HELP HELP! Integrate square root of tanx.?

Answer 1

(1/(2Sqrt(2)))[-2arctan[1-Sqrt(2)Sqrt(tanx)] +
2arctan[1+Sqrt(2)Sqrt(tanx)] +
Ln[-1+Sqrt(2)Sqrt(tanx)-tanx] -
Ln[1+Sqrt(2)Sqrt(tanx)+tanx]]

Answer 2

This question has been asked and answered several
times before. Do a search for questions and
type in sqrt(tan(x)). You will find a very nice
solution there, involving the substitution
y = sqrt(tan(x)).
I also posted a solution under mathematics
a while ago in which I let u = tan x, x = arctan u,
dx = du/(1+u^2). Then let u = t^2, du = 2t dt.
Either way you will end up with the integration
of a rational function.
Let me also state that if you are trying to
integrate sqrt(f(x)), where f(x) is one
of the 6 trig functions, only sqrt(tan(x))
and sqrt(cot(x)) are integrable in terms of
elementary functions.