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-1/(3*x^3)
((z-2)/(4*z^2+16*z+16))/((z/(2*z-4))-((z^2+4)/(2*z^2-8))-(z/(z^2+2*z)))
(a^2+a*b)/(a+b)
(z/c+c/z)/(z^2+c^2)/(5*z^9*c)
Factorizar el polinomio:
z^3-9*z^2+16*z+26
y*x^2+x^4
-y^8+y^5
z^2+14*z+4
Descomponer al cuadrado:
y^4+y^2+1
y^4+y^2-10
y^4+9*y^2-6
y^4-y^2-13
Expresiones idénticas
sin(x/ veintitrés)/ quinientos veintinueve - veintiuno mil ochocientos setenta *sin(veintisiete *x)/(uno + cien *x^ dos)- diecinueve mil seiscientos ochenta y tres *atan(diez *x)*cos(veintisiete *x)- dos mil *sin(veintisiete *x)/(uno + cien *x^ dos)^ dos - ciento sesenta y dos mil *x*cos(veintisiete *x)/(uno + cien *x^ dos)^ dos + ochocientos mil *x^ dos *sin(veintisiete *x)/(uno + cien *x^ dos)^ tres
seno de (x dividir por 23) dividir por 529 menos 21870 multiplicar por seno de (27 multiplicar por x) dividir por (1 más 100 multiplicar por x al cuadrado ) menos 19683 multiplicar por arco tangente de gente de (10 multiplicar por x) multiplicar por coseno de (27 multiplicar por x) menos 2000 multiplicar por seno de (27 multiplicar por x) dividir por (1 más 100 multiplicar por x al cuadrado ) al cuadrado menos 162000 multiplicar por x multiplicar por coseno de (27 multiplicar por x) dividir por (1 más 100 multiplicar por x al cuadrado ) al cuadrado más 800000 multiplicar por x al cuadrado multiplicar por seno de (27 multiplicar por x) dividir por (1 más 100 multiplicar por x al cuadrado ) al cubo
seno de (x dividir por veintitrés) dividir por quinientos veintinueve menos veintiuno mil ochocientos setenta multiplicar por seno de (veintisiete multiplicar por x) dividir por (uno más cien multiplicar por x en el grado dos) menos diecinueve mil seiscientos ochenta y tres multiplicar por arco tangente de gente de (diez multiplicar por x) multiplicar por coseno de (veintisiete multiplicar por x) menos dos mil multiplicar por seno de (veintisiete multiplicar por x) dividir por (uno más cien multiplicar por x en el grado dos) en el grado dos menos ciento sesenta y dos mil multiplicar por x multiplicar por coseno de (veintisiete multiplicar por x) dividir por (uno más cien multiplicar por x en el grado dos) en el grado dos más ochocientos mil multiplicar por x en el grado dos multiplicar por seno de (veintisiete multiplicar por x) dividir por (uno más cien multiplicar por x en el grado dos) en el grado tres
sin(x/23)/529-21870*sin(27*x)/(1+100*x2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x2)2-162000*x*cos(27*x)/(1+100*x2)2+800000*x2*sin(27*x)/(1+100*x2)3
sinx/23/529-21870*sin27*x/1+100*x2-19683*atan10*x*cos27*x-2000*sin27*x/1+100*x22-162000*x*cos27*x/1+100*x22+800000*x2*sin27*x/1+100*x23
sin(x/23)/529-21870*sin(27*x)/(1+100*x²)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x²)²-162000*x*cos(27*x)/(1+100*x²)²+800000*x²*sin(27*x)/(1+100*x²)³
sin(x/23)/529-21870*sin(27*x)/(1+100*x en el grado 2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x en el grado 2) en el grado 2-162000*x*cos(27*x)/(1+100*x en el grado 2) en el grado 2+800000*x en el grado 2*sin(27*x)/(1+100*x en el grado 2) en el grado 3
sin(x/23)/529-21870sin(27x)/(1+100x^2)-19683atan(10x)cos(27x)-2000sin(27x)/(1+100x^2)^2-162000xcos(27x)/(1+100x^2)^2+800000x^2sin(27x)/(1+100x^2)^3
sin(x/23)/529-21870sin(27x)/(1+100x2)-19683atan(10x)cos(27x)-2000sin(27x)/(1+100x2)2-162000xcos(27x)/(1+100x2)2+800000x2sin(27x)/(1+100x2)3
sinx/23/529-21870sin27x/1+100x2-19683atan10xcos27x-2000sin27x/1+100x22-162000xcos27x/1+100x22+800000x2sin27x/1+100x23
sinx/23/529-21870sin27x/1+100x^2-19683atan10xcos27x-2000sin27x/1+100x^2^2-162000xcos27x/1+100x^2^2+800000x^2sin27x/1+100x^2^3
sin(x dividir por 23) dividir por 529-21870*sin(27*x) dividir por (1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x) dividir por (1+100*x^2)^2-162000*x*cos(27*x) dividir por (1+100*x^2)^2+800000*x^2*sin(27*x) dividir por (1+100*x^2)^3
Expresiones semejantes
sin(x/23)/529+21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1-100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)+19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1-100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2-800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2+162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)+2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1-100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1-100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*arctan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3
Expresiones con funciones
Seno sin
sin^2(B)/(1-cos^2(B))+tg^2(B)
sin(pi*x)/(2*pi)+sin(3*pi*x)/(6*pi)
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a))
sin(p/2+a)-cos(p+a)/((-sin(a-2*p)))
Seno sin
sin^2(B)/(1-cos^2(B))+tg^2(B)
sin(pi*x)/(2*pi)+sin(3*pi*x)/(6*pi)
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a))
sin(p/2+a)-cos(p+a)/((-sin(a-2*p)))
Arcotangente arctan
atan(3*pi/2)/(9*pi^2)
atan(x)/2-(x+11)/(2+2*x^2)
atan(sin(x)/(sqrt(3)*(1+cos(x))))/(2*sqrt(3))
atan(sin(2*x)/(sqrt(5)*(1+cos(2*x))))/sqrt(5)
atan(x)/2+x/(2+2*x^2)
Coseno cos
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos(2*t)/(cos(t)+sin(t))
cos(2*a)*tan(2*a)/((2*sin(a)))
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(b)/(cos*b/2)-(sin*b/2)
Seno sin
sin^2(B)/(1-cos^2(B))+tg^2(B)
sin(pi*x)/(2*pi)+sin(3*pi*x)/(6*pi)
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a))
sin(p/2+a)-cos(p+a)/((-sin(a-2*p)))
Coseno cos
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos(2*t)/(cos(t)+sin(t))
cos(2*a)*tan(2*a)/((2*sin(a)))
cos(2*t)*t/(cos(t)+sin(t))-cos(t)
cos(b)/(cos*b/2)-(sin*b/2)
Seno sin
sin^2(B)/(1-cos^2(B))+tg^2(B)
sin(pi*x)/(2*pi)+sin(3*pi*x)/(6*pi)
sin(pi+a)+cos(pi+a)/cos(pi/2-a)-sin(3pi/2-a)1/(a*x-1)-1/(a*x+1)
sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a))
sin(p/2+a)-cos(p+a)/((-sin(a-2*p)))

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3

¿Cómo vas a descomponer esta sin(x/23)/529-21870sin(27x)/(1+100x^2)-19683atan(10x)cos(27x)-2000sin(27x)/(1+100x^2)^2-162000xcos(27x)/(1+100x^2)^2+800000x^2sin(27x)/(1+100x^2)^3 expresión en fracciones?

Solución

Ha introducido [src]

   /x \                                                                                                           
sin|--|                                                                                                2          
   \23/   21870*sin(27*x)                                2000*sin(27*x)   162000*x*cos(27*x)   800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
  529                 2                                              2                  2                     3   
             1 + 100*x                                   /         2\       /         2\          /         2\    
                                                         \1 + 100*x /       \1 + 100*x /          \1 + 100*x /

$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} + \left(- \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} + \left(\left(\left(\frac{\sin{\left(\frac{x}{23} \right)}}{529} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1}\right) - \cos{\left(27 x \right)} 19683 \operatorname{atan}{\left(10 x \right)}\right) - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}\right)\right)$$

sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - (162000*x)*cos(27*x)/(1 + 100*x^2)^2 + ((800000*x^2)*sin(27*x))/(1 + 100*x^2)^3

Simplificación general [src]

            3                                                                                                                            2                                   
/         2\  /                                    /x \\   /                      2\                                         /         2\                         2          
\1 + 100*x / *|-10412307*atan(10*x)*cos(27*x) + sin|--|| + \-1058000 - 105800000*x /*(81*x*cos(27*x) + sin(27*x)) - 11569230*\1 + 100*x / *sin(27*x) + 423200000*x *sin(27*x)
              \                                    \23//                                                                                                                     
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              3                                                                              
                                                                                  /         2\                                                                               
                                                                              529*\1 + 100*x /

$$\frac{423200000 x^{2} \sin{\left(27 x \right)} + \left(- 105800000 x^{2} - 1058000\right) \left(81 x \cos{\left(27 x \right)} + \sin{\left(27 x \right)}\right) + \left(100 x^{2} + 1\right)^{3} \left(\sin{\left(\frac{x}{23} \right)} - 10412307 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)}\right) - 11569230 \left(100 x^{2} + 1\right)^{2} \sin{\left(27 x \right)}}{529 \left(100 x^{2} + 1\right)^{3}}$$

((1 + 100*x^2)^3*(-10412307*atan(10*x)*cos(27*x) + sin(x/23)) + (-1058000 - 105800000*x^2)*(81*x*cos(27*x) + sin(27*x)) - 11569230*(1 + 100*x^2)^2*sin(27*x) + 423200000*x^2*sin(27*x))/(529*(1 + 100*x^2)^3)

Respuesta numérica [src]

0.00189035916824197*sin(x/23) - 21870.0*sin(27*x)/(1.0 + 100.0*x^2) - 19683.0*atan(10*x)*cos(27*x) - 0.2*sin(27*x)/(0.01 + x^2)^2 + 0.8*x^2*sin(27*x)/(0.01 + x^2)^3 - 16.2*x*cos(27*x)/(0.01 + x^2)^2

0.00189035916824197*sin(x/23) - 21870.0*sin(27*x)/(1.0 + 100.0*x^2) - 19683.0*atan(10*x)*cos(27*x) - 0.2*sin(27*x)/(0.01 + x^2)^2 + 0.8*x^2*sin(27*x)/(0.01 + x^2)^3 - 16.2*x*cos(27*x)/(0.01 + x^2)^2

Denominador racional [src]

            3 /            2 /            2                                                                                                                             \                        2                           \                         4                           
/         2\  |/         2\  |/         2\  /                      /         2\    /x \         /             2\                     \        /             2\          |            /         2\  /             2\          |           2 /         2\  /             2\          
\1 + 100*x / *|\1 + 100*x / *|\1 + 100*x / *|-11569230*sin(27*x) + \1 + 100*x /*sin|--| - 19683*\529 + 52900*x /*atan(10*x)*cos(27*x)| - 2000*\529 + 52900*x /*sin(27*x)| - 162000*x*\1 + 100*x / *\529 + 52900*x /*cos(27*x)| + 800000*x *\1 + 100*x / *\529 + 52900*x /*sin(27*x)
              \              \              \                                      \23/                                              /                                  /                                                    /                                                     
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                       7                                                                                                                                           
                                                                                                                           /         2\  /             2\                                                                                                                          
                                                                                                                           \1 + 100*x / *\529 + 52900*x /

$$\frac{800000 x^{2} \left(100 x^{2} + 1\right)^{4} \left(52900 x^{2} + 529\right) \sin{\left(27 x \right)} + \left(100 x^{2} + 1\right)^{3} \left(- 162000 x \left(100 x^{2} + 1\right)^{2} \left(52900 x^{2} + 529\right) \cos{\left(27 x \right)} + \left(100 x^{2} + 1\right)^{2} \left(\left(100 x^{2} + 1\right)^{2} \left(\left(100 x^{2} + 1\right) \sin{\left(\frac{x}{23} \right)} - 19683 \left(52900 x^{2} + 529\right) \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 11569230 \sin{\left(27 x \right)}\right) - 2000 \left(52900 x^{2} + 529\right) \sin{\left(27 x \right)}\right)\right)}{\left(100 x^{2} + 1\right)^{7} \left(52900 x^{2} + 529\right)}$$

((1 + 100*x^2)^3*((1 + 100*x^2)^2*((1 + 100*x^2)^2*(-11569230*sin(27*x) + (1 + 100*x^2)*sin(x/23) - 19683*(529 + 52900*x^2)*atan(10*x)*cos(27*x)) - 2000*(529 + 52900*x^2)*sin(27*x)) - 162000*x*(1 + 100*x^2)^2*(529 + 52900*x^2)*cos(27*x)) + 800000*x^2*(1 + 100*x^2)^4*(529 + 52900*x^2)*sin(27*x))/((1 + 100*x^2)^7*(529 + 52900*x^2))

Potencias [src]

                                            /   -I*x     I*x\            / -27*I*x    27*I*x\                                                                                                      
                                            |   -----    ---|            |e          e      |                                                                                                      
        / -27*I*x    27*I*x\                |     23      23|   162000*x*|-------- + -------|          /   -27*I*x    27*I*x\           /   -27*I*x    27*I*x\             2 /   -27*I*x    27*I*x\
        |e          e      |              I*\- e      + e   /            \   2          2   /   1000*I*\- e        + e      /   10935*I*\- e        + e      /   400000*I*x *\- e        + e      /
- 19683*|-------- + -------|*atan(10*x) - ------------------- - ----------------------------- + ----------------------------- + ------------------------------ - ----------------------------------
        \   2          2   /                      1058                              2                               2                              2                                   3           
                                                                        /         2\                    /         2\                      1 + 100*x                        /         2\            
                                                                        \1 + 100*x /                    \1 + 100*x /                                                       \1 + 100*x /

$$- \frac{400000 i x^{2} \left(e^{27 i x} - e^{- 27 i x}\right)}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \left(\frac{e^{27 i x}}{2} + \frac{e^{- 27 i x}}{2}\right)}{\left(100 x^{2} + 1\right)^{2}} - \frac{i \left(e^{\frac{i x}{23}} - e^{- \frac{i x}{23}}\right)}{1058} - 19683 \left(\frac{e^{27 i x}}{2} + \frac{e^{- 27 i x}}{2}\right) \operatorname{atan}{\left(10 x \right)} + \frac{10935 i \left(e^{27 i x} - e^{- 27 i x}\right)}{100 x^{2} + 1} + \frac{1000 i \left(e^{27 i x} - e^{- 27 i x}\right)}{\left(100 x^{2} + 1\right)^{2}}$$

   /x \                                                                                                           
sin|--|                                                                                                2          
   \23/   21870*sin(27*x)                                2000*sin(27*x)   162000*x*cos(27*x)   800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
  529                 2                                              2                  2                     3   
             1 + 100*x                                   /         2\       /         2\          /         2\    
                                                         \1 + 100*x /       \1 + 100*x /          \1 + 100*x /

$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$

sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3

Combinatoria [src]

 /     /x \                                 6    /x \          4    /x \        2    /x \                                                                      2                         3                           4                         2                                      4                                        6                     \ 
-|- sin|--| + 12627230*sin(27*x) - 1000000*x *sin|--| - 30000*x *sin|--| - 300*x *sin|--| + 10412307*atan(10*x)*cos(27*x) + 85698000*x*cos(27*x) + 1996446000*x *sin(27*x) + 8569800000*x *cos(27*x) + 115692300000*x *sin(27*x) + 3123692100*x *atan(10*x)*cos(27*x) + 312369210000*x *atan(10*x)*cos(27*x) + 10412307000000*x *atan(10*x)*cos(27*x)| 
 \     \23/                                      \23/               \23/             \23/                                                                                                                                                                                                                                                            / 
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                   3                                                                                                                                                                   
                                                                                                                                                                       /         2\                                                                                                                                                                    
                                                                                                                                                                   529*\1 + 100*x /

$$- \frac{- 1000000 x^{6} \sin{\left(\frac{x}{23} \right)} + 10412307000000 x^{6} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 30000 x^{4} \sin{\left(\frac{x}{23} \right)} + 115692300000 x^{4} \sin{\left(27 x \right)} + 312369210000 x^{4} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + 8569800000 x^{3} \cos{\left(27 x \right)} - 300 x^{2} \sin{\left(\frac{x}{23} \right)} + 1996446000 x^{2} \sin{\left(27 x \right)} + 3123692100 x^{2} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + 85698000 x \cos{\left(27 x \right)} - \sin{\left(\frac{x}{23} \right)} + 12627230 \sin{\left(27 x \right)} + 10412307 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)}}{529 \left(100 x^{2} + 1\right)^{3}}$$

-(-sin(x/23) + 12627230*sin(27*x) - 1000000*x^6*sin(x/23) - 30000*x^4*sin(x/23) - 300*x^2*sin(x/23) + 10412307*atan(10*x)*cos(27*x) + 85698000*x*cos(27*x) + 1996446000*x^2*sin(27*x) + 8569800000*x^3*cos(27*x) + 115692300000*x^4*sin(27*x) + 3123692100*x^2*atan(10*x)*cos(27*x) + 312369210000*x^4*atan(10*x)*cos(27*x) + 10412307000000*x^6*atan(10*x)*cos(27*x))/(529*(1 + 100*x^2)^3)

Compilar la expresión [src]

   /x \                                                                                                           
sin|--|                                                                                                2          
   \23/   21870*sin(27*x)                                2000*sin(27*x)   162000*x*cos(27*x)   800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
  529                 2                                              2                  2                     3   
             1 + 100*x                                   /         2\       /         2\          /         2\    
                                                         \1 + 100*x /       \1 + 100*x /          \1 + 100*x /

sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3

Abrimos la expresión [src]

   /x \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
sin|--|                                                          21                        17                                                                                                 25                       13                       21                       17                                                                                              25                      13                      9                                                       9                     5                     5                                                                                                                       3                     3                                                      7                      7                      27                      11                                                         27                       15                       11                       23                       19                                                                                                15                        23                                                                                                  19                           2    19                              2    23                             2    15                               19                           23                           15                          2    11                              2    27                              11                          27                          2    7                             7                        2    3                             3                                                 2                                   5                         2    5                               9                          2    9                               13                          25                          2    13                               17                          2    25                               21                           2    17                              2    21      
   \23/                     19                 52216977162240*sin  (x)   46321928110080*sin  (x)                     23                                   15                 9906778275840*sin  (x)   9374675927040*sin  (x)   4775215104000*sin  (x)   4236115968000*sin  (x)                    11                                  27                 905969664000*sin  (x)   857309184000*sin  (x)   408314649600*sin (x)                  7                  37340160000*sin (x)    2579260320*sin (x)     235872000*sin (x)                 3                 590490*sin(x)        54000*sin(x)                                     6552000*sin (x)      71646120*sin (x)                 5                   3953664000*sin (x)    43233315840*sin (x)   134217728000*sin  (x)   219967488000*sin  (x)                   9                 1467670855680*sin  (x)   2286157824000*sin  (x)   2405344481280*sin  (x)   2717908992000*sin  (x)   5449973760000*sin  (x)                    13                                  25                 24999135805440*sin  (x)   29720334827520*sin  (x)                     17                                   21                 59595463065600*sin  (x)      2179989504000000*x *sin  (x)         1087163596800000*x *sin  (x)         914463129600000*x *sin  (x)       441447874560000*x*cos  (x)   220150628352000*x*cos  (x)   185178783744000*x*cos  (x)       87986995200000*x *sin  (x)           53687091200000*x *sin  (x)       17817366528000*x*cos  (x)   10871635968000*x*cos  (x)        1581465600000*x *sin (x)        320246784000*x*cos (x)         2620800000*x *sin (x)           530712000*x*cos (x)       4374000*x*cos(x)             21600000*x *sin(x)           19105632000*x*cos (x)         94348800000*x *sin (x)         3024552960000*x*cos (x)       14936064000000*x *sin (x)        69442043904000*x*cos  (x)   73383542784000*x*cos  (x)      342923673600000*x *sin  (x)       343125393408000*x*cos  (x)      362387865600000*x *sin  (x)       386792423424000*x*cos  (x)      1694446387200000*x *sin  (x)         1910086041600000*x *sin  (x)   
------- - 53635916759040*cos  (x)*atan(10*x) - ----------------------- - ----------------------- - 26748301344768*cos  (x)*atan(10*x) - 22499222224896*cos  (x)*atan(10*x) - ---------------------- - ---------------------- - ---------------------- - ---------------------- - 2164810033152*cos  (x)*atan(10*x) - 1320903770112*cos  (x)*atan(10*x) - --------------------- - --------------------- - -------------------- - 38909984256*cos (x)*atan(10*x) - --------------------- - ------------------ - --------------------- - 64481508*cos (x)*atan(10*x) - ------------- - --------------------- + 531441*atan(10*x)*cos(x) + --------------------- + ---------------- + 2321334288*cos (x)*atan(10*x) + --------------------- + ------------------- + --------------------- + --------------------- + 367483184640*cos (x)*atan(10*x) + ---------------------- + ---------------------- + ---------------------- + ---------------------- + ---------------------- + 8437208334336*cos  (x)*atan(10*x) + 8916100448256*cos  (x)*atan(10*x) + ----------------------- + ----------------------- + 41689735299072*cos  (x)*atan(10*x) + 46995279446016*cos  (x)*atan(10*x) + ----------------------- - ---------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------- - -------------------------- - -------------------------- - ---------------------------------- - ---------------------------------- - ------------------------- - ------------------------- - ---------------------------------- - ---------------------- - ---------------------------------- - --------------------- + --------------------- + ---------------------------------- + --------------------- + ---------------------------------- + ----------------------- + ---------------------------------- + ------------------------- + ------------------------- + ---------------------------------- + -------------------------- + ---------------------------------- + -------------------------- + ---------------------------------- + ----------------------------------
  529                                                          2                         2                                                                                                  2                        2                  2          4             2          4                                                                                     2          4            2          4                 2                                                  2          4                2                2          4                                            2             2          4                                       2          4               2                                               2          4                 2                2          4            2          4                                                    2                  2          4                   2                  2          4             2          4                                                                                            2                         2                                                                                                   2                  2          4            6            2          4            6            2          4            6              2          4                 2          4                 2          4               2          4            6            2          4            6              2          4                2          4              2          4            6            2          4             2          4            6            2          4            2          4            2          4            6            2          4            2          4            6             2          4             2          4            6              2          4                2          4              2          4            6              2          4               2          4            6              2          4               2          4            6            2          4            6
                                                      1 + 100*x                 1 + 100*x                                                                                          1 + 100*x                1 + 100*x          1 + 200*x  + 10000*x     1 + 200*x  + 10000*x                                                                             1 + 200*x  + 10000*x    1 + 200*x  + 10000*x         1 + 100*x                                          1 + 200*x  + 10000*x        1 + 100*x        1 + 200*x  + 10000*x                                    1 + 100*x     1 + 200*x  + 10000*x                               1 + 200*x  + 10000*x       1 + 100*x                                       1 + 200*x  + 10000*x         1 + 100*x        1 + 200*x  + 10000*x    1 + 200*x  + 10000*x                                            1 + 100*x          1 + 200*x  + 10000*x           1 + 100*x          1 + 200*x  + 10000*x     1 + 200*x  + 10000*x                                                                                    1 + 100*x                 1 + 100*x                                                                                           1 + 100*x          1 + 300*x  + 30000*x  + 1000000*x    1 + 300*x  + 30000*x  + 1000000*x    1 + 300*x  + 30000*x  + 1000000*x      1 + 200*x  + 10000*x         1 + 200*x  + 10000*x         1 + 200*x  + 10000*x       1 + 300*x  + 30000*x  + 1000000*x    1 + 300*x  + 30000*x  + 1000000*x      1 + 200*x  + 10000*x        1 + 200*x  + 10000*x      1 + 300*x  + 30000*x  + 1000000*x    1 + 200*x  + 10000*x     1 + 300*x  + 30000*x  + 1000000*x    1 + 200*x  + 10000*x    1 + 200*x  + 10000*x    1 + 300*x  + 30000*x  + 1000000*x    1 + 200*x  + 10000*x    1 + 300*x  + 30000*x  + 1000000*x     1 + 200*x  + 10000*x     1 + 300*x  + 30000*x  + 1000000*x      1 + 200*x  + 10000*x        1 + 200*x  + 10000*x      1 + 300*x  + 30000*x  + 1000000*x      1 + 200*x  + 10000*x       1 + 300*x  + 30000*x  + 1000000*x      1 + 200*x  + 10000*x       1 + 300*x  + 30000*x  + 1000000*x    1 + 300*x  + 30000*x  + 1000000*x

$$- \frac{53687091200000 x^{2} \sin^{27}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{362387865600000 x^{2} \sin^{25}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{1087163596800000 x^{2} \sin^{23}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{1910086041600000 x^{2} \sin^{21}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{2179989504000000 x^{2} \sin^{19}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{1694446387200000 x^{2} \sin^{17}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{914463129600000 x^{2} \sin^{15}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{342923673600000 x^{2} \sin^{13}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{87986995200000 x^{2} \sin^{11}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{14936064000000 x^{2} \sin^{9}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{1581465600000 x^{2} \sin^{7}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{94348800000 x^{2} \sin^{5}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{2620800000 x^{2} \sin^{3}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{21600000 x^{2} \sin{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{10871635968000 x \cos^{27}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{73383542784000 x \cos^{25}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{220150628352000 x \cos^{23}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{386792423424000 x \cos^{21}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{441447874560000 x \cos^{19}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{343125393408000 x \cos^{17}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{185178783744000 x \cos^{15}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{69442043904000 x \cos^{13}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{17817366528000 x \cos^{11}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{3024552960000 x \cos^{9}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{320246784000 x \cos^{7}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{19105632000 x \cos^{5}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{530712000 x \cos^{3}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{4374000 x \cos{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 1320903770112 \cos^{27}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 8916100448256 \cos^{25}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 26748301344768 \cos^{23}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 46995279446016 \cos^{21}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 53635916759040 \cos^{19}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 41689735299072 \cos^{17}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 22499222224896 \cos^{15}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 8437208334336 \cos^{13}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 2164810033152 \cos^{11}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 367483184640 \cos^{9}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 38909984256 \cos^{7}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 2321334288 \cos^{5}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 64481508 \cos^{3}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 531441 \cos{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + \frac{134217728000 \sin^{27}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{905969664000 \sin^{25}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{2717908992000 \sin^{23}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{4775215104000 \sin^{21}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{5449973760000 \sin^{19}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{4236115968000 \sin^{17}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{2286157824000 \sin^{15}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{857309184000 \sin^{13}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{219967488000 \sin^{11}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{37340160000 \sin^{9}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{3953664000 \sin^{7}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{235872000 \sin^{5}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{6552000 \sin^{3}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{54000 \sin{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{1467670855680 \sin^{27}{\left(x \right)}}{100 x^{2} + 1} - \frac{9906778275840 \sin^{25}{\left(x \right)}}{100 x^{2} + 1} + \frac{29720334827520 \sin^{23}{\left(x \right)}}{100 x^{2} + 1} - \frac{52216977162240 \sin^{21}{\left(x \right)}}{100 x^{2} + 1} + \frac{59595463065600 \sin^{19}{\left(x \right)}}{100 x^{2} + 1} - \frac{46321928110080 \sin^{17}{\left(x \right)}}{100 x^{2} + 1} + \frac{24999135805440 \sin^{15}{\left(x \right)}}{100 x^{2} + 1} - \frac{9374675927040 \sin^{13}{\left(x \right)}}{100 x^{2} + 1} + \frac{2405344481280 \sin^{11}{\left(x \right)}}{100 x^{2} + 1} - \frac{408314649600 \sin^{9}{\left(x \right)}}{100 x^{2} + 1} + \frac{43233315840 \sin^{7}{\left(x \right)}}{100 x^{2} + 1} - \frac{2579260320 \sin^{5}{\left(x \right)}}{100 x^{2} + 1} + \frac{71646120 \sin^{3}{\left(x \right)}}{100 x^{2} + 1} - \frac{590490 \sin{\left(x \right)}}{100 x^{2} + 1}$$

sin(x/23)/529 - 53635916759040*cos(x)^19*atan(10*x) - 52216977162240*sin(x)^21/(1 + 100*x^2) - 46321928110080*sin(x)^17/(1 + 100*x^2) - 26748301344768*cos(x)^23*atan(10*x) - 22499222224896*cos(x)^15*atan(10*x) - 9906778275840*sin(x)^25/(1 + 100*x^2) - 9374675927040*sin(x)^13/(1 + 100*x^2) - 4775215104000*sin(x)^21/(1 + 200*x^2 + 10000*x^4) - 4236115968000*sin(x)^17/(1 + 200*x^2 + 10000*x^4) - 2164810033152*cos(x)^11*atan(10*x) - 1320903770112*cos(x)^27*atan(10*x) - 905969664000*sin(x)^25/(1 + 200*x^2 + 10000*x^4) - 857309184000*sin(x)^13/(1 + 200*x^2 + 10000*x^4) - 408314649600*sin(x)^9/(1 + 100*x^2) - 38909984256*cos(x)^7*atan(10*x) - 37340160000*sin(x)^9/(1 + 200*x^2 + 10000*x^4) - 2579260320*sin(x)^5/(1 + 100*x^2) - 235872000*sin(x)^5/(1 + 200*x^2 + 10000*x^4) - 64481508*cos(x)^3*atan(10*x) - 590490*sin(x)/(1 + 100*x^2) - 54000*sin(x)/(1 + 200*x^2 + 10000*x^4) + 531441*atan(10*x)*cos(x) + 6552000*sin(x)^3/(1 + 200*x^2 + 10000*x^4) + 71646120*sin(x)^3/(1 + 100*x^2) + 2321334288*cos(x)^5*atan(10*x) + 3953664000*sin(x)^7/(1 + 200*x^2 + 10000*x^4) + 43233315840*sin(x)^7/(1 + 100*x^2) + 134217728000*sin(x)^27/(1 + 200*x^2 + 10000*x^4) + 219967488000*sin(x)^11/(1 + 200*x^2 + 10000*x^4) + 367483184640*cos(x)^9*atan(10*x) + 1467670855680*sin(x)^27/(1 + 100*x^2) + 2286157824000*sin(x)^15/(1 + 200*x^2 + 10000*x^4) + 2405344481280*sin(x)^11/(1 + 100*x^2) + 2717908992000*sin(x)^23/(1 + 200*x^2 + 10000*x^4) + 5449973760000*sin(x)^19/(1 + 200*x^2 + 10000*x^4) + 8437208334336*cos(x)^13*atan(10*x) + 8916100448256*cos(x)^25*atan(10*x) + 24999135805440*sin(x)^15/(1 + 100*x^2) + 29720334827520*sin(x)^23/(1 + 100*x^2) + 41689735299072*cos(x)^17*atan(10*x) + 46995279446016*cos(x)^21*atan(10*x) + 59595463065600*sin(x)^19/(1 + 100*x^2) - 2179989504000000*x^2*sin(x)^19/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 1087163596800000*x^2*sin(x)^23/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 914463129600000*x^2*sin(x)^15/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 441447874560000*x*cos(x)^19/(1 + 200*x^2 + 10000*x^4) - 220150628352000*x*cos(x)^23/(1 + 200*x^2 + 10000*x^4) - 185178783744000*x*cos(x)^15/(1 + 200*x^2 + 10000*x^4) - 87986995200000*x^2*sin(x)^11/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 53687091200000*x^2*sin(x)^27/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 17817366528000*x*cos(x)^11/(1 + 200*x^2 + 10000*x^4) - 10871635968000*x*cos(x)^27/(1 + 200*x^2 + 10000*x^4) - 1581465600000*x^2*sin(x)^7/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 320246784000*x*cos(x)^7/(1 + 200*x^2 + 10000*x^4) - 2620800000*x^2*sin(x)^3/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 530712000*x*cos(x)^3/(1 + 200*x^2 + 10000*x^4) + 4374000*x*cos(x)/(1 + 200*x^2 + 10000*x^4) + 21600000*x^2*sin(x)/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 19105632000*x*cos(x)^5/(1 + 200*x^2 + 10000*x^4) + 94348800000*x^2*sin(x)^5/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 3024552960000*x*cos(x)^9/(1 + 200*x^2 + 10000*x^4) + 14936064000000*x^2*sin(x)^9/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 69442043904000*x*cos(x)^13/(1 + 200*x^2 + 10000*x^4) + 73383542784000*x*cos(x)^25/(1 + 200*x^2 + 10000*x^4) + 342923673600000*x^2*sin(x)^13/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 343125393408000*x*cos(x)^17/(1 + 200*x^2 + 10000*x^4) + 362387865600000*x^2*sin(x)^25/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 386792423424000*x*cos(x)^21/(1 + 200*x^2 + 10000*x^4) + 1694446387200000*x^2*sin(x)^17/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 1910086041600000*x^2*sin(x)^21/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6)

Denominador común [src]

   /x \                                                                                                                                            
sin|--|                                                   2                       3                        4                                       
   \23/   23870*sin(27*x) + 162000*x*cos(27*x) + 3774000*x *sin(27*x) + 16200000*x *cos(27*x) + 218700000*x *sin(27*x)                             
------- - ------------------------------------------------------------------------------------------------------------ - 19683*atan(10*x)*cos(27*x)
  529                                                   2          4            6                                                                  
                                               1 + 300*x  + 30000*x  + 1000000*x

$$\frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{218700000 x^{4} \sin{\left(27 x \right)} + 16200000 x^{3} \cos{\left(27 x \right)} + 3774000 x^{2} \sin{\left(27 x \right)} + 162000 x \cos{\left(27 x \right)} + 23870 \sin{\left(27 x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1}$$

sin(x/23)/529 - (23870*sin(27*x) + 162000*x*cos(27*x) + 3774000*x^2*sin(27*x) + 16200000*x^3*cos(27*x) + 218700000*x^4*sin(27*x))/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 19683*atan(10*x)*cos(27*x)

Unión de expresiones racionales [src]

/         2\ /                     /         2\ /                      /         2\    /x \            /         2\                     \                       \              2          
\1 + 100*x /*|-1058000*sin(27*x) + \1 + 100*x /*|-11569230*sin(27*x) + \1 + 100*x /*sin|--| - 10412307*\1 + 100*x /*atan(10*x)*cos(27*x)| - 85698000*x*cos(27*x)| + 423200000*x *sin(27*x)
             \                                  \                                      \23/                                             /                       /                         
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                    3                                                                                     
                                                                                        /         2\                                                                                      
                                                                                    529*\1 + 100*x /

$$\frac{423200000 x^{2} \sin{\left(27 x \right)} + \left(100 x^{2} + 1\right) \left(- 85698000 x \cos{\left(27 x \right)} + \left(100 x^{2} + 1\right) \left(\left(100 x^{2} + 1\right) \sin{\left(\frac{x}{23} \right)} - 10412307 \left(100 x^{2} + 1\right) \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 11569230 \sin{\left(27 x \right)}\right) - 1058000 \sin{\left(27 x \right)}\right)}{529 \left(100 x^{2} + 1\right)^{3}}$$

((1 + 100*x^2)*(-1058000*sin(27*x) + (1 + 100*x^2)*(-11569230*sin(27*x) + (1 + 100*x^2)*sin(x/23) - 10412307*(1 + 100*x^2)*atan(10*x)*cos(27*x)) - 85698000*x*cos(27*x)) + 423200000*x^2*sin(27*x))/(529*(1 + 100*x^2)^3)

Parte trigonométrica [src]

         /x \                        /27*x\                /        2/27*x\\                              /27*x\                      /        2/27*x\\                   2    /27*x\     
    2*cot|--|               43740*cot|----|          19683*|-1 + cot |----||*atan(10*x)           4000*cot|----|             162000*x*|-1 + cot |----||          1600000*x *cot|----|     
         \46/                        \ 2  /                \         \ 2  //                              \ 2  /                      \         \ 2  //                        \ 2  /     
------------------ - ----------------------------- - ---------------------------------- - ------------------------------ - ------------------------------ + ------------------------------
    /       2/x \\   /       2/27*x\\ /         2\                    2/27*x\                                          2                                2                                3
529*|1 + cot |--||   |1 + cot |----||*\1 + 100*x /             1 + cot |----|             /       2/27*x\\ /         2\    /       2/27*x\\ /         2\    /       2/27*x\\ /         2\ 
    \        \46//   \        \ 2  //                                  \ 2  /             |1 + cot |----||*\1 + 100*x /    |1 + cot |----||*\1 + 100*x /    |1 + cot |----||*\1 + 100*x / 
                                                                                          \        \ 2  //                 \        \ 2  //                 \        \ 2  //

$$\frac{1600000 x^{2} \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{3} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{162000 x \left(\cot^{2}{\left(\frac{27 x}{2} \right)} - 1\right)}{\left(100 x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{19683 \left(\cot^{2}{\left(\frac{27 x}{2} \right)} - 1\right) \operatorname{atan}{\left(10 x \right)}}{\cot^{2}{\left(\frac{27 x}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{46} \right)}}{529 \left(\cot^{2}{\left(\frac{x}{46} \right)} + 1\right)} - \frac{43740 \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right) \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{4000 \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)}$$

                                                                                                                                  2       
     1                21870            19683*atan(10*x)             2000                      162000*x                    800000*x        
----------- - ---------------------- - ---------------- - ----------------------- - ---------------------------- + -----------------------
       /x \   /         2\                 /pi       \                2                         2                              3          
529*csc|--|   \1 + 100*x /*csc(27*x)    csc|-- - 27*x|    /         2\              /         2\     /pi       \   /         2\           
       \23/                                \2        /    \1 + 100*x / *csc(27*x)   \1 + 100*x / *csc|-- - 27*x|   \1 + 100*x / *csc(27*x)
                                                                                                     \2        /

$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \csc{\left(27 x \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \csc{\left(- 27 x + \frac{\pi}{2} \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\csc{\left(- 27 x + \frac{\pi}{2} \right)}} + \frac{1}{529 \csc{\left(\frac{x}{23} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \csc{\left(27 x \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \csc{\left(27 x \right)}}$$

                                                                                                                             2       
     1                21870            19683*atan(10*x)             2000                    162000*x                 800000*x        
----------- - ---------------------- - ---------------- - ----------------------- - ----------------------- + -----------------------
       /x \   /         2\                sec(27*x)                   2                         2                         3          
529*csc|--|   \1 + 100*x /*csc(27*x)                      /         2\              /         2\              /         2\           
       \23/                                               \1 + 100*x / *csc(27*x)   \1 + 100*x / *sec(27*x)   \1 + 100*x / *csc(27*x)

$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \csc{\left(27 x \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\sec{\left(27 x \right)}} + \frac{1}{529 \csc{\left(\frac{x}{23} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \csc{\left(27 x \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \csc{\left(27 x \right)}}$$

   /  pi   x \            /       pi\                                        /       pi\                                2    /       pi\
cos|- -- + --|   21870*cos|27*x - --|                                2000*cos|27*x - --|                        800000*x *cos|27*x - --|
   \  2    23/            \       2 /                                        \       2 /   162000*x*cos(27*x)                \       2 /
-------------- - -------------------- - 19683*atan(10*x)*cos(27*x) - ------------------- - ------------------ + ------------------------
     529                       2                                                    2                    2                       3      
                      1 + 100*x                                         /         2\         /         2\            /         2\       
                                                                        \1 + 100*x /         \1 + 100*x /            \1 + 100*x /

$$\frac{800000 x^{2} \cos{\left(27 x - \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + \frac{\cos{\left(\frac{x}{23} - \frac{\pi}{2} \right)}}{529} - \frac{21870 \cos{\left(27 x - \frac{\pi}{2} \right)}}{100 x^{2} + 1} - \frac{2000 \cos{\left(27 x - \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{2}}$$

         /x \                        /27*x\                /       2/27*x\\                              /27*x\                      /       2/27*x\\                    2    /27*x\     
    2*tan|--|               43740*tan|----|          19683*|1 - tan |----||*atan(10*x)           4000*tan|----|             162000*x*|1 - tan |----||           1600000*x *tan|----|     
         \46/                        \ 2  /                \        \ 2  //                              \ 2  /                      \        \ 2  //                         \ 2  /     
------------------ - ----------------------------- - --------------------------------- - ------------------------------ - ------------------------------ + ------------------------------
    /       2/x \\   /       2/27*x\\ /         2\                    2/27*x\                                         2                                2                                3
529*|1 + tan |--||   |1 + tan |----||*\1 + 100*x /             1 + tan |----|            /       2/27*x\\ /         2\    /       2/27*x\\ /         2\    /       2/27*x\\ /         2\ 
    \        \46//   \        \ 2  //                                  \ 2  /            |1 + tan |----||*\1 + 100*x /    |1 + tan |----||*\1 + 100*x /    |1 + tan |----||*\1 + 100*x / 
                                                                                         \        \ 2  //                 \        \ 2  //                 \        \ 2  //

$$\frac{1600000 x^{2} \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{3} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{162000 x \left(1 - \tan^{2}{\left(\frac{27 x}{2} \right)}\right)}{\left(100 x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{19683 \left(1 - \tan^{2}{\left(\frac{27 x}{2} \right)}\right) \operatorname{atan}{\left(10 x \right)}}{\tan^{2}{\left(\frac{27 x}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{46} \right)}}{529 \left(\tan^{2}{\left(\frac{x}{46} \right)} + 1\right)} - \frac{43740 \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right) \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{4000 \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)}$$

                                                                                                                                                2          
        1                       21870              19683*atan(10*x)               2000                       162000*x                   800000*x           
------------------ - --------------------------- - ---------------- - ---------------------------- - ----------------------- + ----------------------------
       /  pi   x \   /         2\    /       pi\      sec(27*x)                   2                              2                         3               
529*sec|- -- + --|   \1 + 100*x /*sec|27*x - --|                      /         2\     /       pi\   /         2\              /         2\     /       pi\
       \  2    23/                   \       2 /                      \1 + 100*x / *sec|27*x - --|   \1 + 100*x / *sec(27*x)   \1 + 100*x / *sec|27*x - --|
                                                                                       \       2 /                                              \       2 /

$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \sec{\left(27 x - \frac{\pi}{2} \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\sec{\left(27 x \right)}} + \frac{1}{529 \sec{\left(\frac{x}{23} - \frac{\pi}{2} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \sec{\left(27 x - \frac{\pi}{2} \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x - \frac{\pi}{2} \right)}}$$

   /x \                                                                                    /pi       \                      
sin|--|                                                                        162000*x*sin|-- + 27*x|           2          
   \23/   21870*sin(27*x)                       /pi       \   2000*sin(27*x)               \2        /   800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*sin|-- + 27*x| - -------------- - ----------------------- + -------------------
  529                 2                         \2        /               2                     2                       3   
             1 + 100*x                                        /         2\          /         2\            /         2\    
                                                              \1 + 100*x /          \1 + 100*x /            \1 + 100*x /

$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \sin{\left(27 x + \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \sin{\left(27 x + \frac{\pi}{2} \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$

   /x \                                                                                                           
sin|--|                                                                                                2          
   \23/   21870*sin(27*x)                                2000*sin(27*x)   162000*x*cos(27*x)   800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
  529                 2                                              2                  2                     3   
             1 + 100*x                                   /         2\       /         2\          /         2\    
                                                         \1 + 100*x /       \1 + 100*x /          \1 + 100*x /

sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3

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¿Cómo vas a descomponer esta sin(x/23)/529-21870*sin(27*x)/(1+100*x^2)-19683*atan(10*x)*cos(27*x)-2000*sin(27*x)/(1+100*x^2)^2-162000*x*cos(27*x)/(1+100*x^2)^2+800000*x^2*sin(27*x)/(1+100*x^2)^3 expresión en fracciones?

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¿Cómo vas a descomponer esta sin(x/23)/529-21870sin(27x)/(1+100x^2)-19683atan(10x)cos(27x)-2000sin(27x)/(1+100x^2)^2-162000xcos(27x)/(1+100x^2)^2+800000x^2sin(27x)/(1+100x^2)^3 expresión en fracciones?