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\int \frac{1}{9+4 x^{2}} \mathrm{dx}=\frac{1}{4} \int \frac{1}{(9 / 4)+x^{2}} \mathrm{dx}=\frac{1}{4} \int \frac{1}{(3 / 2)^{2}+x^{2}} \mathrm{dx}