Question

Evaluate the integral of 4 raised to the power of 3 times x, dx

Answer 1

We have to evaluate the integral:

`\int4^(3x)dx`

We start with a substitution:

`\begin{gathered} u=3x \\ (du)/(dx)=3\Rightarrow dx=(du)/(3) \end{gathered}`

Then, we can now apply the substitution and then the rule for exponential functions:

`\int4^(3x)dx=\int4^u(du)/(3)=(1)/(3)\int4^udu`
`(1)/(3)\int4^udu=(1)/(3)\cdot(4^u)/(\ln(4))+C`

We can replace back with x and write:

`(4^u)/(3\ln(4))=(4^(3x))/(3\ln(4))`

Then, the solution to the integral is:

`\int4^(3x)dx=(4^(3x))/(3\ln(4))+C`

This result does not match any of the options.

Answer: none of these.