Evaluate: `intx\ (1-x)^n\ dx`

Explanation

To evaluate the integral \( \int x (1-x)^n \, dx \), we will use substitution. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = 1 - x \). Then, we differentiate to find \( dx \):
\[ dx = -dt \]
Also, we can express \( x \) in terms of \( t \):
...