Integral of derivative over square-root difference form for JEE

Formula

\[\int \frac{f'(x)}{\sqrt{a^2-f(x)^2}}\,dx=\sin^{-1}\!\left(\frac{f(x)}{a}\right)+C\]

Variables: \(a\neq 0\).

Conditions: Usually \(a>0\), \(|f(x)|<a\).

Substitution to inverse sine form.