Evaluate the following integral:

⇒ 2x + 1=A(x – 3) + B(x – 2)

⇒ 2x + 1=(A + B)x – 3A – 2B

Equating similar terms, we get,

A + B=2 and 3A + 2B= – 1

So, A= – 5, B=7

⇒ I = – 5 log |x – 2| + 7 log |x – 3| + c

⇒ I = log |x – 2| ^{– 5} + log |x – 3|⁷ + c