Question

Which of the following rational functions require polynomial long division in order to compute the antiderivative? (Select all that may be multiple answers) \frac{x+10}{x^{2}-5 x+6} \

Answer 1

Answer and Step-by-step explanation:

The given rational function is x2−5x+6x+10​. To compute the antiderivative of a rational function, we usually use partial fraction decomposition. However, if the degree of the numerator is greater than or equal to the degree of the denominator, we must first perform polynomial long division to write the function as the sum of a polynomial and a proper rational function (where the degree of the numerator is less than the degree of the denominator).

In this case, the degree of the numerator (1) is less than the degree of the denominator (2), so we do not need to perform polynomial long division. We can proceed directly to partial fraction decomposition to compute the antiderivative.

So, this rational function does not require polynomial long division in order to compute the antiderivative.