Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x)*log(x^2+2)+2*x*exp(x)/(x^2+2)
¿Cómo vas a descomponer esta exp(x)*log(x^2+2)+2*x*exp(x)/(x^2+2) expresión en fracciones?
Solución
Ha introducido
[src]
x
x / 2 \ 2*x*e
e *log\x + 2/ + ------
2
x + 2
$$\frac{2 x e^{x}}{x^{2} + 2} + e^{x} \log{\left(x^{2} + 2 \right)}$$
exp(x)*log(x^2 + 2) + ((2*x)*exp(x))/(x^2 + 2)
Simplificación general
[src]
/ / 2\ / 2\\ x
\2*x + \2 + x /*log\2 + x //*e
-------------------------------
2
2 + x
$$\frac{\left(2 x + \left(x^{2} + 2\right) \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2}$$
(2*x + (2 + x^2)*log(2 + x^2))*exp(x)/(2 + x^2)
Respuesta numérica
[src]
exp(x)*log(x^2 + 2) + 2.0*x*exp(x)/(2.0 + x^2)
exp(x)*log(x^2 + 2) + 2.0*x*exp(x)/(2.0 + x^2)
Combinatoria
[src]
/ / 2\ 2 / 2\\ x
\2*x + 2*log\2 + x / + x *log\2 + x //*e
-----------------------------------------
2
2 + x
$$\frac{\left(x^{2} \log{\left(x^{2} + 2 \right)} + 2 x + 2 \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2}$$
(2*x + 2*log(2 + x^2) + x^2*log(2 + x^2))*exp(x)/(2 + x^2)
Denominador racional
[src]
/ / 2\ 2 / 2\\ x
\2*x + 2*log\2 + x / + x *log\2 + x //*e
-----------------------------------------
2
2 + x
$$\frac{\left(x^{2} \log{\left(x^{2} + 2 \right)} + 2 x + 2 \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2}$$
(2*x + 2*log(2 + x^2) + x^2*log(2 + x^2))*exp(x)/(2 + x^2)
Unión de expresiones racionales
[src]
/ / 2\ / 2\\ x
\2*x + \2 + x /*log\2 + x //*e
-------------------------------
2
2 + x
$$\frac{\left(2 x + \left(x^{2} + 2\right) \log{\left(x^{2} + 2 \right)}\right) e^{x}}{x^{2} + 2}$$
(2*x + (2 + x^2)*log(2 + x^2))*exp(x)/(2 + x^2)
Parte trigonométrica
[src]
/ 2\ 2*x*(cosh(x) + sinh(x))
(cosh(x) + sinh(x))*log\2 + x / + -----------------------
2
2 + x
$$\frac{2 x \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{x^{2} + 2} + \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right) \log{\left(x^{2} + 2 \right)}$$
(cosh(x) + sinh(x))*log(2 + x^2) + 2*x*(cosh(x) + sinh(x))/(2 + x^2)