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

Evaluate the integral of 4 raised to the power of 3 times x, dx-example-1
User Intsco
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1 Answer

7 votes

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.

User JuanGG
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