Question Detail
Question
Evaluate ∫ Cos(ln x) / x dx.
Correct Answer
Option D is the correct answer.
Detailed Explanation
To evaluate the integral ∫ Cos(ln x) / x dx, use u-substitution.Let u = ln x.Then, differentiate u with respect to x: du/dx = 1/x, which means du = (1/x) dx.Substitute u and du into the integral:∫ Cos(u) duThe integral of Cos(u) with respect to u is sin(u).∫ Cos(u) du = sin(u) + CFinally, substitute back u = ln x:sin(ln x) + C.
Hint
Consider a u-substitution where u is the argument of the cosine function.