Use partial fraction decomposition to find {eq}\displaystyle \int \dfrac {x^2 + 1} {x^3 - 6 x^2 + 9 x}\ dx {/eq}.
Question:
Use partial fraction decomposition to find {eq}\displaystyle \int \dfrac {x^2 + 1} {x^3 - 6 x^2 + 9 x}\ dx {/eq}.
Integration with Partial Fractions Decomposition:
In mathematics, integration is the inverse process of derivatives that is also called the antiderivatives. The notation of integration is {eq}\int {f(x)} dx {/eq}, where {eq}f(x) {/eq} is called the integrand. The partial fraction decomposition is a method that is used to decompose a given complex rational expression into simpler fractions.
Answer and Explanation: 1
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Given Data:
- The given problem is: {eq}I = \int {\dfrac{{{x^2} + 1}}{{{x^3} - 6{x^2} + 9x}}} dx {/eq}.
Rewrite the integrand as:
{eq}\begin{alig...
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Learn more about this topic:
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Chapter 13 / Lesson 10Learn about integration by partial fractions. Explore how to make partial fractions and then how to integrate fractions. See examples of integrating fractions.