Differentiation and integration (anti-differentiation) constitute one of the fundamental techniques used in higher mathematics. These operations are inverse of each other. While differentiation (to the extent of school mathematics) is relatively simple and straightforward, integration, in general, is a much more involving task. There are various classical methods to evaluate elementary integrals, e.g. substitution, integration by parts, partial fraction decomposition or more advanced techniques like the residue theorem, or Cauchy's integral formula. The paper deals with some types of elementary functions whose integrals can be evaluated by intelligent guess and differentiation.

Faculty of Engineering of the Slovak University of Agriculture belongs among the six of its faculties. This faculty is attended by students from different types of secondary schools. The study outlines of the faculty contain two semesters in mathematics which should provide students with a theoretical base for further study of major subjects. Students learn here the basics of differential and integral calculus. In the subject of Mathematics 2 they learn to evaluate indefinite and definite integrals. In our paper we focus on how students cope with this part of mathematics and what causes most problems in this area.

One of the most important computational techniques in higher mathematics is differentiation and its counterpart, integration (anti-differentiation). While differentiation is a routine and relatively simple procedure, integration, in general, is a much more involving task. Close (inverse) relationship between differentiation and anti-differentiation (evaluation of indefinite integrals) in some cases reveals the possibility to derive the form of the antiderivative and evaluate this antiderivative by differentiation and subsequent comparison of coefficients. This paper is a sequel to [4] and deals with some other types of elementary functions whose integrals can be evaluated by differentiation.

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