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MTH 102 MTH 102 Past Questions Objective Question
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Question

Evaluate ∫ 1/(x2+4x+7) dx
Options
A <i>(1/&radic;2) tan<sup>-1</sup>((x+3)/&radic;2) + C</i>
B <i>(1/&radic;3) tan<sup>-1</sup>((x+2)/&radic;3) + C</i>
Correct Answer
C <i>(1/&radic;6) tan<sup>-1</sup>((x+7)/&radic;6) + C</i>
D <i>(1/&radic;5) tan<sup>-1</sup>((x+6)/&radic;5) + C</i>
Correct Answer

Option B is the correct answer.

Detailed Explanation

To evaluate this integral, we first complete the square in the denominator.x2+4x+7 = (x2+4x+4) + 3 = (x+2)2 + 3.The integral becomes: ∫ 1/((x+2)2 + 3) dx.This is in the form of the inverse tangent integral: ∫ 1/(u2 + a2) du = (1/a) ∙ tan-1(u/a) + C.Here, u = x+2, so du = dx. And a2 = 3, so a = √3.Substitute these values into the formula:(1/√3) ∙ tan-1((x+2)/√3) + C. This matches option B.

Hint

Complete the square in the denominator to transform the integral into the form ∫ 1/(u2 + a2) du. Then, use the standard integral for inverse tangent.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 786 of 930
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