计算In=∫-11(x2一1)ndx.

admin2015-08-14  31

问题 计算In=∫-11(x2一1)ndx.

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答案由分部积分可得 In=x(x2一1)n|-11一2n∫-11x2(x2—1)n-1dx =-2n∫-11(x2一1)ndx一2n∫-11(x2—1)n-1dx =一2nIn一2nIn-1, [*]

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