Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)/acos(x)+exp(x)/(sqrt(1-x^2)*acos(x)^2)
¿Cómo vas a descomponer esta exp(x)/acos(x)+exp(x)/(sqrt(1-x^2)*acos(x)^2) expresión en fracciones?
Solución
Ha introducido
[src]
x x
e e
------- + --------------------
acos(x) ________
/ 2 2
\/ 1 - x *acos (x)
$$\frac{e^{x}}{\operatorname{acos}{\left(x \right)}} + \frac{e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
exp(x)/acos(x) + exp(x)/((sqrt(1 - x^2)*acos(x)^2))
Denominador racional
[src]
________
2 x 2 2 x / 2 x
- acos (x)*e + x *acos (x)*e - \/ 1 - x *acos(x)*e
-------------------------------------------------------
/ 2\ 3
\-1 + x /*acos (x)
$$\frac{x^{2} e^{x} \operatorname{acos}^{2}{\left(x \right)} - \sqrt{1 - x^{2}} e^{x} \operatorname{acos}{\left(x \right)} - e^{x} \operatorname{acos}^{2}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{3}{\left(x \right)}}$$
(-acos(x)^2*exp(x) + x^2*acos(x)^2*exp(x) - sqrt(1 - x^2)*acos(x)*exp(x))/((-1 + x^2)*acos(x)^3)
Combinatoria
[src]
/ ________ \ | / 2 | x \1 + \/ 1 - x *acos(x)/*e ------------------------------ ___________________ 2 \/ -(1 + x)*(-1 + x) *acos (x)
$$\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 1\right) e^{x}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{acos}^{2}{\left(x \right)}}$$
(1 + sqrt(1 - x^2)*acos(x))*exp(x)/(sqrt(-(1 + x)*(-1 + x))*acos(x)^2)
Respuesta numérica
[src]
exp(x)/acos(x) + (1.0 - x^2)^(-0.5)*exp(x)/acos(x)^2
exp(x)/acos(x) + (1.0 - x^2)^(-0.5)*exp(x)/acos(x)^2
Denominador común
[src]
________
/ 2 x x
\/ 1 - x *acos(x)*e + e
---------------------------
________
/ 2 2
\/ 1 - x *acos (x)
$$\frac{\sqrt{1 - x^{2}} e^{x} \operatorname{acos}{\left(x \right)} + e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
(sqrt(1 - x^2)*acos(x)*exp(x) + exp(x))/(sqrt(1 - x^2)*acos(x)^2)
Unión de expresiones racionales
[src]
/ ________ \
| / 2 | x
\1 + \/ 1 - x *acos(x)/*e
----------------------------
________
/ 2 2
\/ 1 - x *acos (x)
$$\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 1\right) e^{x}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
(1 + sqrt(1 - x^2)*acos(x))*exp(x)/(sqrt(1 - x^2)*acos(x)^2)
Parte trigonométrica
[src]
cosh(x) + sinh(x) cosh(x) + sinh(x)
----------------- + --------------------
acos(x) ________
/ 2 2
\/ 1 - x *acos (x)
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
(cosh(x) + sinh(x))/acos(x) + (cosh(x) + sinh(x))/(sqrt(1 - x^2)*acos(x)^2)