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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 List of integrals of hyperbolic functions ： ウィキペディア英語版 List of integrals of hyperbolic functions The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant ''a'' is assumed to be nonzero, and ''C'' denotes the constant of integration. ==Integrals involving only hyperbolic sine functions== $\backslash int\backslash sinh\; ax\backslash ,dx\; =\; \backslash frac\backslash cosh\; ax+C\backslash ,$ $\backslash int\backslash sinh^2\; ax\backslash ,dx\; =\; \backslash frac\backslash sinh\; 2ax\; -\; \backslash frac+C\backslash ,$ $\backslash int\backslash sinh^n\; ax\backslash ,dx\; =\; \backslash frac\backslash sinh^\; ax\backslash cosh\; ax\; -\; \backslash frac\backslash int\backslash sinh^\; ax\backslash ,dx\; \backslash qquad\backslash mboxn>0\backslash mbox\backslash ,$ : also: $\backslash int\backslash frac\; =\; \backslash frac\; \backslash ln\backslash left|\backslash tanh\backslash frac\backslash right|+C\backslash ,$ : also: $\backslash int\backslash frac\; =\; \backslash frac\; \backslash ln\backslash left|\backslash frac\backslash right|+C\backslash ,$ : $\backslash int\backslash frac\; =\; \backslash frac\; \backslash ln\backslash left|\backslash frac\backslash right|+C\backslash ,$ : $\backslash int\backslash frac\; =\; \backslash frac\; \backslash ln\backslash left|\backslash frac\backslash right|+C\backslash ,$ $\backslash int\backslash frac\; =\; -\backslash frac-\backslash frac\backslash int\backslash frac\; \backslash qquad\backslash mboxn\backslash neq\; 1\backslash mbox\backslash ,$ $\backslash int\; x\backslash sinh\; ax\backslash ,dx\; =\; \backslash frac\; x\backslash cosh\; ax\; -\; \backslash frac\backslash sinh\; ax+C\backslash ,$ $\backslash int\; \backslash sinh\; ax\; \backslash sinh\; bx\backslash ,dx\; =\; \backslash frac\; (a\backslash sinh\; bx\; \backslash cosh\; ax\; -\; b\backslash cosh\; bx\; \backslash sinh\; ax)+C\; \backslash qquad\backslash mboxa^2\backslash neq\; b^2\backslash mbox\backslash ,$ 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「List of integrals of hyperbolic functions」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.