Question Detail

MTH 102 MTH 102 Past Questions Objective Question

Question

Solve ∫1/(x ln x) dx
Options
A e<sup>x</sup> / x
B ln x / x
C ln(ln x)
Correct Answer
D (ln x)² / 2
Correct Answer

Option C is the correct answer.

Detailed Explanation

To solve ∫1/(x ln x) dx, use u-substitution.Let u = ln x.Then, the differential du = (1/x) dx.Substitute these into the integral:∫(1/u) duThis is a standard integral:= ln|u| + CSubstitute back u = ln x:= ln|ln x| + CThis matches option C.

Hint

Consider a substitution for ln x. What is its derivative?

Question Info