There are some definite integrals whose indefinite form can not be evaluated. For example the Gaussian integral, the integral of sinx/x etc. For the first we could use double integration and the apply the polar substitutions while for the second one may use Laplace transformations. Could you please give a list of the most important definite integrals whose indefinite form can not be solved? And also what are the most interesting and important techniques to evaluate such definite integrals? Are there good references including methods to solve them?
Any help will be appreciated.