Note that $\displaystyle \frac{d}{dx} \ln x = \frac{1}{x}$.
The Fundamental Theorem of Calculus states that if F'(x) is the derivative of F(x), then $\displaystyle \int _a ^b F'(x) \cdot dx = F(b) - F(a)$.
In your question, this means $\displaystyle \int _{0.025} ^{0.075} \frac{1}{r} \cdot dr = \ln (0.075) - \ln (0.025)$, which is $\displaystyle \ln \left(\frac{0.075}{0.025}\right)$ by the rules of logarithms.