Sr Examen
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?
Solución
Ha introducido
[src]
/x\
atan|-| 3
\3/ x + 15*x
------- + ------------------------
648 2 4
17496 + 3888*x + 216*x
$$\frac{x^{3} + 15 x}{216 x^{4} + \left(3888 x^{2} + 17496\right)} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648}$$
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 /
$$\frac{3 x^{3} + 45 x + \left(x^{4} + 18 x^{2} + 81\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{4} + 18 x^{2} + 81\right)}$$
(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
$$\frac{648 x^{3} + 9720 x + \left(216 x^{4} + 3888 x^{2} + 17496\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{139968 x^{4} + 2519424 x^{2} + 11337408}$$
(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
$$\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648}$$
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
$$\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648}$$
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 /
$$\frac{x^{4} \operatorname{atan}{\left(\frac{x}{3} \right)} + 3 x^{3} + 18 x^{2} \operatorname{atan}{\left(\frac{x}{3} \right)} + 45 x + 81 \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{2} + 9\right)^{2}}$$
(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
$$\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648}$$
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
$$\frac{x^{3} + 15 x}{216 x^{4} + 3888 x^{2} + 17496} + \frac{\operatorname{atan}{\left(\frac{x}{3} \right)}}{648}$$
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 /
$$\frac{3 x \left(x^{2} + 15\right) + \left(x^{4} + 18 x^{2} + 81\right) \operatorname{atan}{\left(\frac{x}{3} \right)}}{648 \left(x^{4} + 18 x^{2} + 81\right)}$$
((81 + x^4 + 18*x^2)*atan(x/3) + 3*x*(15 + x^2))/(648*(81 + x^4 + 18*x^2))