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Integral calculus of real single variable functions is a traditional part of university mathematics courses. In order to determine the indefinite integrals of functions the wellknown methods - integration by parts and an array of ingenious substitutions in form of strict algorithmic procedures are applied which enable one to arrive at the result corresponding to the given class of functions. The high level of algorithmization in this part of mathematics makes students believe that the algorithms are the only ways leading to correct solutions. This paper aims to argue that such a belief is a misconception. Similarly to many other mathematics branches, integral calculus is not really deprived of the splendid opportunities to perform mathematical experimentation and employ diverse solving strategies.