Thread: Calc problem integrate

hi, i wasn't sure how to integrate the following expression by substitution so any help would be appreciated:

1/[x(ln(x)]

Originally Posted by clockingly

hi, i wasn't sure how to integrate the following expression by substitution so any help would be appreciated:

1/[x(ln(x)]

INT.[1 / [x*ln(x)]]dx

Let u = ln(x)
So, du = (1/x)dx

INT.[1 / [x*ln(x)]]dx
= INT.[1 / [ln(x)]] (1/x)dx
= INT.[1/u]du
= ln|u| +C
= ln|ln(x)| +C ------------answer.