∫ x-3/x^2-9 dx =

Question

\(\int \frac{x-3}{x^2 -9} dx = \)

(A) \(log|x^2 - 9| + K\)

(B) \(log|x-3|+K\)

(C) \(log|\frac{x-3}{x+3}| + K\)

(D) \(log|x+3|+K\)

Answer 1

Correct option is (D) \(log|x+3|+K\)

\(\int \frac{x-3}{x^2 -9} dx = \int \frac{x-3}{(x-3)(x +3)}dx\)

\(= \int \frac 1{x + 3} dx\)

\(= log|x + 3|+ K\)