Final answer:
To solve this integral, use partial fraction decomposition to simplify the integrand and find the values of A, B, and C. Then, integrate each term separately and sum the results.
Step-by-step explanation:
To solve the integral ∫ (2x-3)/(x³-3x-10) dx, we can use partial fraction decomposition to simplify the integrand. First, we factor the denominator: x³-3x-10 = (x-2)(x+1)(x+5). Then, we express the integrand as the sum of partial fractions:
(2x-3)/(x³-3x-10) = A/(x-2) + B/(x+1) + C/(x+5)
Next, we find the values of A, B, and C by equating the numerator in the original integrand with the sum of the numerators in the partial fractions. We then integrate each term separate, and sum the results to obtain the final solution.