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, we use a substitution. Let u = ln x. Then, the differential du = (1/x) dx. Substituting these into the integral, we get ∫ Cos(u) du. The integral of Cos(u) with respect to u is sin(u) + C. Finally, substitute back u = ln x to get the result: sin(lnx) + C.
Hint
Consider a substitution for the argument of the cosine function.