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In this paper, a compact formula for the evaluation of the J"tan2m+1 ax and Jtan2max is presented. This new formula requires much less effort when compared to reduction formulas given in the literature. The organization of this paper is as follows. The formulas currently available for the evaluation of this integral are reviewed in the introduction. The new formulas are derived in section 2 and then extended to the evaluation of the integrals J cot2"1 ax and J cot2"1"*"1 ax.
In section 3 the relation between reduction formulas and series solutions is established.