CAS gives me a weird answer for simple rational integral

Question

The integral $$\int \frac{x^8dx}{x^3+x^2+2}$$ Does not seem to be solvable by most CAS's. This was tested on Maple and WolframAlpha and the result returned is

What is the weird summation doing at the right of the integral? The answer in the answer key is $$ \frac{x^6}6- \frac{x^4}{4} - \frac{2x^3}{3} + \frac{x^2}{2} + 4x + 3\ln(x+1) + \frac{11}{8}\ln(x^2-x+2)-\frac{171}{12\sqrt7}\arctan\left(\frac{2x-1}{\sqrt{7}}\right)+C $$

Answer 1

Since $x^3+x^2+2$ is irreducible over $\Bbb Q$, it is natural that trying to compute a primitive of $\frac{x^8}{x^3+x^2+2}$ will lead to a complex expression. And the function that you mention at the end of your question is not such a primitive, since its derivative is$$\frac{x^8+\frac{11}4x^2-\frac{11}4x+\frac{11}2}{x^3+x+1}.$$

Answer 2

just a start

$$ \left( x^{8} \right) = \left( x^{3} + x^{2} + 2 \right) \cdot \color{magenta}{ \left( x^{5} - x^{4} + x^{3} - 3 x^{2} + 5 x - 7 \right) } + \left( 13 x^{2} - 10 x + 14 \right) $$

Then $$ 13 x^{2} - 10 x + 14 = 13 x^2 + \frac{26}{3} x - \frac{56}{3} x + 14 $$