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Putting x = a tan t converts dx/(x^2 + a^2) into the family
A(1/2a) tan^-1(x/a) + C
Ba tan^-1(x/a) + C
C(1/a) tan^-1(x/a) + C
D(1/a^2) tan^-1(x/a) + C
Answer & Solution
Correct answer: C. (1/a) tan^-1(x/a) + C
Putting x = a tan t gives dx = a sec^2 t dt, so the integral reduces to t/a.
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