Integral of reciprocal linear over interval for JEE

Formula

\[\int_0^a \frac{1}{x+b}\,dx=\log\left|\frac{a+b}{b}\right|\]

Variables: \(a,b\) are constants.

Conditions: No singularity on \([0,a]\); in particular \(b\neq 0\) and \(-b\notin[0,a]\).

Basic definite logarithmic evaluation.