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MTH 102 MTH 102 Past Questions Objective Question
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Question

Evaluate ∫ (e^(2x) + e^(-2x)) / (e^(2x) - e^(-2x)) dx
Options
A 1/4 ln|e^(2x) - e^(-2x)| + C
B 1/2 ln|e^(2x) + e^(-2x)| + C
C 1/2 ln|e^(2x) - e^(-2x)| + C
Correct Answer
D 1/4 ln|e^(2x) + e^(-2x)| + C
Correct Answer

Option C is the correct answer.

Detailed Explanation

Use substitution. Let u = e2x - e-2x (the denominator).Then, du = d/dx [e2x - e-2x] dx.du = (2e2x - (-2e-2x)) dx = (2e2x + 2e-2x) dx = 2(e2x + e-2x) dx.From this, (e2x + e-2x) dx = (1/2)du.Substitute u and (1/2)du into the integral: ∫ (1/u) * (1/2)du = (1/2) ∫ (1/u)du.The integral of 1/u is ln|u|. So, we get (1/2)ln|u| + C.Substitute u back: (1/2)ln|e2x - e-2x| + C.

Hint

Consider a substitution for the denominator of the integrand.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 557 of 930
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