  The construction of an explicit basis for a free multiarrangement is not easy
in general. Inspired by the integral expressions for quasi-invariants of
quantum Calogero-Moser systems, we present integral expressions for specific
bases of certain multiarrangements. Our construction covers the cases of three
lines in dimension $2$ (previously examined by Wakamiko) and free
multiarrangements associated with complex reflection groups (Hoge, Mano,
R\"ohrle, Stump). Furthermore, we propose a conjectural basis for the module of
logarithmic vector fields of the extended Catalan arrangement of type $B_2$.
