Answer
$$\frac{{{3^{2x}}}}{{2\left( {\ln 3} \right)}} + C$$
Work Step by Step
$$\eqalign{
& \int {{3^{2x}}} dx \cr
& {\text{use the integration formula }}\int {{a^{kx}}} dx = \frac{{{a^{kx}}}}{{k\left( {\ln a} \right)}} + C{\text{ with }}k \ne 0.{\text{ see page 361 }} \cr
& {\text{for this exercise we can set }}a = 10{\text{ and }}k = 2.{\text{ then}} \cr
& \int {{3^{2x}}} dx = \frac{{{3^{2x}}}}{{2\left( {\ln 3} \right)}} + C \cr} $$