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ggrree
 3 years ago
integral of:
tan^78 (x) * sec^4 (x)
ggrree
 3 years ago
integral of: tan^78 (x) * sec^4 (x)

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badreferences
 3 years ago
Best ResponseYou've already chosen the best response.2Is... that tan(x)^78? Good... Gods...

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.2I'm not doing 78 half angle identity integrals.

ggrree
 3 years ago
Best ResponseYou've already chosen the best response.0Apparently there's a clever way to do it

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.2You should make your teacher mad and do 70 half angle identity integrals.

Hermeezey
 3 years ago
Best ResponseYou've already chosen the best response.1Holy crap! thats a lot Tangents, anways: \[\sec^4x = \sec^2x \sec^2x = (\tan^2x +1)(\sec^2x)\] now use a USub where: \[u=tanx\] \[du=\sec^2x dx\] so now we have: u^78 (u^2 + 1) du distributing the u^78, we get: u^80  u^78 du now just integrate and we get (1/81) (u^81) + (1/79) (u^79) now plug back in the tanx (1/81) (tan^81x) + (1/79)(tan^79x)

Hermeezey
 3 years ago
Best ResponseYou've already chosen the best response.1i might have made a mistake somwhere, i mean, THATS A LOT O TANGENTS haha

badreferences
 3 years ago
Best ResponseYou've already chosen the best response.2Whoa man, that's like, clever. I was thinking also of something clever, like a series representation of each new half angle integral, but your method was by far the best.

Hermeezey
 3 years ago
Best ResponseYou've already chosen the best response.1Haha I just learned how to integrate the trig stuff so its still fresh in my mind. But I think it would be pretty smart to use a Series representation for each of the halfangles

ggrree
 3 years ago
Best ResponseYou've already chosen the best response.0That's the right answer. Thanks!
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