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


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

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

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Given Data:

  • The given problem is: {eq}\int {\dfrac{{{x^2} + 1}}{{\left( {x - 3} \right){{\left( {x - 2} \right)}^2}}}} dx {/eq}.

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How to Integrate Functions With Partial Fractions


Chapter 13 / Lesson 10

Learn about integration by partial fractions. Explore how to make partial fractions and then how to integrate fractions. See examples of integrating fractions.

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