Thank you for reporting, we will resolve it shortly
Q.
$ \int{\log 2x\,\,dx} $ is equal to
Jharkhand CECEJharkhand CECE 2007
Solution:
Let $I=\int \log 2 x d x$ or $I=\int 1 \cdot \log 2 x d x \Rightarrow $
$$
\begin{array}{l}
I=\log 2 x \int 1 \cdot d x-\int\left\{\left(\frac{d}{d x} \log 2 x\right) \int 1 d x\right) d x \Rightarrow \\
I=x \log 2 x-\int \frac{1}{2 x} \cdot 2 \cdot x \quad d x \Rightarrow I=x \log 2 x-x+c
\end{array}
$$