Evaluate {eq}\displaystyle \int \frac{x^{2}+1}{(x-3)(x-2)^{2}} \ dx {/eq}

Question:

Function Integration by Partial Fractions:

In the method of partial fraction decomposition to find the integral, we expressed the rational functions into the sum of two or more simple fractions. This method of integration works when the degree of the numerator is less than the degree of the denominator. For example, {eq}\dfrac{{2{x} - 3}}{{\left( {x - 2} \right)\left( {x + 1} \right)}} {/eq} can be split in the form of {eq}\dfrac{A}{{x - 2}} + \dfrac{B}{{x + 1}} {/eq} with the help of partial fraction decomposition.

Answer and Explanation: 1