### Integration Problem and Coefficient Determination#### Problem StatementEvaluate the integral:\[ \int \frac{-9x - 132}{x^2 + 4x - 32} \, dx \]#### ObjectiveDetermine the numerical values of the coefficients \( A \) and \( B \), where \( A \leq B \).#### ApproachTo break down the integral, we express the rational function as a sum of simpler fractions:\[ \frac{A}{\text{denominator}} + \frac{B}{\text{denominator}} \]#### Calculation and Syntax ValidationInitial expressions for \( A \) and \( B \) are:\[ A = \frac{5}{(x-4)} + \frac{11}{(x+8)} \quad \text{(syntax incomplete)} \]\[ B = \frac{?}{?} \quad \text{(syntax incomplete)} \]Note: The expressions include placeholders and indicate incomplete syntax, requiring correction for accurate calculation of \( A \) and \( B \).This problem involves finding the correct partial fractions and integrating them to determine the values of \( A \) and \( B \).

Name: ### Integration Problem and Coefficient Determination#### Problem Sta
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: ### Integration Problem and Coefficient Determination#### Problem StatementEvaluate the integral:\[ \int \frac{-9x - 132}{x^2 + 4x - 32} \, dx \]#### ObjectiveDetermine the numerical values of the coefficients \( A \) and \( B \), where \( A \leq B