Evaluate the following.

{eq}\displaystyle \int \dfrac {5 x^3 - 3 x^2 + 2 x - 1}{x^4 + x^2} \ dx {/eq}


Evaluate the following.

{eq}\displaystyle \int \dfrac {5 x^3 - 3 x^2 + 2 x - 1}{x^4 + x^2} \ dx {/eq}

Case III - Partial Fractions Decomposition Method:

Case III of the method of decomposition into partial fractions, is defined when the denominator of the fraction is an irreducible second degree polynomial. Remember that these polynomials have two complex conjugate roots. For example, if the denominator is the polynomial {eq}\, x^2+a^2 \, {/eq} the method proposes a fraction of the type: $$\begin{align} \frac{Ax+B}{x^2+a^2} \\[0.3cm] \end{align} \\ $$

Answer and Explanation: 1

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$$\begin{align} f(x) &= \frac{5x^3-3x^2+2x-1}{x^4+x^2} \\[0.3cm] \end{align} \\ $$

The given fraction is proper , we can apply the simple...

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Partial Fractions: Rules, Formula & Examples


Chapter 3 / Lesson 26

Learn about what partial fractions are and their formula. Understand the method of how to do partial fractions from the rational and improper functions.

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