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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 irrational functions ： ウィキペディア英語版 List of integrals of irrational functions The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, see lists of integrals. Throughout this article the constant of integration is omitted for brevity. == Integrals involving ''r'' = √''a''2 + ''x''2 == : $\backslash int\; r\; \backslash ;dx\; =\; \backslash frac\backslash left(x\; r\; +a^2\backslash ,\backslash ln\backslash left(x+r\backslash right)\backslash right)$ : $\backslash int\; r^3\; \backslash ;dx\; =\; \backslash fracxr^3+\backslash fraca^2xr+\backslash fraca^4\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; r^5\; \backslash ;\; dx\; =\; \backslash fracxr^5+\backslash fraca^2xr^3+\backslash fraca^4xr+\backslash fraca^6\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; x\; r\backslash ;dx=\backslash frac$ : $\backslash int\; x\; r^3\backslash ;dx=\backslash frac$ : $\backslash int\; x\; r^\backslash ;dx=\backslash frac$ : $\backslash int\; x^2\; r\backslash ;dx=\; \backslash frac-\backslash frac-\backslash frac\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; x^2\; r^3\backslash ;dx=\; \backslash frac-\backslash frac-\backslash frac-\backslash frac\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; x^3\; r\; \backslash ;\; dx\; =\; \backslash frac\; -\; \backslash frac$ : $\backslash int\; x^3\; r^3\; \backslash ;\; dx\; =\; \backslash frac-\backslash frac$ : $\backslash int\; x^3\; r^\; \backslash ;\; dx\; =\; \backslash frac\; -\; \backslash frac$ : $\backslash int\; x^4\; r\backslash ;dx=\; \backslash frac-\backslash frac+\backslash frac+\backslash frac\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; x^4\; r^3\backslash ;dx=\; \backslash frac-\backslash frac+\backslash frac+\backslash frac+\backslash frac\backslash ln\backslash left(x+r\backslash right)$ : $\backslash int\; x^5\; r\; \backslash ;\; dx\; =\; \backslash frac\; -\; \backslash frac\; +\; \backslash frac$ : $\backslash int\; x^5\; r^3\; \backslash ;\; dx\; =\; \backslash frac\; -\; \backslash frac\; +\; \backslash frac$ : $\backslash int\; x^5\; r^\; \backslash ;\; dx\; =\; \backslash frac\; -\; \backslash frac+\backslash frac$ : $\backslash int\backslash frac\; =\; r-a\backslash ln\backslash left|\backslash frac\backslash right|\; =\; r\; -\; a\backslash ,\; \backslash operatorname\backslash frac$ : $\backslash int\backslash frac\; =\; \backslash frac+a^2r-a^3\backslash ln\backslash left|\backslash frac\backslash right|$ : $\backslash int\backslash frac\; =\; \backslash frac+\backslash frac+a^4r-a^5\backslash ln\backslash left|\backslash frac\backslash right|$ : $\backslash int\backslash frac\; =\; \backslash frac+\backslash frac+\backslash frac+a^6r-a^7\backslash ln\backslash left|\backslash frac\backslash right|$ : $\backslash int\backslash frac\; =\; \backslash operatorname\backslash frac\; =\; \backslash ln\backslash left(\; \backslash frac\; \backslash right)$ : $\backslash int\backslash frac\; =\; \backslash frac$ : $\backslash int\backslash frac\; =\; r$ : $\backslash int\backslash frac\; =\; -\backslash frac$ : $\backslash int\backslash frac\; =\; \backslash fracr-\backslash frac\backslash ,\backslash operatorname\backslash frac\; =\; \backslash fracr-\backslash frac\backslash ln\backslash left(\; \backslash frac\; \backslash right)$ : $\backslash int\backslash frac\; =\; -\backslash frac\backslash ,\backslash operatorname\backslash frac\; =\; -\backslash frac\backslash ln\backslash left|\backslash frac\backslash right|$ 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 irrational 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.