Integral of (sec(x/8))^2tan(x/8)

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Integral of (sec(x/8))^2tan(x/8)

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Hi Math Sorcerer, thanks for all your help!

I just completed this problem on your Udemy course and it really has me stumped. I completed the other way, considering the odd tangent, saved a secant·tangent and did a U-sub with secant.

Doing it this way I arrived to the answer 4sec^2(x/8) instead of 4tan^2(x/8). These are not equal, please help!

stephenevans