1) Let's evaluate this integral using the due properties. We can start out by raising 4 to the 3rd power before actually integrating:
2) Now, let's apply the following property, and rewrite the logarithm we have just found:
![\begin{gathered} \int a^xdx=(a^x)/(\ln a) \\ \int64^xdx=(64^x)/(\ln(64)) \\ \frac{64^(x)}{\operatorname{\ln}(64)}=(2^(6x))/(\ln(2)^6)\Rightarrow(2^(6x))/(6\ln(2)) \end{gathered}]()
3) Let's rewrite those power and that log:
![\begin{gathered} (2^(6x))/(2\cdot\:3\ln\left(2\right))=(2^(6x-1))/(3\ln\left(2\right)) \\ \\ \int\:4^(3x)dx=\frac{2^(6x-1)}{3\operatorname{\ln}(2)}+C \\ \end{gathered}]()
Note that among the options there is one equivalent option, then the answer is:
![A)\int64^xdx=\frac{4^(3x)}{6\operatorname{\ln}(2)}+C]()