Question Detail
Question
Evaluate ∫ Cos(lnx)/x dx
Correct Answer
Option D is the correct answer.
Detailed Explanation
To evaluate the integral ∫ Cos(lnx)/x dx, we use u-substitution.Let u = lnx.Then, the derivative of u with respect to x is du/dx = 1/x, which means du = (1/x) dx.Substituting u and du into the integral, we get:∫ Cos(u) duThe integral of Cos(u) with respect to u is sin(u) + C.Now, substitute back u = lnx:sin(lnx) + CTherefore, the correct option is D.
Hint
Consider a substitution for the argument of the cosine function.