calculus – Double integral over a typical region.

Question:Let R be the region in $xy$-plane bounded by the curves $y=x^2,y=4x^2,xy=1,xy=5$.
Then find the value of line integral $iintfrac{y^2}{x}dydx$.

I found it tough and time taking if I evaluate this integral from general method,is there any theorem which make it easy?Since the question is asked in competitive exam so I hope there must be an easy and fast way to solve it.

Any help will be appreciable

Thanks in advance