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¿cómo vas a descomponer esta expresión en fracciones?:
(z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
(x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)
1/(3*sqrt(1-x^2/9))
(z*z-1/2*z)/(z*z-z+1)*z/(z-1/2)
Factorizar el polinomio:
z^3/4-2*z^3/9+7*z^3/12
z^3+5*z^2+4*z-10
z^2-8*p^z-z+4*p+16*p^2
z^10*g^20-1
Descomponer al cuadrado:
-y^4+y^2+5
-y^4+y^2+15
y^4-y^2+11
y^4-y^2+1
Expresiones idénticas
cot(cinco *x)^ dos *(- quince - quince *cot(cinco *x)^ dos)*asin(sqrt(x))+cot(cinco *x)^ tres /(dos *sqrt(x)*sqrt(uno -x))
cotangente de (5 multiplicar por x) al cuadrado multiplicar por ( menos 15 menos 15 multiplicar por cotangente de (5 multiplicar por x) al cuadrado ) multiplicar por ar coseno de eno de ( raíz cuadrada de (x)) más cotangente de (5 multiplicar por x) al cubo dividir por (2 multiplicar por raíz cuadrada de (x) multiplicar por raíz cuadrada de (1 menos x))
cotangente de (cinco multiplicar por x) en el grado dos multiplicar por ( menos quince menos quince multiplicar por cotangente de (cinco multiplicar por x) en el grado dos) multiplicar por ar coseno de eno de ( raíz cuadrada de (x)) más cotangente de (cinco multiplicar por x) en el grado tres dividir por (dos multiplicar por raíz cuadrada de (x) multiplicar por raíz cuadrada de (uno menos x))
cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(√(x))+cot(5*x)^3/(2*√(x)*√(1-x))
cot(5*x)2*(-15-15*cot(5*x)2)*asin(sqrt(x))+cot(5*x)3/(2*sqrt(x)*sqrt(1-x))
cot5*x2*-15-15*cot5*x2*asinsqrtx+cot5*x3/2*sqrtx*sqrt1-x
cot(5*x)²*(-15-15*cot(5*x)²)*asin(sqrt(x))+cot(5*x)³/(2*sqrt(x)*sqrt(1-x))
cot(5*x) en el grado 2*(-15-15*cot(5*x) en el grado 2)*asin(sqrt(x))+cot(5*x) en el grado 3/(2*sqrt(x)*sqrt(1-x))
cot(5x)^2(-15-15cot(5x)^2)asin(sqrt(x))+cot(5x)^3/(2sqrt(x)sqrt(1-x))
cot(5x)2(-15-15cot(5x)2)asin(sqrt(x))+cot(5x)3/(2sqrt(x)sqrt(1-x))
cot5x2-15-15cot5x2asinsqrtx+cot5x3/2sqrtxsqrt1-x
cot5x^2-15-15cot5x^2asinsqrtx+cot5x^3/2sqrtxsqrt1-x
cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3 dividir por (2*sqrt(x)*sqrt(1-x))
Expresiones semejantes
cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))-cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))
cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1+x))
cot(5*x)^2*(-15+15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))
cot(5*x)^2*(15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))
cot(5*x)^2*(-15-15*cot(5*x)^2)*arcsin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))
Expresiones con funciones
Cotangente cot
cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2)
cot(p/(2-a))-tan(p+a)+sin(3*p/(2-a))/cos(p+a)
cot(4*x)^2*(-12-12*cot(4*x)^2)*atan(x^3)+3*x^2*cot(4*x)^3/(1+x^6)
cot(4*x)^2*(-12-12*cot(4*x)^2)*acot(2*x^3)-6*x^2*cot(4*x)^3/(1+4*x^6)
cot(x)^cot(pi/(4+x))*((-1-cot(pi/(4+x))^2)*log(cot(x))+(-1-cot(x)^2)*cot(pi/(4+x))/cot(x))
Cotangente cot
cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2)
cot(p/(2-a))-tan(p+a)+sin(3*p/(2-a))/cos(p+a)
cot(4*x)^2*(-12-12*cot(4*x)^2)*atan(x^3)+3*x^2*cot(4*x)^3/(1+x^6)
cot(4*x)^2*(-12-12*cot(4*x)^2)*acot(2*x^3)-6*x^2*cot(4*x)^3/(1+4*x^6)
cot(x)^cot(pi/(4+x))*((-1-cot(pi/(4+x))^2)*log(cot(x))+(-1-cot(x)^2)*cot(pi/(4+x))/cot(x))
Arcoseno arcsin
asin(x/(sqrt(5)*|x-1|)-3/(sqrt(5)*|x-1|))
asin(x)/(x*log(5))+log(x)/(sqrt(1-x^2)*log(5))
asin(x/(sqrt(2)*|x-1|)-sqrt(2)/|x-1|)
asinh((3*x)/(sqrt(7)*|x+1|)-5/(sqrt(7)*|x+1|))/2
asinh(x/(sqrt(3)*|x|)-2/(sqrt(3)*|x|))-asinh((2*x-1)/sqrt(3))/2+sqrt(x^2-x+1)
Raíz cuadrada sqrt
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x)
sqrt(x)*(-1+4*x)+(2*x^2-x)/(2*sqrt(x))
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2)^2)
Cotangente cot
cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2)
cot(p/(2-a))-tan(p+a)+sin(3*p/(2-a))/cos(p+a)
cot(4*x)^2*(-12-12*cot(4*x)^2)*atan(x^3)+3*x^2*cot(4*x)^3/(1+x^6)
cot(4*x)^2*(-12-12*cot(4*x)^2)*acot(2*x^3)-6*x^2*cot(4*x)^3/(1+4*x^6)
cot(x)^cot(pi/(4+x))*((-1-cot(pi/(4+x))^2)*log(cot(x))+(-1-cot(x)^2)*cot(pi/(4+x))/cot(x))
Raíz cuadrada sqrt
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x)
sqrt(x)*(-1+4*x)+(2*x^2-x)/(2*sqrt(x))
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2)^2)
Raíz cuadrada sqrt
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
sqrt(-x/(-1+x))*(-1+x/(-1+x))*(2/x+2/(-1+x)+(-1+x/(-1+x))/x)/(4*x)
sqrt(x)*(-1+4*x)+(2*x^2-x)/(2*sqrt(x))
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2)^2)

Simplificación de expresiones/ Descomposición en fracciones simples/ cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x))

¿Cómo vas a descomponer esta cot(5x)^2(-15-15cot(5x)^2)asin(sqrt(x))+cot(5x)^3/(2sqrt(x)sqrt(1-x)) expresión en fracciones?

Solución

Ha introducido [src]

                                                    3         
   2      /            2     \     /  ___\       cot (5*x)    
cot (5*x)*\-15 - 15*cot (5*x)/*asin\\/ x / + -----------------
                                                 ___   _______
                                             2*\/ x *\/ 1 - x

$$\left(- 15 \cot^{2}{\left(5 x \right)} - 15\right) \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

(cot(5*x)^2*(-15 - 15*cot(5*x)^2))*asin(sqrt(x)) + cot(5*x)^3/(((2*sqrt(x))*sqrt(1 - x)))

Simplificación general [src]

       3                  2          /  ___\
    cot (5*x)       15*cot (5*x)*asin\\/ x /
----------------- - ------------------------
    ___   _______             2             
2*\/ x *\/ 1 - x           sin (5*x)

$$- \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x)) - 15*cot(5*x)^2*asin(sqrt(x))/sin(5*x)^2

Respuesta numérica [src]

cot(5*x)^2*(-15.0 - 15.0*cot(5*x)^2)*asin(sqrt(x)) + 0.5*x^(-0.5)*(1.0 - x)^(-0.5)*cot(5*x)^3

cot(5*x)^2*(-15.0 - 15.0*cot(5*x)^2)*asin(sqrt(x)) + 0.5*x^(-0.5)*(1.0 - x)^(-0.5)*cot(5*x)^3

Denominador racional [src]

    _______    3            3/2    2          /  ___\       3/2    4          /  ___\        ___    2          /  ___\        ___    4          /  ___\
- \/ 1 - x *cot (5*x) - 30*x   *cot (5*x)*asin\\/ x / - 30*x   *cot (5*x)*asin\\/ x / + 30*\/ x *cot (5*x)*asin\\/ x / + 30*\/ x *cot (5*x)*asin\\/ x /
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        ___                                                                            
                                                                    2*\/ x *(-1 + x)

$$\frac{- 30 x^{\frac{3}{2}} \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - 30 x^{\frac{3}{2}} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - \sqrt{1 - x} \cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \left(x - 1\right)}$$

(-sqrt(1 - x)*cot(5*x)^3 - 30*x^(3/2)*cot(5*x)^2*asin(sqrt(x)) - 30*x^(3/2)*cot(5*x)^4*asin(sqrt(x)) + 30*sqrt(x)*cot(5*x)^2*asin(sqrt(x)) + 30*sqrt(x)*cot(5*x)^4*asin(sqrt(x)))/(2*sqrt(x)*(-1 + x))

Unión de expresiones racionales [src]

   2      /     ___   _______ /        2     \     /  ___\           \
cot (5*x)*\30*\/ x *\/ 1 - x *\-1 - cot (5*x)/*asin\\/ x / + cot(5*x)/
----------------------------------------------------------------------
                              ___   _______                           
                          2*\/ x *\/ 1 - x

$$\frac{\left(30 \sqrt{x} \sqrt{1 - x} \left(- \cot^{2}{\left(5 x \right)} - 1\right) \operatorname{asin}{\left(\sqrt{x} \right)} + \cot{\left(5 x \right)}\right) \cot^{2}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

cot(5*x)^2*(30*sqrt(x)*sqrt(1 - x)*(-1 - cot(5*x)^2)*asin(sqrt(x)) + cot(5*x))/(2*sqrt(x)*sqrt(1 - x))

Combinatoria [src]

    2      /                 ___   _______     /  ___\        ___   _______    2          /  ___\\ 
-cot (5*x)*\-cot(5*x) + 30*\/ x *\/ 1 - x *asin\\/ x / + 30*\/ x *\/ 1 - x *cot (5*x)*asin\\/ x // 
---------------------------------------------------------------------------------------------------
                                             ___   _______                                         
                                         2*\/ x *\/ 1 - x

$$- \frac{\left(30 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + 30 \sqrt{x} \sqrt{1 - x} \operatorname{asin}{\left(\sqrt{x} \right)} - \cot{\left(5 x \right)}\right) \cot^{2}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

-cot(5*x)^2*(-cot(5*x) + 30*sqrt(x)*sqrt(1 - x)*asin(sqrt(x)) + 30*sqrt(x)*sqrt(1 - x)*cot(5*x)^2*asin(sqrt(x)))/(2*sqrt(x)*sqrt(1 - x))

Potencias [src]

      3                                                     
   cot (5*x)         2      /            2     \     /  ___\
--------------- + cot (5*x)*\-15 - 15*cot (5*x)/*asin\\/ x /
    ___________                                             
2*\/ x*(1 - x)

$$\left(- 15 \cot^{2}{\left(5 x \right)} - 15\right) \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x \left(1 - x\right)}}$$

cot(5*x)^3/(2*sqrt(x*(1 - x))) + cot(5*x)^2*(-15 - 15*cot(5*x)^2)*asin(sqrt(x))

Abrimos la expresión [src]

                                                                                                    15                                                                                                                                                                                                             9                                                                                                                                                                                                          5                                                                                                                                                                                                          13                                                                                                                                                                                                           3                                                                                                                                                                                                           11                                                                                                                                                                                                           7                                                                                                                                                              12        /  ___\                                                                                                               8        /  ___\                                                                                                              4        /  ___\                                                                                                              16        /  ___\                                                                             6        /  ___\                                         2        /  ___\                                         10        /  ___\                                                                           20        /  ___\                                                                             8        /  ___\                                                                            18        /  ___\                                                                             4        /  ___\                                                                            14        /  ___\                                                                                                              6        /  ___\                                                                                                               10        /  ___\                                                 
                                                                                                 cot  (x)                                                                                                                                                                                                  1300*cot (x)                                                                                                                                                                                                750*cot (x)                                                                                                                                                                                                 30*cot  (x)                                                                                                                                                                                                 125*cot (x)                                                                                                                                                                                                 315*cot  (x)                                                                                                                                                                                                1575*cot (x)                                                                                                                                                 242250*cot  (x)*asin\\/ x /                                                                                                     232500*cot (x)*asin\\/ x /                                                                                                      9375*cot (x)*asin\\/ x /                                                                                                      9300*cot  (x)*asin\\/ x /                                                                     1650*cot (x)*asin\\/ x /                                  375*cot (x)*asin\\/ x /                                   15*cot  (x)*asin\\/ x /                                                                     15*cot  (x)*asin\\/ x /                                                                      300*cot (x)*asin\\/ x /                                                                     600*cot  (x)*asin\\/ x /                                                                     1500*cot (x)*asin\\/ x /                                                                   69000*cot  (x)*asin\\/ x /                                                                                                     75000*cot (x)*asin\\/ x /                                                                                                     345000*cot  (x)*asin\\/ x /                                                 
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2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   2*\/ x *\/ 1 - x  - 2600*\/ x *\/ 1 - x *cot (x) - 1500*\/ x *\/ 1 - x *cot  (x) - 60*\/ x *\/ 1 - x *cot (x) + 250*\/ x *\/ 1 - x *cot  (x) + 630*\/ x *\/ 1 - x *cot (x) + 3150*\/ x *\/ 1 - x *cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 100*cot (x) - 20*cot (x) + 25*cot (x) + 110*cot (x)   1 - 100*cot (x) - 20*cot (x) + 25*cot (x) + 110*cot (x)   1 - 100*cot (x) - 20*cot (x) + 25*cot (x) + 110*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 100*cot (x) - 20*cot (x) + 25*cot (x) + 110*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 100*cot (x) - 20*cot (x) + 25*cot (x) + 110*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)   1 - 23000*cot  (x) - 5000*cot  (x) - 4600*cot (x) - 40*cot (x) + 620*cot (x) + 625*cot  (x) + 15500*cot  (x) + 16150*cot (x)

$$- \frac{15 \cot^{20}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} + \frac{600 \cot^{18}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} - \frac{9300 \cot^{16}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} + \frac{69000 \cot^{14}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} - \frac{242250 \cot^{12}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} + \frac{345000 \cot^{10}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} - \frac{232500 \cot^{8}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} + \frac{75000 \cot^{6}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} - \frac{9375 \cot^{4}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{625 \cot^{16}{\left(x \right)} - 5000 \cot^{14}{\left(x \right)} + 15500 \cot^{12}{\left(x \right)} - 23000 \cot^{10}{\left(x \right)} + 16150 \cot^{8}{\left(x \right)} - 4600 \cot^{6}{\left(x \right)} + 620 \cot^{4}{\left(x \right)} - 40 \cot^{2}{\left(x \right)} + 1} + \frac{\cot^{15}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} - \frac{30 \cot^{13}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} + \frac{315 \cot^{11}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} - \frac{1300 \cot^{9}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} + \frac{1575 \cot^{7}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} - \frac{750 \cot^{5}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} + \frac{125 \cot^{3}{\left(x \right)}}{250 \sqrt{x} \sqrt{1 - x} \cot^{12}{\left(x \right)} - 1500 \sqrt{x} \sqrt{1 - x} \cot^{10}{\left(x \right)} + 3150 \sqrt{x} \sqrt{1 - x} \cot^{8}{\left(x \right)} - 2600 \sqrt{x} \sqrt{1 - x} \cot^{6}{\left(x \right)} + 630 \sqrt{x} \sqrt{1 - x} \cot^{4}{\left(x \right)} - 60 \sqrt{x} \sqrt{1 - x} \cot^{2}{\left(x \right)} + 2 \sqrt{x} \sqrt{1 - x}} - \frac{15 \cot^{10}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{25 \cot^{8}{\left(x \right)} - 100 \cot^{6}{\left(x \right)} + 110 \cot^{4}{\left(x \right)} - 20 \cot^{2}{\left(x \right)} + 1} + \frac{300 \cot^{8}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{25 \cot^{8}{\left(x \right)} - 100 \cot^{6}{\left(x \right)} + 110 \cot^{4}{\left(x \right)} - 20 \cot^{2}{\left(x \right)} + 1} - \frac{1650 \cot^{6}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{25 \cot^{8}{\left(x \right)} - 100 \cot^{6}{\left(x \right)} + 110 \cot^{4}{\left(x \right)} - 20 \cot^{2}{\left(x \right)} + 1} + \frac{1500 \cot^{4}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{25 \cot^{8}{\left(x \right)} - 100 \cot^{6}{\left(x \right)} + 110 \cot^{4}{\left(x \right)} - 20 \cot^{2}{\left(x \right)} + 1} - \frac{375 \cot^{2}{\left(x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{25 \cot^{8}{\left(x \right)} - 100 \cot^{6}{\left(x \right)} + 110 \cot^{4}{\left(x \right)} - 20 \cot^{2}{\left(x \right)} + 1}$$

cot(x)^15/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) - 1300*cot(x)^9/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) - 750*cot(x)^5/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) - 30*cot(x)^13/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) + 125*cot(x)^3/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) + 315*cot(x)^11/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) + 1575*cot(x)^7/(2*sqrt(x)*sqrt(1 - x) - 2600*sqrt(x)*sqrt(1 - x)*cot(x)^6 - 1500*sqrt(x)*sqrt(1 - x)*cot(x)^10 - 60*sqrt(x)*sqrt(1 - x)*cot(x)^2 + 250*sqrt(x)*sqrt(1 - x)*cot(x)^12 + 630*sqrt(x)*sqrt(1 - x)*cot(x)^4 + 3150*sqrt(x)*sqrt(1 - x)*cot(x)^8) - 242250*cot(x)^12*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) - 232500*cot(x)^8*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) - 9375*cot(x)^4*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) - 9300*cot(x)^16*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) - 1650*cot(x)^6*asin(sqrt(x))/(1 - 100*cot(x)^6 - 20*cot(x)^2 + 25*cot(x)^8 + 110*cot(x)^4) - 375*cot(x)^2*asin(sqrt(x))/(1 - 100*cot(x)^6 - 20*cot(x)^2 + 25*cot(x)^8 + 110*cot(x)^4) - 15*cot(x)^10*asin(sqrt(x))/(1 - 100*cot(x)^6 - 20*cot(x)^2 + 25*cot(x)^8 + 110*cot(x)^4) - 15*cot(x)^20*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) + 300*cot(x)^8*asin(sqrt(x))/(1 - 100*cot(x)^6 - 20*cot(x)^2 + 25*cot(x)^8 + 110*cot(x)^4) + 600*cot(x)^18*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) + 1500*cot(x)^4*asin(sqrt(x))/(1 - 100*cot(x)^6 - 20*cot(x)^2 + 25*cot(x)^8 + 110*cot(x)^4) + 69000*cot(x)^14*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) + 75000*cot(x)^6*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8) + 345000*cot(x)^10*asin(sqrt(x))/(1 - 23000*cot(x)^10 - 5000*cot(x)^14 - 4600*cot(x)^6 - 40*cot(x)^2 + 620*cot(x)^4 + 625*cot(x)^16 + 15500*cot(x)^12 + 16150*cot(x)^8)

Denominador común [src]

                                                               3         
        2          /  ___\         4          /  ___\       cot (5*x)    
- 15*cot (5*x)*asin\\/ x / - 15*cot (5*x)*asin\\/ x / + -----------------
                                                            ___   _______
                                                        2*\/ x *\/ 1 - x

$$- 15 \cot^{4}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} - 15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

-15*cot(5*x)^2*asin(sqrt(x)) - 15*cot(5*x)^4*asin(sqrt(x)) + cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x))

Parte trigonométrica [src]

                                                2            
                                 /       2/5*x\\      /  ___\
                              15*|1 + tan |---|| *asin\\/ x /
             1                   \        \ 2 //             
--------------------------- - -------------------------------
    ___   _______    3                  2         2/5*x\     
2*\/ x *\/ 1 - x *tan (5*x)        4*tan (5*x)*tan |---|     
                                                   \ 2 /

$$- \frac{15 \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \tan^{2}{\left(\frac{5 x}{2} \right)} \tan^{2}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

          /             2      \                                               
   2      |       15*csc (5*x) |     /  ___\                                   
csc (5*x)*|-15 - --------------|*asin\\/ x /                                   
          |         2/pi      \|                                               
          |      csc |-- - 5*x||                             3                 
          \          \2       //                          csc (5*x)            
-------------------------------------------- + --------------------------------
                  2/pi      \                      ___   _______    3/pi      \
               csc |-- - 5*x|                  2*\/ x *\/ 1 - x *csc |-- - 5*x|
                   \2       /                                        \2       /

$$\frac{\left(- \frac{15 \csc^{2}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} - 15\right) \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{2}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$

        4          /  ___\                 3                 
  15*csc (5*x)*asin\\/ x /              csc (5*x)            
- ------------------------ + --------------------------------
          2/pi      \            ___   _______    3/pi      \
       csc |-- - 5*x|        2*\/ x *\/ 1 - x *csc |-- - 5*x|
           \2       /                              \2       /

$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{4}{\left(5 x \right)}}{\csc^{2}{\left(- 5 x + \frac{\pi}{2} \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$

       3                                     /  ___\ 
    cot (5*x)         15*(1 - cos(20*x))*asin\\/ x / 
----------------- - ---------------------------------
    ___   _______                   3               3
2*\/ x *\/ 1 - x    8*(1 - cos(5*x)) *(1 + cos(5*x))

$$- \frac{15 \left(1 - \cos{\left(20 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{8 \left(1 - \cos{\left(5 x \right)}\right)^{3} \left(\cos{\left(5 x \right)} + 1\right)^{3}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

                                                2            
                                 /       2/5*x\\      /  ___\
                              15*|1 - tan |---|| *asin\\/ x /
             1                   \        \ 2 //             
--------------------------- - -------------------------------
    ___   _______    3                   4/5*x\    4/5*x\    
2*\/ x *\/ 1 - x *tan (5*x)        16*cos |---|*tan |---|    
                                          \ 2 /     \ 2 /

$$- \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \cos^{4}{\left(\frac{5 x}{2} \right)} \tan^{4}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

        6          /  ___\                 3                 
  15*csc (5*x)*asin\\/ x /              csc (5*x)            
- ------------------------ + --------------------------------
             2                   ___   _______    3/pi      \
        4*csc (10*x)         2*\/ x *\/ 1 - x *csc |-- - 5*x|
                                                   \2       /

$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{6}{\left(5 x \right)}}{4 \csc^{2}{\left(10 x \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \csc^{3}{\left(- 5 x + \frac{\pi}{2} \right)}}$$

                                    6          /  ___\
             1                15*csc (5*x)*asin\\/ x /
--------------------------- - ------------------------
    ___   _______    3                   2            
2*\/ x *\/ 1 - x *tan (5*x)         4*csc (10*x)

$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{6}{\left(5 x \right)}}{4 \csc^{2}{\left(10 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

        4/      pi\     /  ___\             3/      pi\      
  15*sec |5*x - --|*asin\\/ x /          sec |5*x - --|      
         \      2 /                          \      2 /      
- ----------------------------- + ---------------------------
               2                      ___   _______    3     
            sec (5*x)             2*\/ x *\/ 1 - x *sec (5*x)

$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{4}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$

        2/pi      \     /  ___\                               
  15*sin |-- + 5*x|*asin\\/ x /               3               
         \2       /                        sin (10*x)         
- ----------------------------- + ----------------------------
               4                       ___   _______    6     
            sin (5*x)             16*\/ x *\/ 1 - x *sin (5*x)

$$- \frac{15 \sin^{2}{\left(5 x + \frac{\pi}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{4}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$

             1                      2         4          /  ___\
--------------------------- - 15*cos (5*x)*csc (5*x)*asin\\/ x /
    ___   _______    3                                          
2*\/ x *\/ 1 - x *tan (5*x)

$$- 15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{4}{\left(5 x \right)} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

                                    2          /  ___\
             1                15*cos (5*x)*asin\\/ x /
--------------------------- - ------------------------
    ___   _______    3                  4             
2*\/ x *\/ 1 - x *tan (5*x)          sin (5*x)

$$- \frac{15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{4}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

           /            2      \                                           
   2       |      15*sin (10*x)|     /  ___\                               
sin (10*x)*|-15 - -------------|*asin\\/ x /                               
           |            4      |                           3               
           \       4*sin (5*x) /                        sin (10*x)         
-------------------------------------------- + ----------------------------
                     4                              ___   _______    6     
                4*sin (5*x)                    16*\/ x *\/ 1 - x *sin (5*x)

$$\frac{\left(-15 - \frac{15 \sin^{2}{\left(10 x \right)}}{4 \sin^{4}{\left(5 x \right)}}\right) \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{4}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$

                                    2          /  ___\
   3              1           15*cot (5*x)*asin\\/ x /
cot (5*x)*----------------- - ------------------------
              ___   _______             2             
          2*\/ x *\/ 1 - x           sin (5*x)

$$\frac{1}{2 \sqrt{x} \sqrt{1 - x}} \cot^{3}{\left(5 x \right)} - \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}}$$

/          15   \     /  ___\                              
|-15 - ---------|*asin\\/ x /                              
|         2     |                                          
\      tan (5*x)/                            1             
----------------------------- + ---------------------------
             2                      ___   _______    3     
          tan (5*x)             2*\/ x *\/ 1 - x *tan (5*x)

$$\frac{\left(-15 - \frac{15}{\tan^{2}{\left(5 x \right)}}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{\tan^{2}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

          /            2     \                                          
   2      |      15*csc (5*x)|     /  ___\                              
csc (5*x)*|-15 - ------------|*asin\\/ x /                              
          |          2       |                           3              
          \       sec (5*x)  /                        csc (5*x)         
------------------------------------------ + ---------------------------
                   2                             ___   _______    3     
                sec (5*x)                    2*\/ x *\/ 1 - x *sec (5*x)

$$\frac{\left(- \frac{15 \csc^{2}{\left(5 x \right)}}{\sec^{2}{\left(5 x \right)}} - 15\right) \operatorname{asin}{\left(\sqrt{x} \right)} \csc^{2}{\left(5 x \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\csc^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$

          /            2     \                                          
   2      |      15*cos (5*x)|     /  ___\                              
cos (5*x)*|-15 - ------------|*asin\\/ x /                              
          |          2       |                           3              
          \       sin (5*x)  /                        cos (5*x)         
------------------------------------------ + ---------------------------
                   2                             ___   _______    3     
                sin (5*x)                    2*\/ x *\/ 1 - x *sin (5*x)

$$\frac{\left(-15 - \frac{15 \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \sin^{3}{\left(5 x \right)}}$$

        2           /  ___\               3               
  15*sin (10*x)*asin\\/ x /            sin (10*x)         
- ------------------------- + ----------------------------
              6                    ___   _______    6     
         4*sin (5*x)          16*\/ x *\/ 1 - x *sin (5*x)

$$- \frac{15 \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{6}{\left(5 x \right)}} + \frac{\sin^{3}{\left(10 x \right)}}{16 \sqrt{x} \sqrt{1 - x} \sin^{6}{\left(5 x \right)}}$$

                                      6                      
                       /       2/5*x\\     2          /  ___\
       3            15*|1 + cot |---|| *cot (5*x)*asin\\/ x /
    cot (5*x)          \        \ 2 //                       
----------------- - -----------------------------------------
    ___   _______                           2                
2*\/ x *\/ 1 - x             /       2     \     6/5*x\      
                          64*\1 + cot (5*x)/ *cot |---|      
                                                  \ 2 /

$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{6} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{64 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \cot^{6}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

       3                  2          /  ___\
    cot (5*x)       15*cot (5*x)*asin\\/ x /
----------------- - ------------------------
    ___   _______             2             
2*\/ x *\/ 1 - x           sin (5*x)

$$- \frac{15 \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

       3                         /  ___\     
    cot (5*x)             30*asin\\/ x /     
----------------- - -------------------------
    ___   _______                      2     
2*\/ x *\/ 1 - x    (1 - cos(10*x))*tan (5*x)

$$- \frac{30 \operatorname{asin}{\left(\sqrt{x} \right)}}{\left(1 - \cos{\left(10 x \right)}\right) \tan^{2}{\left(5 x \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

        2/       pi\     /  ___\                                   
  15*cos |10*x - --|*asin\\/ x /                 3                 
         \       2 /                          cos (5*x)            
- ------------------------------ + --------------------------------
              6/      pi\              ___   _______    3/      pi\
         4*cos |5*x - --|          2*\/ x *\/ 1 - x *cos |5*x - --|
               \      2 /                                \      2 /

$$- \frac{15 \cos^{2}{\left(10 x - \frac{\pi}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \cos^{6}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$

                                                6                      
                                 /       2/5*x\\     2          /  ___\
                              15*|1 + tan |---|| *tan (5*x)*asin\\/ x /
             1                   \        \ 2 //                       
--------------------------- - -----------------------------------------
    ___   _______    3                                2                
2*\/ x *\/ 1 - x *tan (5*x)            /       2     \     6/5*x\      
                                    64*\1 + tan (5*x)/ *tan |---|      
                                                            \ 2 /

$$- \frac{15 \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{6} \tan^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{64 \left(\tan^{2}{\left(5 x \right)} + 1\right)^{2} \tan^{6}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

        6/      pi\     /  ___\             3/      pi\      
  15*sec |5*x - --|*asin\\/ x /          sec |5*x - --|      
         \      2 /                          \      2 /      
- ----------------------------- + ---------------------------
             2/       pi\             ___   _______    3     
        4*sec |10*x - --|         2*\/ x *\/ 1 - x *sec (5*x)
              \       2 /

$$- \frac{15 \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{6}{\left(5 x - \frac{\pi}{2} \right)}}{4 \sec^{2}{\left(10 x - \frac{\pi}{2} \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$

                                       2                      
                       /        2/5*x\\     4/5*x\     /  ___\
       3            15*|-1 + cot |---|| *tan |---|*asin\\/ x /
    cot (5*x)          \         \ 2 //      \ 2 /            
----------------- - ------------------------------------------
    ___   _______                        4/5*x\               
2*\/ x *\/ 1 - x                   16*sin |---|               
                                          \ 2 /

$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)^{2} \tan^{4}{\left(\frac{5 x}{2} \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \sin^{4}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

        2          /  ___\                 3                 
  15*cos (5*x)*asin\\/ x /              cos (5*x)            
- ------------------------ + --------------------------------
          4/      pi\            ___   _______    3/      pi\
       cos |5*x - --|        2*\/ x *\/ 1 - x *cos |5*x - --|
           \      2 /                              \      2 /

$$- \frac{15 \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\cos^{4}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$

          /             2      \                                               
   2      |       15*cos (5*x) |     /  ___\                                   
cos (5*x)*|-15 - --------------|*asin\\/ x /                                   
          |         2/      pi\|                                               
          |      cos |5*x - --||                             3                 
          \          \      2 //                          cos (5*x)            
-------------------------------------------- + --------------------------------
                  2/      pi\                      ___   _______    3/      pi\
               cos |5*x - --|                  2*\/ x *\/ 1 - x *cos |5*x - --|
                   \      2 /                                        \      2 /

$$\frac{\left(- \frac{15 \cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}} - 15\right) \cos^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{\cos^{2}{\left(5 x - \frac{\pi}{2} \right)}} + \frac{\cos^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x} \cos^{3}{\left(5 x - \frac{\pi}{2} \right)}}$$

                                                2                2            
                                 /       2/5*x\\  /       2/5*x\\      /  ___\
                              15*|1 + tan |---|| *|1 - tan |---|| *asin\\/ x /
             1                   \        \ 2 //  \        \ 2 //             
--------------------------- - ------------------------------------------------
    ___   _______    3                                4/5*x\                  
2*\/ x *\/ 1 - x *tan (5*x)                     16*tan |---|                  
                                                       \ 2 /

$$- \frac{15 \left(1 - \tan^{2}{\left(\frac{5 x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \tan^{4}{\left(\frac{5 x}{2} \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

                                                       /  ___\ 
             1                  15*(1 - cos(20*x))*asin\\/ x / 
--------------------------- - ---------------------------------
    ___   _______    3                        3               3
2*\/ x *\/ 1 - x *tan (5*x)   8*(1 - cos(5*x)) *(1 + cos(5*x))

$$- \frac{15 \left(1 - \cos{\left(20 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)}}{8 \left(1 - \cos{\left(5 x \right)}\right)^{3} \left(\cos{\left(5 x \right)} + 1\right)^{3}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

               /            2/      pi\\                                          
               |      15*sec |5*x - --||                                          
   2/      pi\ |             \      2 /|     /  ___\                              
sec |5*x - --|*|-15 - -----------------|*asin\\/ x /             3/      pi\      
    \      2 / |             2         |                      sec |5*x - --|      
               \          sec (5*x)    /                          \      2 /      
---------------------------------------------------- + ---------------------------
                        2                                  ___   _______    3     
                     sec (5*x)                         2*\/ x *\/ 1 - x *sec (5*x)

$$\frac{\left(-15 - \frac{15 \sec^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}}\right) \operatorname{asin}{\left(\sqrt{x} \right)} \sec^{2}{\left(5 x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(5 x \right)}} + \frac{\sec^{3}{\left(5 x - \frac{\pi}{2} \right)}}{2 \sqrt{x} \sqrt{1 - x} \sec^{3}{\left(5 x \right)}}$$

                                    2           /  ___\
             1                15*sin (10*x)*asin\\/ x /
--------------------------- - -------------------------
    ___   _______    3                    6            
2*\/ x *\/ 1 - x *tan (5*x)          4*sin (5*x)

$$- \frac{15 \sin^{2}{\left(10 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \sin^{6}{\left(5 x \right)}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x} \tan^{3}{\left(5 x \right)}}$$

                                      2                      
                       /       2/5*x\\     2          /  ___\
       3            15*|1 + cot |---|| *cot (5*x)*asin\\/ x /
    cot (5*x)          \        \ 2 //                       
----------------- - -----------------------------------------
    ___   _______                       2/5*x\               
2*\/ x *\/ 1 - x                   4*cot |---|               
                                         \ 2 /

$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \cot^{2}{\left(5 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}}{4 \cot^{2}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

                                      2                 2            
                       /       2/5*x\\  /        2/5*x\\      /  ___\
       3            15*|1 + cot |---|| *|-1 + cot |---|| *asin\\/ x /
    cot (5*x)          \        \ 2 //  \         \ 2 //             
----------------- - -------------------------------------------------
    ___   _______                            4/5*x\                  
2*\/ x *\/ 1 - x                       16*cot |---|                  
                                              \ 2 /

$$- \frac{15 \left(\cot^{2}{\left(\frac{5 x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{5 x}{2} \right)} + 1\right)^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{16 \cot^{4}{\left(\frac{5 x}{2} \right)}} + \frac{\cot^{3}{\left(5 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$

cot(5*x)^3/(2*sqrt(x)*sqrt(1 - x)) - 15*(1 + cot(5*x/2)^2)^2*(-1 + cot(5*x/2)^2)^2*asin(sqrt(x))/(16*cot(5*x/2)^4)

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¿Cómo vas a descomponer esta cot(5*x)^2*(-15-15*cot(5*x)^2)*asin(sqrt(x))+cot(5*x)^3/(2*sqrt(x)*sqrt(1-x)) expresión en fracciones?

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¿Cómo vas a descomponer esta cot(5x)^2(-15-15cot(5x)^2)asin(sqrt(x))+cot(5x)^3/(2sqrt(x)sqrt(1-x)) expresión en fracciones?