\displaystyle $\begin{align}
\int\limits_0^{+\infty} \frac{C}{x} e^{-(\ln x - 1)^2} dx & = \left[ \begin{array}{l}
t = \sqrt{2}(\ln x - 1) \\
dt = \sqrt{2} \frac{dx}{x}
\end{array} \right] = \int\limits_{-\infty}^{+\infty} C e^{-\frac{t^2}{2}} \frac{dt}{\sqrt{2}} = C \sqrt{\pi} \int\limits_{-\infty}^{+\infty} \frac{1}{\sqrt{2 \pi}} e^{-\frac{t^2}{2}} dt \\
& = C \sqrt{\pi}
\end{align}$