Sr Examen
Integral de (1/(2*pi))*exp(-((ln(x)*ln(x)))/2)/x dx
Solución
Ha introducido
[src]
oo / | | / -log(x)*log(x) \ | | ---------------| | | 2 | | |e | | |----------------| | \ 2*pi / | ------------------ dx | x | / 1
$$\int\limits_{1}^{\infty} \frac{\frac{1}{2 \pi} e^{\frac{\left(-1\right) \log{\left(x \right)} \log{\left(x \right)}}{2}}}{x}\, dx$$
Integral((exp((-log(x)*log(x))/2)/((2*pi)))/x, (x, 1, oo))
Respuesta (Indefinida)
[src]
/
|
| 2
/ | -log (x)
| | ---------
| / -log(x)*log(x) \ | 2
| | ---------------| | e
| | 2 | | ---------- dx
| |e | | x
| |----------------| |
| \ 2*pi / /
| ------------------ dx = C + ----------------
| x 2*pi
|
/
$$\int \frac{\frac{1}{2 \pi} e^{\frac{\left(-1\right) \log{\left(x \right)} \log{\left(x \right)}}{2}}}{x}\, dx = C + \frac{\int \frac{e^{- \frac{\log{\left(x \right)}^{2}}{2}}}{x}\, dx}{2 \pi}$$
Respuesta
[src]
oo
/
|
| 2
| -log (x)
| ---------
| 2
| e
| ---------- dx
| x
|
/
1
-----------------
2*pi
$$\frac{\int\limits_{1}^{\infty} \frac{e^{- \frac{\log{\left(x \right)}^{2}}{2}}}{x}\, dx}{2 \pi}$$
=
=
oo
/
|
| 2
| -log (x)
| ---------
| 2
| e
| ---------- dx
| x
|
/
1
-----------------
2*pi
$$\frac{\int\limits_{1}^{\infty} \frac{e^{- \frac{\log{\left(x \right)}^{2}}{2}}}{x}\, dx}{2 \pi}$$
Integral(exp(-log(x)^2/2)/x, (x, 1, oo))/(2*pi)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.