Evaluate the following indefinite integral using the method of Partial Fractions.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x+1}{(x-4)(x-3)}dx$

a$.$ Assume that the integrand can be written as the sum of the following two fractions:

$\frac{A}{x-4}+\frac{B}{x-3}$

Set up a system of equations and solve for the constants A and $B.$

b$.$ Use the partial fraction decomposition of the integrand to rewrite the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

c$.$ Use the partial fraction decomposition to find the antiderivative of the original rational expression Use $+K$ for the constant of integration.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-x+1}{(x-4)(x-3)}dx=$

$$

Practice Another Version to get another random partial fractions problem.