The conjectural newform theory for generic representations of p-adic SO2n+1 was formulated by P.-Y. Tsai in her thesis in which Tsai also verified the conjecture when the representations are supercuspidal. The main purpose of this work is to compute the Rankin–Selberg integrals for SO2n+1×GLr with 1≤r≤n attached to newforms and also oldforms under the validity of the conjecture.