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Find \(\int \frac{2 dx}{x^2-64}\).(a) –\(log⁡\left |\frac{x+8}{x-8}\right |+C\)(b) \(\frac{3}{2} log⁡\left |\frac{x+8}{x-8}\right |+C\)(c) \(log⁡\left |\frac{x+8}{x-8}\right |+C\)(d) \(\frac{1}{8} log⁡\left |\frac{x-8}{x+8}\right |+C\)The question was asked in my homework.Question is taken from Integrals of Some Particular Functions topic in chapter Integrals of Mathematics – Class 12

Answer»

The correct choice is (d) \(\frac{1}{8} log⁡\left |\frac{x-8}{x+8}\right |+C\)

The best EXPLANATION: \(\INT \frac{2 dx}{x^2-64}=2\int \frac{dx}{x^2-8^2}\)

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

∴\(2\int \frac{dx}{x^2-8^2}=2(\frac{1}{(2(8))} log⁡|\frac{x-8}{x+8}|)+2C_1\)

=\(\frac{1}{8} log⁡|\frac{x-8}{x+8}|+C\)


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