Question Detail

MTH 102 MTH 102 Past Questions Objective Question
Take CBT

Question

Evaluate ∫ Cos(ln x) / x dx
Options
A sec(ln x) + C
B tan(ln x) + C
C cot(ln x) + C
D sin(ln x) + C
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

This integral can be solved using substitution.Let u = ln x.Then, find the differential du:du = d/dx(ln x) dxdu = (1/x) dxNotice that (1/x) dx is present in the integrand. Substitute u and du into the integral:∫ Cos(u) duThis is a standard integral:= sin(u) + CFinally, substitute back u = ln x:= sin(ln x) + CThis matches option D.

Hint

Identify a part of the integrand whose derivative is also present, suggesting a u-substitution.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 776 of 930
Previous Course Details Next