use the table of integrals to find the indefinite integral $\int x^{4}\ln(2x)dx$.
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$\int x^{4}\ln(2x)dx=\square$

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Accepted Answer

# Explanation:
## Step1: Use integral formula
The formula for $\int x^{n}\ln(ax)dx=\frac{x^{n + 1}}{(n+1)^{2}}[(n + 1)\ln(ax)-1]+C$, where $n = 4$ and $a=2$.
## Step2: Substitute values
Substitute $n = 4$ and $a = 2$ into the formula:
$$
\begin{align*}
\int x^{4}\ln(2x)dx&=\frac{x^{4+1}}{(4 + 1)^{2}}[(4+1)\ln(2x)-1]+C\
&=\frac{x^{5}}{25}(5\ln(2x)-1)+C\
&=\frac{1}{5}x^{5}\ln(2x)-\frac{1}{25}x^{5}+C
\end{align*}
$$

# Answer:
$\frac{1}{5}x^{5}\ln(2x)-\frac{1}{25}x^{5}+C$

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Explanation:

Step1: Use integral formula

Step2: Substitute values

Answer: