In this video basic methods of exponential integration are discussed. The formula E^(function) is introduced, where the derivative of the function is multiplied by the exponential function. Several examples are provided to illustrate how to apply this formula, including exponential functions with linear and quadratic arguments, as well as trigonometric functions. The key idea is to recognize the pattern of an exponential function raised to a function, and check if the derivative of that function is present. If it is, the integral can be easily solved using the formula. Various examples are worked through, including cases where constants need to be added or compensated for to apply the formula. The video concludes by emphasizing the importance of regular practice when working with exponential integration.