Partial fractions for irreducible quadratic factor for JEE

Formula

\[\frac{P(x)}{x^2+px+q}=\frac{Ax+B}{x^2+px+q}\]

Variables: \(A,B\) are constants.

Conditions: For proper rational decomposition when \(x^2+px+q\) is irreducible over reals.

Rational functions leading to logarithm and arctangent forms.