Evaluate the following integral.
{eq}\displaystyle \int \dfrac {x^3 + 10 x^2 + 3 x + 36} {(x - 1) (x^2 + 4)^2}\ dx {/eq}
Question:
Evaluate the following integral.
{eq}\displaystyle \int \dfrac {x^3 + 10 x^2 + 3 x + 36} {(x - 1) (x^2 + 4)^2}\ dx {/eq}
Simple Fractions Method:
In the simple fraction method for decomposing a rational fraction, the most complicated case is when the complex roots are multiple. For example if we have the fraction:
$$\dfrac{q(x)}{(x^2+a^2)^2}
$$
The decomposition of the rational fraction is as follows:
$$\begin{align} \dfrac{q(x)}{(x^2+a^2)^2}&= \frac{ax+b}{x^2+a^2}+\frac{cx+d}{(x^2+a^2)^2}\\[0.3cm] \end{align} $$
Answer and Explanation: 1
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View this answerGiven:
$$\int \ \frac{x^3+10x^2+3x+36}{(x-1)(x^2+4)^2}\ dx $$
Part 1. Express the integrand as a sum of partial fractions. The fraction is...
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Chapter 3 / Lesson 26Learn about what partial fractions are and their formula. Understand the method of how to do partial fractions from the rational and improper functions.