Question

Write out the form of the partial fraction decomposition of the function appearing in the integral: ∫(−7x−181)/(x²+9x−22) x. Determine the numerical values of the coefficients A and B where ≤ and ∫(−7x−181)/(x²+9x−22) x = A/denominator + B/denominator

Answer 1

To find the partial fraction decomposition, factor the denominator and express the function as a sum of fractions. Multiply both sides by the common denominator to get rid of the fractions, and then solve for the coefficients A and B.

Step-by-step explanation:

To find the partial fraction decomposition of the function, we first factor the denominator: x² + 9x - 22 = (x - 1)(x + 22).

Then, we write the function as A/(x - 1) + B/(x + 22).

Next, we multiply both sides of the equation by the common denominator (x - 1)(x + 22) to clear the fractions.

Finally, we simplify and compare coefficients to solve for A and B.