Final answer:
While the provided integral seems incorrect due to the degree of the numerator exceeding the denominator, a correct application of partial fractions to a proper rational function involves expressing the integrand as a sum of simpler fractions and integrating each term separately.
Step-by-step explanation:
The integral in question falls under the branch of calculus and requires the use of partial fractions to simplify the expression before integration. Unfortunately, the question presents an improper function, and the integral cannot be evaluated as is because the function, x´ - 2x² + 4x - 3, is not divisible by the quadratic x² - 2x + 1. However, if we assume that the student mistyped and the integral might involve a correct rational function, then the process below outlines the correct approach for using partial fractions in solving an integral.
To evaluate a similar integral using partial fractions, one would first ensure that the numerator has a lower degree than the denominator. If not, polynomial division must be used to rewrite the integral into a proper form. Once the integral is proper, one can decompose the denominator into linear factors (if possible) and then express the integrand as a sum of simpler fractions. Finally, each of these simpler fractions can be integrated individually.
For example, if given a proper rational function ∫(Ax+B)/(x+1)(x-1)² dx, you would express it using partial fractions as A/(x+1) + B/(x-1) + C/(x-1)². After finding the constants A, B, and C, you would integrate each term separately to find the solution.