1.

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) \(\frac{7}{6} log⁡|\frac{x-3}{x+3}|+C\)I have been asked this question during an interview for a job.My query is from Integrals of Some Particular Functions topic in section Integrals of Mathematics – Class 12

Answer»

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 \(\int \frac{dx}{x^2-a^2}=\frac{1}{2A} log⁡|\frac{x-a}{x+a}|+C\)

∴\(7\int \frac{dx}{x^2-3^2}=7(\frac{1}{2(3)} log⁡|\frac{x-3}{x+3}|)+7C_1\)

=\(\frac{7}{6} log⁡|\frac{x-3}{x+3}|+C\)


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