Integral of cot^3(x), calculus 2 tutorial

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Integral of cot^3(x), using cot and csc
integral of (cot(x))^3,
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#blackpenredpen #math #calculus #apcalculus
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Just bombed this problem on a quiz... Great explanation!

jonathanwever
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What is your explain for:
-1/2(Cotx)^2–In(sinx)+C = -1/2(Cscx)^2+In(Cscx)+C

acmontolivo
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When i used u=csc(x) i get the wrong integral for some reason.

republicofvegans
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Some people find [ - (csc² x )/ 2 - ln|sin x| + C ] as result while others find [ - (cot² x)/ 2 - ln|sin x| + C ]. Which one is correct, man?

blackcitadel
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So just a thought. Maybe work on finding a general solution for powers of trig functions like the integral of (sin(x))^n equals such and such

Econcrafter
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could we have expressed cot^3(x) as cos^3(x)/sin^3(x) and used u substitution if we did not know the integral of cot(x)?

Nithesh
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wowww 💙💙💙 can I borrow ur brain tom I have quiz on cal lmao

tennymalubs