118e57…: “Upon the proud calculation”

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Compute the following indefinite integral:

(Use $C$ for the constant of integration)

\[ \int \frac {2x+4}{x^2+9} \d x \begin{prompt}=\answer {\ln (x^2+9)+\frac {4}{3}\arctan \left (\frac {x}{3}\right )+C}\end{prompt} \]

(Hint: Try Splitting the fraction!)