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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x/3)/648+(x^3+15*x)/(17496+3888*x^2+216*x^4)

¿Cómo vas a descomponer esta atan(x/3)/648+(x^3+15*x)/(17496+3888*x^2+216*x^4) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /x\                           
atan|-|           3               
    \3/          x  + 15*x        
------- + ------------------------
  648                   2        4
          17496 + 3888*x  + 216*x
x3+15x216x4+(3888x2+17496)+atan⁡(x3)648\frac{x^{3} + 15 x}{216 x^{4} + \left(3888 x^{2} + 17496\right)} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648} 
atan(x/3)/648 + (x^3 + 15*x)/(17496 + 3888*x^2 + 216*x^4)
Simplificación general [src] 
   3          /      4       2\     /x\
3*x  + 45*x + \81 + x  + 18*x /*atan|-|
                                    \3/
---------------------------------------
             /      4       2\         
         648*\81 + x  + 18*x /
3x3+45x+(x4+18x2+81)atan⁡(x3)648(x4+18x2+81)\frac{3 x^{3} + 45 x + \left(x^{4} + 18 x^{2} + 81\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{4} + 18 x^{2} + 81\right)} 
(3*x^3 + 45*x + (81 + x^4 + 18*x^2)*atan(x/3))/(648*(81 + x^4 + 18*x^2))
Respuesta numérica [src] 
0.00154320987654321*atan(x/3) + (x^3 + 15.0*x)/(17496.0 + 216.0*x^4 + 3888.0*x^2)
0.00154320987654321*atan(x/3) + (x^3 + 15.0*x)/(17496.0 + 216.0*x^4 + 3888.0*x^2)
Denominador racional [src] 
     3            /             4         2\     /x\
648*x  + 9720*x + \17496 + 216*x  + 3888*x /*atan|-|
                                                 \3/
----------------------------------------------------
                            4            2          
         11337408 + 139968*x  + 2519424*x
648x3+9720x+(216x4+3888x2+17496)atan⁡(x3)139968x4+2519424x2+11337408\frac{648 x^{3} + 9720 x + \left(216 x^{4} + 3888 x^{2} + 17496\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{139968 x^{4} + 2519424 x^{2} + 11337408} 
(648*x^3 + 9720*x + (17496 + 216*x^4 + 3888*x^2)*atan(x/3))/(11337408 + 139968*x^4 + 2519424*x^2)
Compilar la expresión [src] 
    /x\                           
atan|-|           3               
    \3/          x  + 15*x        
------- + ------------------------
  648                  4         2
          17496 + 216*x  + 3888*x
x3+15x216x4+3888x2+17496+atan⁡(x3)648\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648} 
atan(x/3)/648 + (x^3 + 15*x)/(17496 + 216*x^4 + 3888*x^2)
Parte trigonométrica [src] 
    /x\                           
atan|-|           3               
    \3/          x  + 15*x        
------- + ------------------------
  648                  4         2
          17496 + 216*x  + 3888*x
x3+15x216x4+3888x2+17496+atan⁡(x3)648\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648} 
atan(x/3)/648 + (x^3 + 15*x)/(17496 + 216*x^4 + 3888*x^2)
Combinatoria [src] 
   3                 /x\    4     /x\       2     /x\
3*x  + 45*x + 81*atan|-| + x *atan|-| + 18*x *atan|-|
                     \3/          \3/             \3/
-----------------------------------------------------
                                2                    
                        /     2\                     
                    648*\9 + x /
x4atan⁡(x3)+3x3+18x2atan⁡(x3)+45x+81atan⁡(x3)648(x2+9)2\frac{x^{4} \operatorname{atan}{\left(\frac{x}{3} \right)} + 3 x^{3} + 18 x^{2} \operatorname{atan}{\left(\frac{x}{3} \right)} + 45 x + 81 \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{2} + 9\right)^{2}} 
(3*x^3 + 45*x + 81*atan(x/3) + x^4*atan(x/3) + 18*x^2*atan(x/3))/(648*(9 + x^2)^2)
Denominador común [src] 
    /x\                           
atan|-|           3               
    \3/          x  + 15*x        
------- + ------------------------
  648                  4         2
          17496 + 216*x  + 3888*x
x3+15x216x4+3888x2+17496+atan⁡(x3)648\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648} 
atan(x/3)/648 + (x^3 + 15*x)/(17496 + 216*x^4 + 3888*x^2)
Potencias [src] 
    /x\                           
atan|-|           3               
    \3/          x  + 15*x        
------- + ------------------------
  648                  4         2
          17496 + 216*x  + 3888*x
x3+15x216x4+3888x2+17496+atan⁡(x3)648\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648} 
atan(x/3)/648 + (x^3 + 15*x)/(17496 + 216*x^4 + 3888*x^2)
Unión de expresiones racionales [src] 
/      4       2\     /x\       /      2\
\81 + x  + 18*x /*atan|-| + 3*x*\15 + x /
                      \3/                
-----------------------------------------
              /      4       2\          
          648*\81 + x  + 18*x /
3x(x2+15)+(x4+18x2+81)atan⁡(x3)648(x4+18x2+81)\frac{3 x \left(x^{2} + 15\right) + \left(x^{4} + 18 x^{2} + 81\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{4} + 18 x^{2} + 81\right)} 
((81 + x^4 + 18*x^2)*atan(x/3) + 3*x*(15 + x^2))/(648*(81 + x^4 + 18*x^2))
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