# $$\int \frac{dx}{(x^2-9)}$$ equals ______

Category: Questions$$\int \frac{dx}{(x^2-9)}$$ equals ______
Editor">Editor Staff asked 11 months ago

\int \frac{dx}{(x^2-9)} equals ______

(a) \frac{1}{6} log \frac{x+3}{x-3} + C

(b) \frac{1}{6} log \frac{x-3}{x+3} + C

(c) \frac{1}{5} log \frac{x+3}{x-3} + C

(d) \frac{1}{3} log \frac{x+3}{x-3} + C

This question was addressed to me in an interview for job.

My question is from Integration by Partial Fractions in section Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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Editor">Editor Staff answered 11 months ago

The correct answer is (b) \frac{1}{6} log \frac{x-3}{x+3} + C

The explanation is: \int \frac{dx}{(x^2-9)}=\frac{A}{(x-3)} + \frac{B}{(x+3)}

By simplifying, it we get \frac{A(x+3)+B(x-3)}{(x^2-9)} = \frac{(A+B)x+3A-3B}{(x^2-9)}

By solving the equations, we get, A+B=0 and 3A-3B=1

By solving these 2 equations, we get values of A=1/6 and B=-1/6.

Now by putting values in the equation and integrating it we get value,

\frac{1}{6} log (\frac{x-3}{x+3}) + C.