`int(dx)/(sqrt(x-x^(2)))` equal is :

Options

A. `2ssin^(-1)sqrt(x)+C`
B. `sin^(-1)(2x-1)+C`
C. `C-2cos^(-1)(2x-1)`
D. `cos^(-1)2sqrt(x-x^(2))+C`

Explanation

To solve the integral \( I = \int \frac{dx}{\sqrt{x - x^2}} \), we will follow these steps:

### Step 1: Simplify the Expression Under the Square Root
We start with the integral:
\[ I = \int \frac{dx}{\sqrt{x - x^2}} \]
We can factor the expression inside the square root:
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