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anonymous
 5 years ago
integrate tan to the power 5X
anonymous
 5 years ago
integrate tan to the power 5X

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\tan(x)^{5x}\] Is that the expression?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0variable in the exponent, consider logarthmic manipulation: integrate 5x ln tan theta

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, you didn't say tan of what

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'd guess (in the absence of any variable except x) that it is: \[\tan^{5}x \] But of course, I could be wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The prince has stepped in his concubine to satisfy one of his maidens

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0INweton integrate it.that is the correct question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Rewrite it as \[\tan x(\sec^2x 1)(\sec^2x 1) \] Expand and do it termbyterm. Reduction formulae seems unnecessary, and I can;t see anything quicker right now :@.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You simply let tan x be u and integrate u^5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0OK, I'll do a little more. That expand to \[\tan x \sec^4x  2\tan x\ \sec^2x + \tan x \] And note that \[\frac{\mathbb{d}}{\mathbb{d}x}\frac{1}{n}\ \sec^nx =\tan x\ \sec^nx \] Again, probably something far quicker.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Chaguanas, that doesn't work well because you'll end up with a factor \(cos^2x\) from the substitution of dx.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think it does work (sec^2x = 1 + tan^2x) but it's not MUCH nicer. Again, pretty tired so may be wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, looking at what comes out I'd wager not nicer full stop.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Alternative method: tables: integration tan^u du=(1/(n1)) tan^(n1) u  integral tan^(n2) u du
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