209k views
3 votes
The form of the partial fraction decomposition of rational function given below:

(5x² + 2x + 18) Bx + C 1)(x2 + 4) X-[ x + 4]
Now evaluate the indefinite integral:
(5x² + 2x + 18) f = dx = 1)(x2 +4)

User Oxfn
by
7.9k points

1 Answer

6 votes

Final answer:

The task involves performing partial fraction decomposition on the rational function (5x² + 2x + 18)/(x² + 4) and then integrating the resulting simpler fractions.

Step-by-step explanation:

The subject in question involves the concept of partial fraction decomposition of a rational function and evaluating its indefinite integral. The given rational function is (5x² + 2x + 18)/(x² + 4). The student is tasked with finding the partial fraction decomposition, which typically would involve expressing the function as a sum of simpler fractions of the form Ax + B and/or C/(Dx + E). After finding the correct form, the next step involves integrating these simpler fractions. However, it's important to note that in the case of (5x² + 2x + 18)/(x² + 4), the numerator is already a polynomial of the same degree as the denominator, suggesting that the first step might involve polynomial long division before proceeding to partial fractions, if necessary.

User Cdalto
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories