Interesting. I spent over an hour on this one but I haven't been able to finish it. The only method I can think of is integrating by parts
int (u dv) = u.v - int (v du)
int Arcsin x = sqrt(1-x^2) + x.Arcsin(x) and
int Log(a/x) = x + xLog(a/x)
so, if this is correct you just have to pick the right values and continue solving the next integral. I haven't given up on this one so I'll keep trying to solve it.