This Simple Trig Integral Is Trickier Than It Looks
Автор: Calculus Diaries
Загружено: 2025-12-30
Просмотров: 530
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In this video, we evaluate the integral of tan(x)*sqrt(sec(x)+tan(x)) dx using a clever substitution that turns a messy trigonometric expression into a surprisingly clean result. This problem looks simple at first glance, but it hides a beautiful trick that makes the integration almost effortless once you see it.
The hurdle lies in expressing tan(x) and sec(x) in terms of the new substitution variable. I rely on the identity that sec^2(x)-tan^2(x) = 1, which is utilized along with the substitution, u^2=sec(x)+tan(x).
This type of integral frequently appears in advanced calculus, trigonometric substitution problems, and math competition settings. If you enjoy elegant calculus techniques and smart substitutions, this video is for you.
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#calculus #integralcalculus #integrationtechniques #integration #trigonometricalidentities #maths
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