Evaluate `int sec^(-1)xdx`

Explanation

Put `sec^(-1)x=t` so that x =`sect` and `dx=sect tant dt`
`therefore intsec^(-1)xdx=intt(sect tant) dt = t(sect)-int(1.sectdt)`
`tsect=ln|sect+tant|+C`
`tsect-ln|sect + sqrt(sec^(2)t-1)|+C=x(sec^(-1)x)-ln|x+sqrt(x^(2)-1)|+C`