Summary: An algorithm is presented for integrating expressions of the form \(\int ge^ fdx\), where f and g are rational functions of x, in terms of a class of special functions called the special incomplete \(\Gamma\) functions. This class of special functions includes the exponential integral, the error function, the sine and cosine integrals, and the Fresnel integrals. The algorithm presented here is an improvement over those published previously for integrating with special functions in the following ways: (i) This algorithm combines all the above special functions into one algorithm, whereas previously they were treated separately. (ii) Previous algorithms require that the underlying field of constants be algebraically closed. This algorithm, however, works over any field of characteristic zero in which the basic field operations can be carried out. (iii) This algorithm does not rely on Risch’s solution of the differential equation \(y'+fy=g\). Instead, a more direct method of undetermined coefficients is used.