Question Detail
Question
Evaluate ∫ Cos(ln x) / x dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
This integral can be solved using u-substitution.Let u = ln x.Then, find the differential du: du = d/dx(ln x) dx = (1⁄x) dx.Substitute u and du into the integral:∫ Cos(u) duIntegrate with respect to u:= sin(u) + CSubstitute back u = ln x:= sin(ln x) + C.This matches option D.
Hint
Look for a function whose derivative is also present in the integrand. Try u-substitution with u = ln x.