Find \int \frac{2 dx}{x^2-64}.

Category: QuestionsFind \int \frac{2 dx}{x^2-64}.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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