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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 trigonometric functions ： ウィキペディア英語版 List of integrals of trigonometric functions The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometric functions, see Trigonometric integral. Generally, if the function $\backslash sin(x)$ is any trigonometric function, and $\backslash cos(x)$ is its derivative, : $\backslash int\; a\backslash cos\; nx\backslash ;\backslash mathrmx\; =\; \backslash frac\backslash sin\; nx+C$ In all formulas the constant ''a'' is assumed to be nonzero, and ''C'' denotes the constant of integration. == Integrands involving only sine == : $\backslash int\backslash sin\; ax\backslash ;\backslash mathrmx\; =\; -\backslash frac\backslash cos\; ax+C\backslash ,\backslash !$ : $\backslash int\backslash sin^2\; \backslash ;\backslash mathrmx\; =\; \backslash frac\; -\; \backslash frac\; \backslash sin\; 2ax\; +C=\; \backslash frac\; -\; \backslash frac\; \backslash sin\; ax\backslash cos\; ax\; +C\backslash !$ : $\backslash int\backslash sin^3\; \backslash ;\backslash mathrmx\; =\; \backslash frac\; -\; \backslash frac\; +C\backslash !$ : $\backslash int\; x\backslash sin^2\; \backslash ;\backslash mathrmx\; =\; \backslash frac\; -\; \backslash frac\; \backslash sin\; 2ax\; -\; \backslash frac\; \backslash cos\; 2ax\; +C\backslash !$ : $\backslash int\; x^2\backslash sin^2\; \backslash ;\backslash mathrmx\; =\; \backslash frac\; -\; \backslash left(\; \backslash frac\; -\; \backslash frac\; \backslash right)\; \backslash sin\; 2ax\; -\; \backslash frac\; \backslash cos\; 2ax\; +C\backslash !$ : $\backslash int\backslash sin\; b\_1x\backslash sin\; b\_2x\backslash ;\backslash mathrmx\; =\; \backslash frac-\backslash frac+C\; \backslash qquad\backslash mbox|b\_1|\backslash neq|b\_2|\backslash mbox\backslash ,\backslash !$ : $\backslash int\backslash sin^n\; \backslash ;\backslash mathrmx\; =\; -\backslash frac\; +\; \backslash frac\backslash int\backslash sin^\; ax\backslash ;\backslash mathrmx\; \backslash qquad\backslash mboxn>0\backslash mbox\backslash ,\backslash !$ : $\backslash int\backslash frac\; =\; -\backslash frac\backslash ln\backslash right|\}+C$ : $\backslash int\backslash frac\; =\; \backslash frac+\backslash frac\backslash int\backslash frac\; \backslash qquad\backslash mboxn>1\backslash mbox\backslash ,\backslash !$ : $\backslash int\; x\backslash sin\; ax\backslash ;\backslash mathrmx\; =\; \backslash frac-\backslash frac+C\backslash ,\backslash !$ : $\backslash int\; x^n\backslash sin\; ax\backslash ;\backslash mathrmx\; =\; -\backslash frac\backslash cos\; ax+\backslash frac\backslash int\; x^\backslash cos\; ax\backslash ;\backslash mathrmx\; =\; \backslash sum\_^\; (-1)^\; \backslash frac\}\backslash frac\; \backslash cos\; ax\; +\backslash sum\_^(-1)^k\; \backslash frac\}\backslash frac\; \backslash sin\; ax\; \backslash qquad\backslash mboxn>0\backslash mbox\backslash ,\backslash !$ : $\backslash int\backslash frac\; \backslash mathrmx\; =\; \backslash sum\_^\backslash infty\; (-1)^n\backslash frac\; +C\backslash ,\backslash !$ : $\backslash int\backslash frac\; \backslash mathrmx\; =\; -\backslash frac\backslash int\backslash fracx\backslash ,\backslash !$ : $\backslash int\backslash frac\; =\; \backslash frac\backslash tan\backslash left(\backslash frac\backslash mp\backslash frac\backslash right)+C$ : $\backslash int\backslash frac\; =\; \backslash frac\backslash tan\backslash left(\backslash frac\; -\; \backslash frac\backslash right)+\backslash frac\backslash ln\backslash left|\backslash cos\backslash left(\backslash frac-\backslash frac\backslash right)\backslash right|+C$ : $\backslash int\backslash frac\; =\; \backslash frac\backslash cot\backslash left(\backslash frac\; -\; \backslash frac\backslash right)+\backslash frac\backslash ln\backslash left|\backslash sin\backslash left(\backslash frac-\backslash frac\backslash right)\backslash right|+C$ : $\backslash int\backslash frac\; =\; \backslash pm\; x+\backslash frac\backslash tan\backslash left(\backslash frac\backslash mp\backslash frac\backslash right)+C$ 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 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.