Question

Evaluate the following :
$\int \frac{dx}{\sqrt{2ax-x^2}}$.

Answer 1

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

$=\int \frac{dx}{\sqrt{2ax-x^2-a^2+a^2}}$

$=\int \frac{dx}{\sqrt{a^2-(a^2-2ax+x^2)}}$

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

$={\sin }^{-1}\left(\frac{x-a}{a}\right)+c$ [Using formula]