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Integral of (cot4x)^5 (csc4x)^7

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ah! good one! Looks easy, but there's some algebra and trig identities involved. Rather than slog through it here, I refer you to

http://www.wolframalpha.com/input/?i=integral+%28cot4x%29^5+%28csc4x%29^7

and hit the "step by step solution" button.
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