Key points are not available for this paper at this time.
JR(x, P(x) dx, where R(x, y) is a rational function and P (x) is a linear or quadratic polynomial, we are forced to expand our dictionary of elementary functions if we wish to handle polynomials of higher degree. In particular, when P(x) is cubic or quartic, then the required functions are called elliptic functions. Of course, when we teach calculus, we have to stop somewhere. It does not seem unreasonable simply to stick with the familiar functions arising in the linear and quadratic situations, while employing numerical methods to calculate the cubic and quartic cases. The availability of easy-to-use computer algebra systems such as Maple and Mathematica makes this course of action even more understandable.
Mladenov et al. (Sat,) studied this question.