I recently had an unusual experience involving academics and wanted to share. There's no moral, comment, or witty observation here, just an at-the-time frustrating story.
I was working on a graded free-response homework assignment for my online Calculus AB class, specifically about integrals concerning inverse trigonometric functions and logarithms. The first three questions were fairly simple, but the final (fourth) one was unlike anything I had seen in the instructional materials.
The problem required me to integrate something that looked somewhat like it would become an inverse tangent. However, the normal tricks of fraction rearranging and substitution were ineffective; the degree of the numerator was just 1 too low. (Another part of the same question required me to take an integral superficially very similar to this, except the techniques they taught me actually worked.)
Though they didn't teach me partial fractions, I knew of the existence of such things and looked up how to perform the decomposition. (Having to learn or re-learn concepts using external sources is par for the course for my use of this online learning platform.) The decomposition didn't work; I had subtly miscopied the denominator and the real denominator could not be factored in a way that could be decomposed. I then learned and tried integration by parts, but it failed for various and sundry reasons.
At this point, I had been working on the problem for half a Sunday and throughout various classes on Monday for a total of several hours. Unable to get anywhere, I went to ask the on-campus calculus teacher. We worked at it for half an hour; he tried things that I hadn't seen before at all. After lots of complicated-looking approaches, we discovered that the problem was more or less impossible.
He suggested that I "reinterpret" the problem and simply change the denominator to something I can deal with. I did so, solved the revised problem, and included some analogy of this account in my submission.
The teacher gave me a perfect score.
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