Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

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

Option D is the correct answer.

Detailed Explanation

To evaluate the integral, use u-substitution. Let u = ln x. Then the differential du = (1/x) dx. Substituting these into the integral gives ∫ Cos(u) du. The integral of Cos(u) with respect to u is Sin(u) + C. Substituting back u = ln x, we get Sin(ln x) + C.

Hint

Consider using u-substitution. What would be a good choice for 'u' in this integral?

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 633 of 930
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