$\displaystyle \int \frac{sec(\sqrt{x})dx}{\sqrt{x}}$
Surely you see it.
If we let $\displaystyle u=\sqrt{x}$, then $\displaystyle du=\frac{1}{2\sqrt{x}}dx$
and $\displaystyle 2du=\frac{1}{\sqrt{x}}dx$
See?. The 2du replaces the $\displaystyle \frac{1}{\sqrt{x}}dx$ in your integral.
Then, we get $\displaystyle 2\int sec(u)du$