How to determine the antiderivative of function ln x/square root x?

f(x) = ln x / sqrtx

==> u=
ln x ==> du = 1/x dx

==> dv = (1/sqrtx) ==> v =
2sqrtx

==> Int u dv = u*v - INt v
du

= 2sqrtx*ln x - Int (2sqrtx/x) dx

= 2sqrtx*lnx - 2*Int 1/sqrtx dx

= 2sqrtx*lnx -
2*2sqrtx

= 2sqrtx*lnx - 4 sqrtx

=
2sqrtx(lnx -2)

(((To prove tthat Int 1/sqrtx dx = 2sqrtx
:

Let u= sqrtx ==> du = (1/2sqrtx)
dx

==> du = 1/2u dx

==>
2u du = dx

==> Int 1/sqrtx dx = Int 1/u * 2u du = Int 2 du =
2u = 2sqrtx ))))

==> Int lnx/sqrtx =
2sqrtx*(lnx -2).