Answer
The statement is True.
Work Step by Step
$$
\int \ln (4x) dx
$$
Integration by parts should be used to determine this integral as follows:
Let $u=\ln (4x)$ and $dv =dx$, so that:
$$
\begin{aligned}
\int \ln (4x) dx &= \int \ln (4x) dx \\
&\quad \left[\begin{array}{c}{u=\ln (4x) , \quad\quad dv= dx} \\ {d u= \frac{4dx}{4x} , \quad\quad v=x }\end{array}\right] , \text { then }\\
&= x \ln (4x) -\int x . \frac{4dx}{4x}\\
&= x \ln (4x) -\int dx\\
&= x \ln (4x) -x.\\
\end{aligned}
$$
Therefore The statement is True.
