This monograph contains a collection of integrals, some more challenging than others, with their worked-out solutions as indefinite integrals. The integrals were randomly selected, modified, or designed with the condition of having closed forms solutions with common functions. This list is meant for helping readers in practicing and getting hints for working out solutions to similar integrals that they might encounter. Readers might want to add their own favorite integrals to this list. We also present the application of some integrals in engineering related topics. For example, nonuniform loading, hydrostatic force, moment of inertia, polar moment of inertia, etc. We introduce an up-to-date online software tool, WolframAlpha, that can be used for comparing our answers for the integrals listed. However, readers may want to update to WolframAlpha Pro for recovering some of the integrals’ step-by-step solutions. In addition, similar CAS (computer algebra system) tools like Maple, Mathematica, or Mathcad may also be employed.