Find the following integral: $\int(4 e^{3 x}+1) d x$

(N/A) To find the integral $\int(4 e^{3 x}+1) d x$,we use the linearity property of integration:
$\int(4 e^{3 x}+1) d x = 4 \int e^{3 x} d x + \int 1 d x$
We know that $\int e^{ax} d x = \frac{e^{ax}}{a} + C$ and $\int 1 d x = x + C$.
Applying these formulas:
$= 4 \left( \frac{e^{3 x}}{3} \right) + x + C$
$= \frac{4}{3} e^{3 x} + x + C$
where $C$ is an arbitrary constant.