By using the properties of definite integrals, evaluate the integrals`int_0^1x(1-x)^n dx`

Explanation

To evaluate the integral \( I = \int_0^1 x(1-x)^n \, dx \) using the properties of definite integrals, we can follow these steps:

### Step 1: Define the Integral
Let \( I = \int_0^1 x(1-x)^n \, dx \).

### Step 2: Use the Property of Definite Integrals
We can use the property of definite integrals which states:
\[
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