Sr Examen
¿Cómo vas a descomponer esta log(e+1/x)/2-1/(2*x*(e+1/x)) expresión en fracciones?
Solución
Ha introducido
[src]
/ 1\
log|E + -|
\ x/ 1
---------- - -----------
2 / 1\
2*x*|E + -|
\ x/
$$\frac{\log{\left(e + \frac{1}{x} \right)}}{2} - \frac{1}{2 x \left(e + \frac{1}{x}\right)}$$
log(E + 1/x)/2 - 1/((2*x)*(E + 1/x))
Simplificación general
[src]
/1 + E*x\
-1 + (1 + E*x)*log|-------|
\ x /
---------------------------
2*(1 + E*x)
$$\frac{\left(e x + 1\right) \log{\left(\frac{e x + 1}{x} \right)} - 1}{2 \left(e x + 1\right)}$$
(-1 + (1 + E*x)*log((1 + E*x)/x))/(2*(1 + E*x))
Respuesta numérica
[src]
0.5*log(E + 1/x) - 0.5/(x*(2.71828182845905 + 1/x))
0.5*log(E + 1/x) - 0.5/(x*(2.71828182845905 + 1/x))
Denominador común
[src]
/ 1\
log|E + -|
\ x/ 1
---------- - ---------
2 2 + 2*E*x
$$\frac{\log{\left(e + \frac{1}{x} \right)}}{2} - \frac{1}{2 e x + 2}$$
log(E + 1/x)/2 - 1/(2 + 2*E*x)
Denominador racional
[src]
/ 1\
-2*x + 2*x*(1 + E*x)*log|E + -|
\ x/
-------------------------------
4*x*(1 + E*x)
$$\frac{2 x \left(e x + 1\right) \log{\left(e + \frac{1}{x} \right)} - 2 x}{4 x \left(e x + 1\right)}$$
(-2*x + 2*x*(1 + E*x)*log(E + 1/x))/(4*x*(1 + E*x))
Unión de expresiones racionales
[src]
/1 + E*x\
-1 + (1 + E*x)*log|-------|
\ x /
---------------------------
2*(1 + E*x)
$$\frac{\left(e x + 1\right) \log{\left(\frac{e x + 1}{x} \right)} - 1}{2 \left(e x + 1\right)}$$
(-1 + (1 + E*x)*log((1 + E*x)/x))/(2*(1 + E*x))
Combinatoria
[src]
/ 1\ / 1\
-1 + E*x*log|E + -| + log|E + -|
\ x/ \ x/
--------------------------------
2*(1 + E*x)
$$\frac{e x \log{\left(e + \frac{1}{x} \right)} + \log{\left(e + \frac{1}{x} \right)} - 1}{2 \left(e x + 1\right)}$$
(-1 + E*x*log(E + 1/x) + log(E + 1/x))/(2*(1 + E*x))
Parte trigonométrica
[src]
/1 \
log|- + cosh(1) + sinh(1)|
\x / 1
-------------------------- - ---------------------------
2 /1 \
2*x*|- + cosh(1) + sinh(1)|
\x /
$$\frac{\log{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)} + \frac{1}{x} \right)}}{2} - \frac{1}{2 x \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)} + \frac{1}{x}\right)}$$
log(1/x + cosh(1) + sinh(1))/2 - 1/(2*x*(1/x + cosh(1) + sinh(1)))