This work focus on the application of the polynomial touchard and gegenbauer with the Galerkin method, to a specific type of integro-differential equations, as discussed for example in [1, 2, 4, 6, 7]. In addition, we considered second order integro-differential equations. The results were different depending on whether the Galerkin-Touchard method was used or the Galerkin Gegenbauer method, our research shows that the method is speed, stable, effective and provides satisfactory results, as demonstrated by the examples presented.