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# Integrate the rational functions $\frac{(x^2+1)(x^2+2)}{(x^2+3)(x^2+4)}$

$\begin{array}{1 1}x-\frac{2}{3}\tan^{-1}\big(\frac{x}{\sqrt 3}\big)+3\tan^{-1}\big(\frac{x}{2}\big)+c. \\x+\frac{2}{3}\tan^{-1}\big(\frac{x}{\sqrt 3}\big)-3\tan^{-1}\big(\frac{x}{2}\big)+c. \\ x+\frac{2}{3}\tan^{-1}\big(\frac{x}{\sqrt 3}\big)+3\tan^{-1}\big(\frac{x}{2}\big)+c. \\ \frac{2}{3}\tan^{-1}\big(\frac{x}{\sqrt 3}\big)+3\tan^{-1}\big(\frac{x}{2}\big)+c.\end{array}$