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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 trigonometric functions ： ウィキペディア英語版 List of integrals of inverse trigonometric functions The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete list of integral formulas, see lists of integrals. * The inverse trigonometric functions are also known as the "arc functions". * ''C'' is used for the arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. Thus each function has an infinite number of antiderivatives. * There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as ''sin−1'', ''asin'', or, as is used on this page, ''arcsin''. * For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions. == Arcsine function integration formulas == :$\backslash int\backslash arcsin(x)\backslash ,dx=$ x\arcsin(x)+ }+C :$\backslash int\; x\backslash arcsin(a\backslash ,x)\backslash ,dx=$ \frac- \frac+ \frac+C :$\backslash int\; x^2\backslash arcsin(a\backslash ,x)\backslash ,dx=$ \frac+ \frac+C :$\backslash int\; x^m\backslash arcsin(a\backslash ,x)\backslash ,dx=$ \frac\,-\, \frac\int \frac}\,dx\quad(m\ne-1) :$\backslash int\backslash arcsin(a\backslash ,x)^2\backslash ,dx=$ -2\,x+x\arcsin(a\,x)^2+ \frac+C :$\backslash int\backslash arcsin(a\backslash ,x)^n\backslash ,dx=$ x\arcsin(a\,x)^n\,+\, \frac}\,-\, n\,(n-1)\int\arcsin(a\,x)^\,dx :$\backslash int\backslash arcsin(a\backslash ,x)^n\backslash ,dx=$ \frac\,+\, \frac}\,-\, \frac\int\arcsin(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 trigonometric 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.