Question

How do you evaluate ∫sqrt(lnx)/x dx ?

Answer 1

let u = lnx
du = dx/x

you can finish from here

Answer 2

Alternatively. Let \(x=e^u\) and \(dx = e^udu\).

Answer 3

I have that part down I just dont know what to do after that

Answer 4

you got sqrt(u) du yes?

Answer 5

yes

Answer 6

sqrt(u) = u^(1/2), now use use the power rule

Answer 7

yes which gives me 1/2u^-1/2

Answer 8

If \(n=1/2\) then \(n+1=3/2\) and \(1/(n+1) = 2/3\)

Answer 9

wait, thats the antiderivative , don't we need to find the derivative of u first?