integrate tangent radical x?

Answer 1

this works. first make the substitution

u=x^(1/2)

then du = (1/2) x^(-1/2) dx

or dx = 2x^(1/2) du = 2u du

So Int { tan x^(1/2) dx} = 2 Int { u tanu du}.

Now integrate by parts.

Answer 2

rewrite as (sin radical x) / (cos radical x) then try integration by parts two times. If that doesn't work, it's either very difficult or impossible to do