{eq}\int {{{{x^3} - 4x - 10} \over {{x^2} - x - 6}}} \ dx {/eq}



{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

Become a Study.com member to unlock this answer!

View this answer

Rewrite the given indefinite integral.

$$\begin{align*} \int {\dfrac{{{x^3} - 4x - 10}}{{{x^2} - x - 6}}} \;dx &= \int {\dfrac{{x\left( {{x^2} - x -...

See full answer below.

Learn more about this topic:

Partial Fraction Decomposition: Rules & Examples


Chapter 3 / Lesson 25

Learn about how to carry out partial fraction decomposition with polynomial fractions. Discover example equations and walkthroughs of partial fraction decomposition.

Related to this Question

Explore our homework questions and answers library