What is the integral of 1 x? - Mathematics Stack Exchange Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers
Can a limit of an integral be moved inside the integral? Taking the limit inside the integral is not always allowed There are several theorems that allow you to do so The major ones being Lebesgue dominated convergence theorem and Monotone convergence theorem The uniform convergence mentioned in the comments is a special case of Dominated convergence theorem