Answer:
The integral of \(\ln(1-x)\) with respect to \(x\) can be found using integration by parts. The integration by parts formula is given by:
\[ \int u \, dv = uv - \int v \, du \]
Let's choose \(u = \ln(1-x)\) and \(dv = dx\). Then, differentiate \(u\) and integrate \(dv\) to find \(du\) and \(v\):
\[ du = \frac{1}{1-x} \, dx \]
\[ v = x \]
Now, apply the integration by parts formula:
\[ \int \ln(1-x) \, dx = x \ln(1-x) - \int x \left(\frac{1}{1-x}\right) \, dx \]
You can simplify and solve the remaining integral on the right-hand side.
