Start by drawing a sketch.

It is easiest to evaluate this integral using horizontal strips. You can see that the region is bounded on the left by the y = 1/x graph, but since we are integrating over x first, that means it's bounded by x = 1/y, and the region is bounded on the right by the y = sqrt(x) graph, but since we are integrating over x first, that means it's bounded by x = y^2.

We can also see that the horizontal strips are bounded below by y = 1 and bounded above by y = 3.

So