Please help me with this one:
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)
Knowing that
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.
This cannot be computed nicely
Now we are only interested in the second integral. First let
Giving us
Integration by parts gives that this is equivalent to
Now for the second integral we only care about the first term...so in that we let
After simplification this gives us
This looks kind of messy but isnt too bad...do all the undone work...there is your integral