Find the value of the integral ∫ In$$(x)dx$$.

Correct option is A

​$$\begin{aligned}&\text{Let:} \\&\quad u = \ln(x) \Rightarrow \frac{du}{dx} = \frac{1}{x} \\&\quad dv = dx \Rightarrow v = x \\\\&\text{Apply the \textbf{integration by parts} formula:} \\&\quad \int u \, dv = uv - \int v \, du \\\\&\text{So,} \\&\int \ln(x) \, dx = x \ln(x) - \int x \cdot \frac{1}{x} \, dx = x \ln(x) - \int 1 \, dx \\&= x \ln(x) - x + C\end{aligned}$$​​