Use partial fractions to find the integral: {eq}\int \frac{x^2 + 12x + 12}{x^3 - 4x} \, \mathrm{d}x {/eq}.
Question:
Use partial fractions to find the integral: {eq}\int \frac{x^2 + 12x + 12}{x^3 - 4x} \, \mathrm{d}x {/eq}.
Method of Decomposition into Partial Fractions:
The rational fraction defined by the quotient between a polynomial of second degree and a polynomial of third degree is a proper rational fraction. If the roots of the third degree polynomial are different real numbers {eq}\, x_0 \, {/eq}, {eq}\, x_1 \, {/eq} and {eq}\, x_2 \, {/eq}, by applying the method of decomposition into partial fractions, we get $$\frac{a}{x-x_0} + \frac{b}{x-x_1} + \frac{c}{x-x_2} $$.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven:
$$\begin{align} f(x) &= \frac{x^2+12x+12}{x^3-4x} \\[0.3cm] \end{align} \\ $$
The given fraction is proper, we can apply the simple...
See full answer below.
Learn more about this topic:
from
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.