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 Well, first look at the comments by  below.  Up above, someone points to the section titled List_of_integrals_of_trigonometric_functions#Integrals_of_trigonometric_functions_containing_only_secant.  That section has a recursion formula for integrals of powers of secant.  But it doesn't show where the formula comes from.  This article does, and the derivation really doesn't fit in that other article.    

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