Question

\(\int \frac{x+2}{x^2-7x+12}dx\) is equal to

• A. \(-5log|x-3|+6log|x-4|+c\)
• B. \(-5log|x-3|-6log|x-4|+c\)
• C. \(5log|x-3|-6log|x-4|+c\)
• D. \(5log|x-3|+6log|x-4|+c\)

Hint:

Factor the denominator as $(x-3)(x-4)$ and split into partial fractions.

Answer 1

The Correct Option is A

Step 1: Compare coefficients
$x+2=A(x-4)+B(x-3)$. Matching $x$: $A+B=1$. Matching constants: $-4A-3B=2$.
Solving gives $A=-5$ and $B=6$. Integrating each term gives option (A).

Final Answer:
Option (A). \[ \boxed{\text{(A)}} \]