The discussion revolves around the integration of a rational function, specifically the integral of (2x+1) divided by the product of two quadratic expressions. Participants are exploring different methods for simplifying the integral.
There is a clear inclination towards using partial fractions as a preferred method for this integral. Participants are actively questioning the rationale behind using long division and exploring the implications of the degrees of the polynomials involved.
Participants note that the original poster's approach of foiling the denominator may not be necessary and that the degrees of the polynomials play a crucial role in determining the method of integration.
Why would you try long division? You are dividing something "smaller" into something "bigger". It is as if you are suggesting that to evaluate \frac{7}{584} you divide 584 by 7.Cacophony said:I've foiled this out to look like:
∫(2x+1)/(x^4+3x³+4x²+3x+1)
I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or should I use a different approach?
Or when the degrees are equal.iRaid said:Definitely do partial fractions. The only time you do long division is when the degree on top is bigger than the bottom.