how do i find the integral of t*sec(t)^-1 dt ?

i figure set u=t v=ln(sec(t))

du=1 dt dv=sec(t)^-1 dt

I'm going to use S for the integral symbol.

then i'd get t*ln(sec(t)) - Sln(sec(t))

is this correct so far? how do i find the integral of ln(sec(t))? i don't know what to do at this point