This antiderivative has arguable the highest ratio of “really hard to compute” to “really easy to write”:
As we’ve seen in this series, the answer is
Also, as long as and , there is an alternative answer:
In this concluding post of this series, I’d like to talk about the practical implications of the assumptions that and .
For the sake of simplicity for the rest of this post, let
If I evaluate a definite integral of over an interval that contains neither or , then either or can be used. Courtesy of Mathematica:
However, if the region of integration contains either or (or both), then only using returns the correct answer.