Question

What's the indefinite integral of 1/(xln(x)) via substitution?

I set u = lnx then solved for dx to get x du. From here I subbed the values into my integral to get 1/ln(u). I wasn't sure how to do this part, but I got 1/(lnxln(lnx)-lnx) + C which I don't think is right...

Answer 1

1 dx 1 du
S 1/(xln(x)) = S -------- = S ------ = ln u = ln(lnx) answer
x ln x u

let u= ln x then

1 dx
du= -----
x

Answer 2

ln(lnx) +C ANSWER