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Integral cot^4 (x) dx?

Substitution right? Anyone kind enough to show how.

Rewrite cot^4 as (csc^2 - 1)^2.
Expand that bracket.
Rewrite csc^4 as csc^2 (1+cot^2).

Then you still have to make a couple of substitutions to integrate some of the terms, but it's easier than doing it at the beginning.

Reply 2

the_world_was_a_beachball

thanks, i'll give it a go. I was hoping there would be a magic substitution involving cot but your way sounds more practical.

Reply 3

James

Yes, I'm not sure if there's such a 'magic substitution' but it makes sense to use some of the identities to split the integrand into several terms of smaller powers. And it helps that csc^2 cot^2 is easy to integrate!