Integral of reciprocal quadratic root form for JEE

Formula

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

Variables: \(a\) is a nonzero constant.

Conditions: Usually \(a>0\).

Standard inverse trigonometric form; partial fractions and substitution.