Question

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

Answer 1

Now,

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

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

$=\int \frac{d(x-a)}{\sqrt{a^2-\left\{\right(x-a{)}^2\}}}$

$={\sin }^{-1}\frac{x-a}{a}+c$ [ Where $c$ is an integrating constant]