My analysis book makes the following statement:
Every rational function with real coefficients can be integrated in terms of
- rational functions,
- logarithm functions,
- arctangent functions.
Does it mean that after polynomial division, partial fraction expansion, completing the square, substituting where needed, and knowing that
\begin{align} \\ \int \frac{dx}{(x-a)^n} &= -\frac{1}{n-1} \frac{1}{(x-a)^{n-1}} \ \ \ (n \neq 1) \\ \int \frac{dx}{x-a} &= \log|x-a| \\ \int \frac{dx}{x^2+1} &= \arctan x \end{align}
one can integrate any rational function?