Question Detail
Question
Evaluate the integral $\int \frac{\cos(\ln x)}{x} dx$.
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 $du$: $du = \frac{1}{x} dx$.Substitute $u$ and $du$ into the integral:$\int \cos(u) du$The integral of $\cos(u)$ with respect to $u$ is $\sin(u) + C$.Substitute back $u = \ln x$:$\sin(\ln x) + C$.
Hint
Consider a substitution for the argument of the cosine function.