1.

Find \(\int \frac{8 dx}{x^2-16}\).(a) \(log⁡\left |\frac{4+x}{4-x}\right |+C\)(b) –\(log⁡\left |\frac{4+x}{4-x}\right |+C\)(c) \(8 log⁡\left |\frac{4+x}{4-x}\right |+C\)(d) \(\frac{1}{8} log⁡\left |\frac{4+x}{4-x}\right |+C\)The question was asked in class test.Origin of the question is Integrals of Some Particular Functions in chapter Integrals of Mathematics – Class 12

Answer»

Correct OPTION is (a) \(log⁡\left |\frac{4+x}{4-x}\right |+C\)

To elaborate: \(\INT \frac{8dx}{16-x^2}=8\int \frac{dx}{4^2-x^2}\)

By using the formula \(\int \frac{dx}{a^2-x^2}=\frac{1}{2A} \left |\frac{a+x}{a-x}\right |+C\)

∴\(8\int \frac{dx}{4^2-x^2}=8(\frac{1}{2(4)} log⁡\left |\frac{4+x}{4-x}\right |)+8C_1\)

\(8\int \frac{dx}{4^2-x^2}=log⁡\left |\frac{4+x}{4-x}\right |+C\)


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