Question Detail

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) duThe integral of Cos(u) with respect to u is Sin(u).So, ∫ Cos(u) du = Sin(u) + C.Finally, substitute back u = ln x:Sin(ln x) + C.Thus, option D is correct.