1. ## Integral

Hello I was wondering if anyone could give me a hand with this.

Integrate $\int\frac{dx}{\sqrt{2x-x^2}}$.

2. Originally Posted by slevvio
Hello I was wondering if anyone could give me a hand with this.

Integrate $\int\frac{dx}{\sqrt{2x-x^2}}$.
Complete the square in the denominator
$= \int\frac{dx}{\sqrt{1 + -1 + 2x-x^2}}$

$= \int \frac{dx}{\sqrt{1 - (x - 1)^2)}}$

Let y = x - 1, so dy = dx
$= \int \frac{dy}{\sqrt{1 - y^2}}$

Does this look familiar?

-Dan

3. thanks!

4. $\int\frac{dx}{\sqrt{2x-x^2}} = sin^{-1}(x-1) + c$ ?

5. Originally Posted by slevvio
$\int\frac{dx}{\sqrt{2x-x^2}} = sin^{-1}(x-1) + c$ ?

6. :d