Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-5*exp(-5*x)/(x^2+4)-2*x*exp(-5*x)/(x^2+4)^2
¿Cómo vas a descomponer esta -5*exp(-5*x)/(x^2+4)-2*x*exp(-5*x)/(x^2+4)^2 expresión en fracciones?
Solución
Ha introducido
[src]
-5*x -5*x
-5*e 2*x*e
-------- - ---------
2 2
x + 4 / 2 \
\x + 4/
$$- \frac{2 x e^{- 5 x}}{\left(x^{2} + 4\right)^{2}} + \frac{\left(-1\right) 5 e^{- 5 x}}{x^{2} + 4}$$
(-5*exp(-5*x))/(x^2 + 4) - (2*x)*exp(-5*x)/(x^2 + 4)^2
Simplificación general
[src]
/ 2\ -5*x
-\20 + 2*x + 5*x /*e
-------------------------
2
/ 2\
\4 + x /
$$- \frac{\left(5 x^{2} + 2 x + 20\right) e^{- 5 x}}{\left(x^{2} + 4\right)^{2}}$$
-(20 + 2*x + 5*x^2)*exp(-5*x)/(4 + x^2)^2
Respuesta numérica
[src]
-5.0*exp(-5*x)/(4.0 + x^2) - 0.125*x*exp(-5*x)/(1 + 0.25*x^2)^2
-5.0*exp(-5*x)/(4.0 + x^2) - 0.125*x*exp(-5*x)/(1 + 0.25*x^2)^2
Compilar la expresión
[src]
-5*x -5*x
5*e 2*x*e
- ------- - ---------
2 2
4 + x / 2\
\4 + x /
$$- \frac{2 x e^{- 5 x}}{\left(x^{2} + 4\right)^{2}} - \frac{5 e^{- 5 x}}{x^{2} + 4}$$
-5*exp(-5*x)/(4 + x^2) - 2*x*exp(-5*x)/(4 + x^2)^2
Denominador racional
[src]
/ 2 \
| / 2\ 5*x / 2\ 5*x| -10*x
\- 5*\4 + x / *e - 2*x*\4 + x /*e /*e
-----------------------------------------------
3
/ 2\
\4 + x /
$$\frac{\left(- 2 x \left(x^{2} + 4\right) e^{5 x} - 5 \left(x^{2} + 4\right)^{2} e^{5 x}\right) e^{- 10 x}}{\left(x^{2} + 4\right)^{3}}$$
(-5*(4 + x^2)^2*exp(5*x) - 2*x*(4 + x^2)*exp(5*x))*exp(-10*x)/(4 + x^2)^3
Denominador común
[src]
/ 2\
-\20 + 2*x + 5*x /
-----------------------------
5*x 4 5*x 2 5*x
16*e + x *e + 8*x *e
$$- \frac{5 x^{2} + 2 x + 20}{x^{4} e^{5 x} + 8 x^{2} e^{5 x} + 16 e^{5 x}}$$
-(20 + 2*x + 5*x^2)/(16*exp(5*x) + x^4*exp(5*x) + 8*x^2*exp(5*x))
Unión de expresiones racionales
[src]
/ 2 \ -5*x
\-20 - 5*x - 2*x/*e
------------------------
2
/ 2\
\4 + x /
$$\frac{\left(- 5 x^{2} - 2 x - 20\right) e^{- 5 x}}{\left(x^{2} + 4\right)^{2}}$$
(-20 - 5*x^2 - 2*x)*exp(-5*x)/(4 + x^2)^2
Potencias
[src]
-5*x -5*x
5*e 2*x*e
- ------- - ---------
2 2
4 + x / 2\
\4 + x /
$$- \frac{2 x e^{- 5 x}}{\left(x^{2} + 4\right)^{2}} - \frac{5 e^{- 5 x}}{x^{2} + 4}$$
-5*exp(-5*x)/(4 + x^2) - 2*x*exp(-5*x)/(4 + x^2)^2
Combinatoria
[src]
/ 2\ -5*x
-\20 + 2*x + 5*x /*e
-------------------------
2
/ 2\
\4 + x /
$$- \frac{\left(5 x^{2} + 2 x + 20\right) e^{- 5 x}}{\left(x^{2} + 4\right)^{2}}$$
-(20 + 2*x + 5*x^2)*exp(-5*x)/(4 + x^2)^2
Parte trigonométrica
[src]
-5*cosh(5*x) + 5*sinh(5*x) 2*x*(-cosh(5*x) + sinh(5*x))
-------------------------- + ----------------------------
2 2
4 + x / 2\
\4 + x /
$$\frac{2 x \left(\sinh{\left(5 x \right)} - \cosh{\left(5 x \right)}\right)}{\left(x^{2} + 4\right)^{2}} + \frac{5 \sinh{\left(5 x \right)} - 5 \cosh{\left(5 x \right)}}{x^{2} + 4}$$
-5*cosh(5*x) + 5*sinh(5*x) 2*x*(-sinh(5*x) + cosh(5*x))
-------------------------- - ----------------------------
2 2
4 + x / 2\
\4 + x /
$$- \frac{2 x \left(- \sinh{\left(5 x \right)} + \cosh{\left(5 x \right)}\right)}{\left(x^{2} + 4\right)^{2}} + \frac{5 \sinh{\left(5 x \right)} - 5 \cosh{\left(5 x \right)}}{x^{2} + 4}$$
5*(-cosh(5*x) + sinh(5*x)) 2*x*(-cosh(5*x) + sinh(5*x))
-------------------------- + ----------------------------
2 2
4 + x / 2\
\4 + x /
$$\frac{2 x \left(\sinh{\left(5 x \right)} - \cosh{\left(5 x \right)}\right)}{\left(x^{2} + 4\right)^{2}} + \frac{5 \left(\sinh{\left(5 x \right)} - \cosh{\left(5 x \right)}\right)}{x^{2} + 4}$$
-5*x -5*x
5*e 2*x*e
- ------- - ---------
2 2
4 + x / 2\
\4 + x /
$$- \frac{2 x e^{- 5 x}}{\left(x^{2} + 4\right)^{2}} - \frac{5 e^{- 5 x}}{x^{2} + 4}$$
5*(-sinh(5*x) + cosh(5*x)) 2*x*(-sinh(5*x) + cosh(5*x))
- -------------------------- - ----------------------------
2 2
4 + x / 2\
\4 + x /
$$- \frac{2 x \left(- \sinh{\left(5 x \right)} + \cosh{\left(5 x \right)}\right)}{\left(x^{2} + 4\right)^{2}} - \frac{5 \left(- \sinh{\left(5 x \right)} + \cosh{\left(5 x \right)}\right)}{x^{2} + 4}$$
-5*(-sinh(5*x) + cosh(5*x))/(4 + x^2) - 2*x*(-sinh(5*x) + cosh(5*x))/(4 + x^2)^2