Calculate the length of a polar curve 
Calculate the length of the polar curve $$\theta (r)=\frac{1}{2}\left( r+\frac{1}{r}\right)$$ from r = 1 to r = 3.

I understand mostly how to get the length of a polar curve by:
$$\int_{a}^{b} \sqrt[]{(f(\theta ))^{2}+(f'(\theta ))^{2}} \ d\theta $$
But in this exercise i dont get how to do it. Maybe i need to write the function $\theta (r)$ in terms of $\theta$
Any ideas or hints? Thanks

Building on my comment, since $rd\theta/dr=\tfrac12(r-\tfrac1r)$, $\int ds=\int_1^3\tfrac12(r+\tfrac1r)dr=2+\tfrac12\ln3$.
