Reintegral Calculus: Research in Integral Calculus, Volume - II is the continuation work of the research on nonelementary (i.e. indefinite nonintegrable) functions for exceptional cases left by the earlier researcher, which was discussed in Reintegral Calculus: Research in Integral Calculus, Volume - I. So it is the collection of research works on the topic entitled "Study of Inverse Trigonometric Nonelementary Functions in Context of Antiderivatives" submitted in the University Department of Mathematics, L. N. Mithila University, Darbhanga, Bihar by the first author under the supervision of second author in 2024. It contains three conjectures on nonelementary functions, relations between elementary, nonelementary, nonintegrable and hypergeometric functions. The readers will find many new scope of research in this book.