f=x^-1
$$\int_{f}^{2f}(f) dx$$
You asked:
Given \(f = {x}^{-1}\) evaluate the expression \(\int_{f}^{2 f}{f}dx\).
MathBot Answer:
\[\int_{f}^{2 f}{f}dx = \int_{{x}^{-1}}^{2 {x}^{-1}}{{x}^{-1}}dx = - \log{\left(\frac{1}{x} \right)} + \log{\left(\frac{2}{x} \right)}\]