Find \int \frac{7dx}{x^2-9}.

Category: QuestionsFind \int \frac{7dx}{x^2-9}.
Editor">Editor Staff asked 11 months ago

Find \int \frac{7dx}{x^2-9}.
(a) \frac{7}{6} log⁡|\frac{x-9}{x+9}|+C
(b) \frac{7}{9} log⁡|\frac{x-3}{x+3}|+C
(c) –\frac{7}{6} log⁡|\frac{x+3}{x-3}|+C
(d) \frac{7}{6} log⁡|\frac{x-3}{x+3}|+C
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My query is from Integrals of Some Particular Functions topic in section Integrals of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (d) \frac{7}{6} log⁡|\frac{x-3}{x+3}|+C
Explanation: \int  \frac{7dx}{x^2-9}=2\int \frac{7dx}{x^2-3^2}
By using the formula \int \frac{dx}{x^2-a^2}=\frac{1}{2a} log⁡|\frac{x-a}{x+a}|+C
∴7\int \frac{dx}{x^2-3^2}=7(\frac{1}{2(3)} log⁡|\frac{x-3}{x+3}|)+7C_1
=\frac{7}{6} log⁡|\frac{x-3}{x+3}|+C