Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(E^x)/(2*sqrt(x))+sqrt(x)*exp(x)/(1+exp(2*x))
¿Cómo vas a descomponer esta atan(E^x)/(2*sqrt(x))+sqrt(x)*exp(x)/(1+exp(2*x)) expresión en fracciones?
Solución
Ha introducido
[src]
/ x\ ___ x
atan\E / \/ x *e
-------- + --------
___ 2*x
2*\/ x 1 + e
$$\frac{\sqrt{x} e^{x}}{e^{2 x} + 1} + \frac{\operatorname{atan}{\left(e^{x} \right)}}{2 \sqrt{x}}$$
atan(E^x)/((2*sqrt(x))) + (sqrt(x)*exp(x))/(1 + exp(2*x))
Simplificación general
[src]
/ 2*x\ / x\
x \1 + e /*atan\e /
x*e + -------------------
2
--------------------------
___ / 2*x\
\/ x *\1 + e /
$$\frac{x e^{x} + \frac{\left(e^{2 x} + 1\right) \operatorname{atan}{\left(e^{x} \right)}}{2}}{\sqrt{x} \left(e^{2 x} + 1\right)}$$
(x*exp(x) + (1 + exp(2*x))*atan(exp(x))/2)/(sqrt(x)*(1 + exp(2*x)))
Respuesta numérica
[src]
0.5*x^(-0.5)*atan(E^x) + x^0.5*exp(x)/(1.0 + exp(2*x))
0.5*x^(-0.5)*atan(E^x) + x^0.5*exp(x)/(1.0 + exp(2*x))
Denominador racional
[src]
/ x\ 2*x x / x\
atan\e /*e + 2*x*e + atan\e /
---------------------------------
___ / 2*x\
2*\/ x *\1 + e /
$$\frac{2 x e^{x} + e^{2 x} \operatorname{atan}{\left(e^{x} \right)} + \operatorname{atan}{\left(e^{x} \right)}}{2 \sqrt{x} \left(e^{2 x} + 1\right)}$$
(atan(exp(x))*exp(2*x) + 2*x*exp(x) + atan(exp(x)))/(2*sqrt(x)*(1 + exp(2*x)))
Combinatoria
[src]
/ x\ 2*x x / x\
atan\e /*e + 2*x*e + atan\e /
---------------------------------
___ / 2*x\
2*\/ x *\1 + e /
$$\frac{2 x e^{x} + e^{2 x} \operatorname{atan}{\left(e^{x} \right)} + \operatorname{atan}{\left(e^{x} \right)}}{2 \sqrt{x} \left(e^{2 x} + 1\right)}$$
(atan(exp(x))*exp(2*x) + 2*x*exp(x) + atan(exp(x)))/(2*sqrt(x)*(1 + exp(2*x)))
Denominador común
[src]
/ x\ 2*x x / x\
atan\e /*e + 2*x*e + atan\e /
---------------------------------
___ ___ 2*x
2*\/ x + 2*\/ x *e
$$\frac{2 x e^{x} + e^{2 x} \operatorname{atan}{\left(e^{x} \right)} + \operatorname{atan}{\left(e^{x} \right)}}{2 \sqrt{x} e^{2 x} + 2 \sqrt{x}}$$
(atan(exp(x))*exp(2*x) + 2*x*exp(x) + atan(exp(x)))/(2*sqrt(x) + 2*sqrt(x)*exp(2*x))
Parte trigonométrica
[src]
___
atan(cosh(x) + sinh(x)) \/ x *(cosh(x) + sinh(x))
----------------------- + -------------------------
___ 1 + cosh(2*x) + sinh(2*x)
2*\/ x
$$\frac{\sqrt{x} \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)} + 1} + \frac{\operatorname{atan}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} \right)}}{2 \sqrt{x}}$$
/ x\ ___
atan\(cosh(1) + sinh(1)) / \/ x *(cosh(x) + sinh(x))
-------------------------- + -------------------------
___ 1 + cosh(2*x) + sinh(2*x)
2*\/ x
$$\frac{\sqrt{x} \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)} + 1} + \frac{\operatorname{atan}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} \right)}}{2 \sqrt{x}}$$
atan((cosh(1) + sinh(1))^x)/(2*sqrt(x)) + sqrt(x)*(cosh(x) + sinh(x))/(1 + cosh(2*x) + sinh(2*x))
Unión de expresiones racionales
[src]
/ 2*x\ / x\ x
\1 + e /*atan\e / + 2*x*e
----------------------------
___ / 2*x\
2*\/ x *\1 + e /
$$\frac{2 x e^{x} + \left(e^{2 x} + 1\right) \operatorname{atan}{\left(e^{x} \right)}}{2 \sqrt{x} \left(e^{2 x} + 1\right)}$$
((1 + exp(2*x))*atan(exp(x)) + 2*x*exp(x))/(2*sqrt(x)*(1 + exp(2*x)))