A number of integral formulas involving a variety of special functions have been developed by many authors. In the project, we have discuses some interesting integrals involving the product of Bessel function of the first kind with Jacobi polynomial, which are expressed in terms of Kampé de Fériet and Srivastava and Daoust functions. Some other integrals involving the product of Bessel (sine and cosine) function with ultra-spherical polynomial, Gegenbauer polynomial, Tchebicheff polynomial, and Legendre polynomial are also established as special cases.