*log(tan(x))   (1 - x)   *\2 + 2*tan (x)/|
(tan(x))            *|- ------------- + --------------------------|
                     |     3 _______              tan(x)          |
                     \   3*\/ 1 - x                               /

$$\left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(2 \tan^{2}{\left(x \right)} + 2\right)}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))/(3*(1 - x)^(1/3)) + (1 - x)^(2/3)*(2 + 2*tan(x)^2)/tan(x))

Abrimos la expresión [src]

                 2/3 /         2/3 /       2   \                \
        2*(1 - x)    |2*(1 - x)   *\1 + tan (x)/   4*log(tan(x))|
(tan(x))            *|-------------------------- - -------------|
                     |          tan(x)                3 _______ |
                     \                              3*\/ 1 - x  /

                              2/3                                                                 2/3            
         2/3         2*(1 - x)                                    2/3                    2*(1 - x)               
2*(1 - x)   *(tan(x))                        2/3         2*(1 - x)             4*(tan(x))            *log(tan(x))
--------------------------------- + 2*(1 - x)   *(tan(x))            *tan(x) - ----------------------------------
              tan(x)                                                                        3 _______            
                                                                                          3*\/ 1 - x

$$2 \left(1 - x\right)^{\frac{2}{3}} \tan{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} + \frac{2 \left(1 - x\right)^{\frac{2}{3}} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{\tan{\left(x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x}}$$

2*(1 - x)^(2/3)*tan(x)^(2*(1 - x)^(2/3))/tan(x) + 2*(1 - x)^(2/3)*tan(x)^(2*(1 - x)^(2/3))*tan(x) - 4*tan(x)^(2*(1 - x)^(2/3))*log(tan(x))/(3*(1 - x)^(1/3))

Denominador común [src]

 /                     2/3                              2/3                        2/3                      2/3                                                   2/3\ 
 |            2*(1 - x)           2            2*(1 - x)                  2*(1 - x)                2*(1 - x)                                2            2*(1 - x)   | 
-\- 6*(tan(x))             - 6*tan (x)*(tan(x))             + 6*x*(tan(x))             + 4*(tan(x))            *log(tan(x))*tan(x) + 6*x*tan (x)*(tan(x))            / 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             3 _______                                                                                 
                                                                           3*\/ 1 - x *tan(x)

$$- \frac{6 x \tan^{2}{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} + 6 x \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} + 4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} - 6 \tan^{2}{\left(x \right)} \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)} - 6 \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$

-(-6*tan(x)^(2*(1 - x)^(2/3)) - 6*tan(x)^2*tan(x)^(2*(1 - x)^(2/3)) + 6*x*tan(x)^(2*(1 - x)^(2/3)) + 4*tan(x)^(2*(1 - x)^(2/3))*log(tan(x))*tan(x) + 6*x*tan(x)^2*tan(x)^(2*(1 - x)^(2/3)))/(3*(1 - x)^(1/3)*tan(x))

Compilar la expresión [src]

                 2/3 /                           2/3 /       2   \\
        2*(1 - x)    |  4*log(tan(x))   2*(1 - x)   *\1 + tan (x)/|
(tan(x))            *|- ------------- + --------------------------|
                     |     3 _______              tan(x)          |
                     \   3*\/ 1 - x                               /

tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))/(3*(1 - x)^(1/3)) + 2*(1 - x)^(2/3)*(1 + tan(x)^2)/tan(x))

Denominador racional [src]

                 2/3                                                  
        2*(1 - x)    /                          /       2   \        \
(tan(x))            *\-4*log(tan(x))*tan(x) + 6*\1 + tan (x)/*(1 - x)/
----------------------------------------------------------------------
                            3 _______                                 
                          3*\/ 1 - x *tan(x)

$$\frac{\left(6 \left(1 - x\right) \left(\tan^{2}{\left(x \right)} + 1\right) - 4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$

tan(x)^(2*(1 - x)^(2/3))*(-4*log(tan(x))*tan(x) + 6*(1 + tan(x)^2)*(1 - x))/(3*(1 - x)^(1/3)*tan(x))

Combinatoria [src]

                    2/3                                                            
           2*(1 - x)    /          2                                          2   \
-2*(tan(x))            *\-3 - 3*tan (x) + 3*x + 2*log(tan(x))*tan(x) + 3*x*tan (x)/
-----------------------------------------------------------------------------------
                                   3 _______                                       
                                 3*\/ 1 - x *tan(x)

$$- \frac{2 \left(3 x \tan^{2}{\left(x \right)} + 3 x + 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} - 3 \tan^{2}{\left(x \right)} - 3\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}}{3 \sqrt[3]{1 - x} \tan{\left(x \right)}}$$

-2*tan(x)^(2*(1 - x)^(2/3))*(-3 - 3*tan(x)^2 + 3*x + 2*log(tan(x))*tan(x) + 3*x*tan(x)^2)/(3*(1 - x)^(1/3)*tan(x))

Parte trigonométrica [src]

                          /                                    /       2/pi    \\       \
                      2/3 |       /   /pi    \\                |    csc |-- - x||       |
             2*(1 - x)    |       |csc|-- - x||            2/3 |        \2     /|       |
/   /pi    \\             |       |   \2     /|   2*(1 - x)   *|1 + ------------|*csc(x)|
|csc|-- - x||             |  4*log|-----------|                |         2      |       |
|   \2     /|             |       \   csc(x)  /                \      csc (x)   /       |
|-----------|            *|- ------------------ + --------------------------------------|
\   csc(x)  /             |       3 _______                       /pi    \              |
                          |     3*\/ 1 - x                     csc|-- - x|              |
                          \                                       \2     /              /

$$\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                     /                               /       2   \       \
                     |                           2/3 |    sin (x)|       |
                 2/3 |       /sin(x)\   2*(1 - x)   *|1 + -------|*cos(x)|
        2*(1 - x)    |  4*log|------|                |       2   |       |
/sin(x)\             |       \cos(x)/                \    cos (x)/       |
|------|            *|- ------------- + ---------------------------------|
\cos(x)/             |     3 _______                  sin(x)             |
                     \   3*\/ 1 - x                                      /

$$\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{4 \log{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                 2/3 /       /  1   \                             \
        2*(1 - x)    |  4*log|------|            2/3 /       2   \|
/  1   \             |       \cot(x)/   2*(1 - x)   *\1 + cot (x)/|
|------|            *|- ------------- + --------------------------|
\cot(x)/             |     3 _______              cot(x)          |
                     \   3*\/ 1 - x                               /

$$\left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}}$$

                      2/3 /                             /   /pi    \\\
             2*(1 - x)    |                             |csc|-- - x|||
/   /pi    \\             |                             |   \2     /||
|csc|-- - x||             |                        4*log|-----------||
|   \2     /|             |         2/3                 \   csc(x)  /|
|-----------|            *|4*(1 - x)   *csc(2*x) - ------------------|
\   csc(x)  /             |                             3 _______    |
                          \                           3*\/ 1 - x     /

$$\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(4 \left(1 - x\right)^{\frac{2}{3}} \csc{\left(2 x \right)} - \frac{4 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                        /                                /         4   \         \
                    2/3 |       /     2   \          2/3 |    4*sin (x)|         |
           2*(1 - x)    |       |2*sin (x)|   (1 - x)   *|1 + ---------|*sin(2*x)|
/     2   \             |  4*log|---------|              |       2     |         |
|2*sin (x)|             |       \ sin(2*x)/              \    sin (2*x)/         |
|---------|            *|- ---------------- + -----------------------------------|
\ sin(2*x)/             |      3 _______                       2                 |
                        \    3*\/ 1 - x                     sin (x)              /

$$\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{\left(1 - x\right)^{\frac{2}{3}} \left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                      2/3 /                     /   /    pi\\\
             2*(1 - x)    |                     |cos|x - --|||
/   /    pi\\             |                     |   \    2 /||
|cos|x - --||             |          2/3   4*log|-----------||
|   \    2 /|             | 4*(1 - x)           \   cos(x)  /|
|-----------|            *|------------- - ------------------|
\   cos(x)  /             |   /      pi\        3 _______    |
                          |cos|2*x - --|      3*\/ 1 - x     |
                          \   \      2 /                     /

$$\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\cos{\left(2 x - \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                 2/3                                        
        2*(1 - x)    /         2/3            4*log(tan(x))\
(tan(x))            *|4*(1 - x)   *csc(2*x) - -------------|
                     |                           3 _______ |
                     \                         3*\/ 1 - x  /

$$\left(4 \left(1 - x\right)^{\frac{2}{3}} \csc{\left(2 x \right)} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

                          /                                    /       2/    pi\\       \
                      2/3 |       /   /    pi\\                |    cos |x - --||       |
             2*(1 - x)    |       |cos|x - --||            2/3 |        \    2 /|       |
/   /    pi\\             |       |   \    2 /|   2*(1 - x)   *|1 + ------------|*cos(x)|
|cos|x - --||             |  4*log|-----------|                |         2      |       |
|   \    2 /|             |       \   cos(x)  /                \      cos (x)   /       |
|-----------|            *|- ------------------ + --------------------------------------|
\   cos(x)  /             |       3 _______                       /    pi\              |
                          |     3*\/ 1 - x                     cos|x - --|              |
                          \                                       \    2 /              /

$$\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} - \frac{4 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                 2/3 /       /  1   \                                    \
        2*(1 - x)    |  4*log|------|                                    |
/  1   \             |       \cot(x)/            2/3 /       1   \       |
|------|            *|- ------------- + 2*(1 - x)   *|1 + -------|*cot(x)|
\cot(x)/             |     3 _______                 |       2   |       |
                     \   3*\/ 1 - x                  \    cot (x)/       /

$$\left(2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{1}{\cot^{2}{\left(x \right)}}\right) \cot{\left(x \right)} - \frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}}$$

                 2/3 /                                       2/3\
        2*(1 - x)    |         1                    4*(1 - x)   |
(tan(x))            *|- 4*-----------*log(tan(x)) + ------------|
                     |      3 _______                 sin(2*x)  |
                     \    3*\/ 1 - x                            /

$$\left(- 4 \frac{1}{3 \sqrt[3]{1 - x}} \log{\left(\tan{\left(x \right)} \right)} + \frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

                 2/3 /                           2/3 /       2   \\
        2*(1 - x)    |  4*log(tan(x))   2*(1 - x)   *\1 + tan (x)/|
(tan(x))            *|- ------------- + --------------------------|
                     |     3 _______              tan(x)          |
                     \   3*\/ 1 - x                               /

                          /                                  /   sec(x)  \\
                          |                             4*log|-----------||
                      2/3 |                                  |   /    pi\||
             2*(1 - x)    |                                  |sec|x - --|||
/   sec(x)  \             |         2/3    /      pi\        \   \    2 //|
|-----------|            *|4*(1 - x)   *sec|2*x - --| - ------------------|
|   /    pi\|             |                \      2 /        3 _______    |
|sec|x - --||             \                                3*\/ 1 - x     /
\   \    2 //

$$\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(4 \left(1 - x\right)^{\frac{2}{3}} \sec{\left(2 x - \frac{\pi}{2} \right)} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                     /                               /       2   \       \
                     |                           2/3 |    sec (x)|       |
                 2/3 |       /sec(x)\   2*(1 - x)   *|1 + -------|*csc(x)|
        2*(1 - x)    |  4*log|------|                |       2   |       |
/sec(x)\             |       \csc(x)/                \    csc (x)/       |
|------|            *|- ------------- + ---------------------------------|
\csc(x)/             |     3 _______                  sec(x)             |
                     \   3*\/ 1 - x                                      /

$$\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(1 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}{\sec{\left(x \right)}} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                          /                                    /         2      \            \
                          |       /   sec(x)  \            2/3 |      sec (x)   |    /    pi\|
                          |  4*log|-----------|   2*(1 - x)   *|1 + ------------|*sec|x - --||
                      2/3 |       |   /    pi\|                |       2/    pi\|    \    2 /|
             2*(1 - x)    |       |sec|x - --||                |    sec |x - --||            |
/   sec(x)  \             |       \   \    2 //                \        \    2 //            |
|-----------|            *|- ------------------ + -------------------------------------------|
|   /    pi\|             |       3 _______                          sec(x)                  |
|sec|x - --||             \     3*\/ 1 - x                                                   /
\   \    2 //

$$\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{2 \left(1 - x\right)^{\frac{2}{3}} \left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} - \frac{4 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                    2/3 /                    /     2   \\
           2*(1 - x)    |                    |2*sin (x)||
/     2   \             |         2/3   4*log|---------||
|2*sin (x)|             |4*(1 - x)           \ sin(2*x)/|
|---------|            *|------------ - ----------------|
\ sin(2*x)/             |  sin(2*x)         3 _______   |
                        \                 3*\/ 1 - x    /

$$\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{2 \left(1 - x\right)^{\frac{2}{3}}} \left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}} - \frac{4 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)}}{3 \sqrt[3]{1 - x}}\right)$$

                 2/3 /         2/3                \
        2*(1 - x)    |4*(1 - x)      4*log(tan(x))|
(tan(x))            *|------------ - -------------|
                     |  sin(2*x)        3 _______ |
                     \                3*\/ 1 - x  /

$$\left(\frac{4 \left(1 - x\right)^{\frac{2}{3}}}{\sin{\left(2 x \right)}} - \frac{4 \log{\left(\tan{\left(x \right)} \right)}}{3 \sqrt[3]{1 - x}}\right) \tan^{2 \left(1 - x\right)^{\frac{2}{3}}}{\left(x \right)}$$

tan(x)^(2*(1 - x)^(2/3))*(4*(1 - x)^(2/3)/sin(2*x) - 4*log(tan(x))/(3*(1 - x)^(1/3)))

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

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