integrate: 3 ln(x) / sqrt(x)?

Answer 1

Looks like an integration by parts.
S (U dV) = UV + S(VdU)
Let U= 3 ln(x)
dU= 3/x dx
let dV= dx/sqrt(x)
and V= 2sqrt(x)
Then UV= 6 ln(x)sqrt(x)
and VdU= 6/(sqrt(x), which integrates to
12 sqrt(x) . So the answer looks like
6* sqrt(x) (ln(x)+2)

Answer 2

Check out Maple 11, then all you have to do is type int(3*ln(x)/sqrt(x),x); and press enter. Easier than writing in for "help" eh?

Answer 3

3 ln(x) / sqrt(x)
=3(Inx)*x^(-1/2)
u=Inx du=dx/x dv=x^-1/2 v=2x^1/2
uv-integral(vdu)
Inx * 2x^1/2-integral(2x^1/2*dx/x)
Inx * 2x^1/2-integral(x^-1/2dx)
Inx * 2x^1/2-2x^1/2
2x^1/2(Inx-1)