Story time
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As an undergrad, I remember seeing the proof for the antiderivative of sec(x).
The key of the proof is to cleverly multiply by sec(x)+tan(x)/sec(x)+tan(x), and pop goes the weasel.pic.twitter.com/Y0iIzvBFFR
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I have to teach my calculus students how to integrate sec(x) pretty soon, maybe this week. It's a bit traumatic since it must make them think "how the hell could anyone have guessed that?"
sec(x) + tan(x) returned itself times sec(x)
That's true.. I know there's another way, but it's probably more traumatic. Write cosine as complex exponentials --> u=e^{ix} --> partial fractions.. Yea, they'll love that.
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Hmm, I should give that a try myself. I've been doing integrals in more different ways in this class than usual, and learning more about what works and what doesn't.
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There's actually another way to do it that I think would be more instructive than sec(x) + tan(x).. Instead multiply by cos(x)/cos(x), then denominator as 1-sin^2(x).. u-sub sin(x) and pop goes the weasel
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