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help me w calculus plz


claire
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ok so this worksheet was due like 2 months ago aand i dont remember shit so im stuck on this 1 problem

evaluating indefinite integrals:

[cool swirly symbol] tan^2(2x) * sec^2(2x) dx

wat i want to know is...what do i set as u

im not sure if i should be doing u = 2x or rewriting the problem as (tan2x*sec2x)^2 (if thats allowed??) and then making it u = tan2xsec2x and then going from there??

for the first method ts like... i tried that but idk wtf im supposed to do w the integral of (tan^2(u) * sec^2(u)) * du/2 ... as in WHAT is the antiderivative of that. we prob did smth like this in class but i m not organized and idk where any of my notes are and i honestly ccccannot remember at all, ty in advance

 

EDIT: i figured it out oops hehe nvm

Edited by claire
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I don't remember anything about calculus because i last studied it 4 years ago and haven't used it since, but according to the internet, dtan(x)/dx = sec²(x)

So yeah, try using u = tan(2x) and turning the integral into ∫u²(dx)*u'(x)dx which nets to ∫u²d(u) or something similar to it

take all of that with a grain of salt, since I don't remember much about it, but I think that the sec²(x) being the derivative of tan(x) is pretty important

Edited by Nobody
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"cool swirly thing"

kekekekeke

i didnt really use integrals till physics tbh. calc made us perform integrals with no purpose, but when you take physics, you make an integral to serve you. and you kinda realize that higher level math exists not to make shit harder, but to make problems easier. 

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s'ok guys i got it but thanks!! 

another question tho... is anybody here fluent in spanish, interested in colombian culture, and very bored :(

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