This article aims to show how through the use of didactic situations, plausible reasoning and problem solving, the student can solve non-routine problems about antiderivatives. The problems were applied to students taking integral calculus in the engineering faculty of a public university in Bogota, Colombia. The results obtained show the effectiveness of these schools in the teaching and learning of mathematics. The didactic situations presented in this work are based on the approach of non-routine challenging problems that are attractive to students and that can lead them to make conjectures about the concepts presented or proposed by the teacher.
Key words: didactic situations, problem solving, plausible reasoning.