Question Detail
Question
Integrate ∫1/(x - xln(x)) dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
First, factor the denominator: ∫1/(x(1 - lnx)) dx.Let u = 1 - lnx.Then, differentiate u with respect to x: du/dx = -1/x, which means dx/x = -du.Substitute these into the integral:∫1/u (-du) = -∫1/u duThe integral of 1/u is ln|u|.So, -ln|u| + C.Substitute back u = 1 - lnx:-ln(|1 - lnx|) + C.
Hint
Look for a substitution that simplifies the denominator. Factoring out 'x' from the denominator is a good first step.