Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Solve ∫ 1/(x ln x) dx.
Options
A ln(x) + C
B ln(ln x) + C
Correct Answer
C ln(x²) + C
D x ln x + C
Correct Answer

Option B is the correct answer.

Detailed Explanation

To solve ∫ 1/(x ln x) dx, use u-substitution. Let u = ln x. Differentiating u with respect to x gives du/dx = 1/x, so du = (1/x) dx. The integral transforms into: ∫ 1/u du. The integral of 1/u with respect to u is ln|u| + C. Substituting back u = ln x, the final answer is ln|ln x| + C.

Hint

Use u-substitution. Let u = ln x and find du. This substitution simplifies the integral into a basic logarithmic form.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 358 of 930
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