Integrate integral (1)/(x²+4) dx and integral (1)/(9-x²) dx

This integral matches the standard form $\int \frac{1}{x^2+a^2} dx = \frac{1}{a} \arctan\left(\frac{x}{a}\right) + C$.
In this case, $a^2 = 4$, so $a = 2$.

The final answer is $\boxed{\frac{1}{2} \arctan\left(\frac{x}{2}\right) + C}$.

This integral matches the standard form $\int \frac{1}{a^2-x^2} dx = \frac{1}{2a} \ln\left|\frac{a+x}{a-x}\right| + C$.
In this case, $a^2 = 9$, so $a = 3$.

The final answer is $\boxed{\frac{1}{6} \ln\left|\frac{3+x}{3-x}\right| + C}$.