Answer
$$\frac{{{7^{2x}}}}{{2\ln 7}} + C$$
Work Step by Step
$$\eqalign{
& \int {{7^{2x}}} dx \cr
& {\text{substitute }}u = 2x,{\text{ }}du = 2dx \cr
& = \frac{1}{2}\int {{7^u}} du \cr
& {\text{find the antiderivative by the formula }}\int {{a^x}} dx = \frac{{{a^x}}}{{\ln a}} + C \cr
& {\text{letting }}a = 10 \cr
& = \frac{1}{2}\left( {\frac{{{7^u}}}{{\ln 7}}} \right) + C \cr
& {\text{with }}u = 2x \cr
& = \frac{1}{2}\left( {\frac{{{7^{2x}}}}{{\ln 7}}} \right) + C \cr
& = \frac{{{7^{2x}}}}{{2\ln 7}} + C \cr} $$
