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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Integral of secant cubed ： ウィキペディア英語版 Integral of secant cubed The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus: :$\backslash int\; \backslash sec^3\; x\; \backslash ,\; dx\; =\; \backslash frac\backslash sec\; x\; \backslash tan\; x\; +\; \backslash frac\backslash ln|\backslash sec\; x\; +\; \backslash tan\; x|\; +\; C.$ There are a number of reasons why this particular antiderivative is worthy of special attention: * The technique used for reducing integrals of higher odd powers of secant to lower ones is fully present in this, the simplest case. The other cases are done in the same way. * The utility of hyperbolic functions in integration can be demonstrated in cases of odd powers of secant (powers of tangent can also be included). * This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves integrating by parts and returning to the same integral one started with (another is the integral of the product of an exponential function with a sine or cosine function; yet another the integral of a power of the sine or cosine function). * This integral is used in evaluating any integral of the form :: $\backslash int\; \backslash sqrt\backslash ,dx,$ : where ''a'' is a constant. In particular, it appears in the problems of: : * rectifying (i.e. finding the arc length of) the parabola. : * rectifying the Archimedean spiral. : * finding the surface area of the helicoid. == Derivations == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Integral of secant cubed」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.