Integral of derivative over quadratic sum form for JEE

Formula

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

Variables: \(a\neq 0\).

Conditions: Usually \(a>0\).

Substitution to inverse tangent form.