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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 inverse hyperbolic functions ： ウィキペディア英語版 List of integrals of inverse hyperbolic functions The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals. * In all formulas the constant ''a'' is assumed to be nonzero, and ''C'' denotes the constant of integration. * For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions. == Inverse hyperbolic sine integration formulas == :$\backslash int\backslash operatorname(a\backslash ,x)\backslash ,dx=$ x\,\operatorname(a\,x)-\frac+C :$\backslash int\; x\backslash ,\backslash operatorname(a\backslash ,x)dx=$ \frac+ \frac- \frac+C :$\backslash int\; x^2\backslash ,\backslash operatorname(a\backslash ,x)dx=$ \frac- \frac+C :$\backslash int\; x^m\backslash ,\backslash operatorname(a\backslash ,x)dx=$ \frac(a\,x)}\,-\, \frac\int\frac}\,dx\quad(m\ne-1) :$\backslash int\backslash operatorname(a\backslash ,x)^2\backslash ,dx=$ 2\,x+x\,\operatorname(a\,x)^2- \frac(a\,x)}+C :$\backslash int\backslash operatorname(a\backslash ,x)^n\backslash ,dx=$ x\,\operatorname(a\,x)^n\,-\, \frac(a\,x)^}\,+\, n\,(n-1)\int\operatorname(a\,x)^\,dx :$\backslash int\backslash operatorname(a\backslash ,x)^n\backslash ,dx=$ -\frac}\,+\, \frac(a\,x)^}\,+\, \frac\int\operatorname(a\,x)^\,dx\quad(n\ne-1,-2) 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 inverse 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.