<p>This work aims to introduce two effective computational methods for solving some types of integral equations using an artificial neural network (ANN). The neural network mentioned is made up of three layers: the input layer, the hidden layer, and the output layer. We consider shifted Gegenbauer polynomials in the hidden layer and hyperbolic functions in the output layer as activation functions. We utilize two techniques for training the neural network, the classical optimization and collocation methods. The convergence and error analysis for the presented methods are derived. Finally, several examples are included to demonstrate the effectiveness and precision of the current techniques. Also, we compare our technique with other numerical schemes.</p>