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.