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inkyvoyd
 one year ago
integrate sqrt(sqrt(tan x))
any way to do this?
inkyvoyd
 one year ago
integrate sqrt(sqrt(tan x)) any way to do this?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{\sqrt{tanx}} ???\]

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0I know how to do sqrt(tan x). it's very messy. but I wonder how to do (tan x)^(1/(2n)) for all natural numbers n

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0so first, sqrt(sqrt(tan x))

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0but it's doable... how though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0did u see the attachment its doable if u have an free hour in ur hand

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0it will only take 1 hour?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0r u asking me or telling me !

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0I dont' know... just wonder if it's doable

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is doable yea , as u can see wolfram puked the answer out however it ll take alot of time

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0I don't mind... but do you know how to start it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes using substitution

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0that's not specific enough...

Empty
 one year ago
Best ResponseYou've already chosen the best response.2I think you can probably rewrite it as \[\int \frac{\sin^{1/4}x}{\cos^{1/4}x} x dx\] And then from there I would try to screw around with some substitutions maybe, I am only kinda guessing this because there ended up being some logarithms and garbage.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2subing \(u^4 = \tan x\) gives \[\int \dfrac{4u^4}{1+u^8}\,du\] which ofcourse is a pain even for those who like partial fractions so much

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you could turn it into a beta integral if it is a definite integral between 0>1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hmm... \[\begin{align*}\frac{u^4}{u^8+1}&=\frac{u^4}{2}\left(\frac{u^4+1}{u^8+1}\frac{u^41}{u^8+1}\right)\\[2ex] &=\frac{u^4}{2}\left(\frac{1+\dfrac{1}{u^4}}{u^4+\dfrac{1}{u^4}}\frac{1\dfrac{1}{u^4}}{u^4+\dfrac{1}{u^4}}\right)\\[2ex] &=\frac{u^4}{2}\left(\frac{1+\dfrac{1}{u^4}}{\left(u^2\dfrac{1}{u^2}\right)^2+2}\frac{1\dfrac{1}{u^4}}{\left(u^2+\dfrac{1}{u^2}\right)^22}\right)\\[2ex] &=\frac{u^3}{4}\left(\frac{2u+\dfrac{2}{u^3}}{\left(u^2\dfrac{1}{u^2}\right)^2+2}\frac{2u\dfrac{2}{u^3}}{\left(u^2+\dfrac{1}{u^2}\right)^22}\right)\end{align*}\] Maybe we can integrate by parts? The rational terms to the right can be integrated "nicely"...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Meh, I wouldn't count on IBP here...

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.0I finally see why the answer is so long.
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