Evaluate.
{eq}\int {{{{x^3} - 4x - 10} \over {{x^2} - x - 6}}} \ dx {/eq}
Question:
Evaluate.
{eq}\int {{{{x^3} - 4x - 10} \over {{x^2} - x - 6}}} \ dx {/eq}
Partial Fraction Decomposition:
In integral calculus, partial fraction decomposition (also called partial fraction expansion) is used to break the complex rational integrand (here, the numerator and denominator expressions should be the polynomial expressions) into a sum of smaller rational expressions. The following integration formula helps us to compute the given indefinite integral.
$$\begin{align*} \int {\dfrac{{dx}}{{x \pm a}}} & = \ln \left| {x \pm a} \right| + C\\[0.3cm] \int {{x^n}} \;dx &= \dfrac{{{x^{n + 1}}}}{{n + 1}} + C \end{align*} $$
Answer and Explanation: 1
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View this answerRewrite the given indefinite integral.
$$\begin{align*} \int {\dfrac{{{x^3} - 4x - 10}}{{{x^2} - x - 6}}} \;dx &= \int {\dfrac{{x\left( {{x^2} - x -...
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Chapter 3 / Lesson 25Learn about how to carry out partial fraction decomposition with polynomial fractions. Discover example equations and walkthroughs of partial fraction decomposition.