Abstract
ABSTRACT We discuss a non-routine technique to solve some classes of integrals, which could enrich the syllabus of a first-year undergraduate calculus course. We begin with the class from which the inspiration originates: integrals of quotients of linear combinations of sines and cosines. Subsequently, we discuss a generalization, dealing with quotients formed by a linear combination of two arbitrary functions on the denominator and a linear combination of their derivatives on the numerator. Finally, for a variation, we consider integrals of quotients of linear combinations of three functions: exponentials, sines, and cosines.
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