Set so that and . Under this change of variable, the given indefinite integral becomes
Of course, there are settings in which the addition of an arbitrary constant is deemed essential.
Although it would be possible to expand the numerator and integrate termwise, it is not a recommended approach to integration! In fact, termwise integration produces a result that does not factor to the compact expression obtained above because of a missing additive constant.
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In fact, termwise integration produces a result that does not factor to the compact expression obtained above because of a missing additive constant of . This can be seen by expanding , that is, from
(which was done in Maple by applying Expand from the Context Panel.)