∫ dx/(a² - x²) (for |x| < a):
Aarcsin(x/a) + C
B(1/2a) ln |(a+x)/(a-x)| + C
C-arctan(x/a) + C
Dln |a-x| + C
Answer & Solution
Correct answer: B. (1/2a) ln |(a+x)/(a-x)| + C
By partial fractions: 1/(a² - x²) = 1/((a-x)(a+x)) = (1/2a)(1/(a-x) + 1/(a+x)). Integrating: (1/2a) ln |(a+x)/(a-x)| + C. Note difference from ∫ dx/(a² + x²) = (1/a) arctan(x/a) + C.
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