Hi!

The third degree polynomial divided by the fifth degree polynomial can be written as an infinite

series as:

Then just integrate it term by term to get the indefinite integral in an infinite series form.

Starting with the 1/x^2 term the coefficients in the series repeat in blocks of 10 in the pattern

1,-1,1,0,0,-1,1,-1,0,0. That is what the 1/(x^10n) handles. So the next 6 terms in the series

would have exponents on the bottom of 12,13,14,17,18,19 and the next 6 would have

22,23,24,27,28,29 for the exponents on the bottom.

The signs in each block of six terms would continue to be 1, -1, 1, -1, 1, -1.

Has anyone got a closed form for the integral? I'd love to see it. If x^5+1 is divided by x-1 I get

x(x+1)(x-1)(x^2+1) + (x+1)/(x-1) but I haven't been able to use this to get a closed form.

Good luck with it!