Without carrying out any integration

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Without carrying out any integration, explain why every antiderivative of the function

g(x)=\dfrac{A}{x-3}+\dfrac{B}{x+2}

(where

A

and

B

are nonzero constants) must contain logarithmic terms of the form

\ln|x-3|

and

\ln|x+2|