The formula is:
$$
\int \frac{d u}{a^{2}+u^{2}}=\frac{1}{a} \arctan \frac{u}{a}+C
$$
This formula is chosen because the integrand in the given problem is in the form of $\frac{1}{x^{2}+1}$, which matches the form of $\frac{1}{a^{2}+u^{2}}$ in the formula.
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