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The Moller experiment and the P2 experiment aim at measuring the weak mixingangle at low scales. The Moller experiment uses $e^- e^- \rightarrow e^-e^-$-scattering, the P2 experiment uses $e^- N \rightarrow e^- N$-scattering.In both cases, two-loop electroweak corrections have to be taken into account,and here in particular diagrams which give rise to large logarithms. In thispaper we compute a set of two-loop electroweak Feynman integrals for point-likeparticles, which are obtained from a box integral by the insertion of a lightfermion loop. By rationalising all occurring square roots we show that theseFeynman integrals can be expressed in terms of multiple polylogarithms. Wepresent the results in a form, which makes the large logarithms manifest. Weprovide highly efficient numerical evaluation routines for these integrals.

Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle