the question is

show

i cant get the first term, i end up with

i proceeded by parts with

v'=1 dv=x

so im left with integrating

which gives me

ive put the values 2artan(2) and arcsin(4/5) in calculator and they are not the same so not sure where im going wrong here.

ALSO as im mentioning arsech my books gives the formula for the log form as

how can this be? for the other inverse hyperbolics they pick the positive, why take both for arsech x? how do i work out arsech (3) say? how do i know whether to pick the = or the - value?