what is integral of log(tanx)dx? show the working?

Answer 1

Need that sec^2 x, huh? Let's produce it in the integrand:

int( log(tan x) * sec^2 x * cos^2 x dx ).

Now you can set:

v = cos^2 x
du = log(tan x) * sec^2 x dx

and integrate by parts. This will get rid of the log.

Hope this helps.