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求解2道不定积分的题目.
DX/√(X+1)+√(X-1)
DX/1+E^X
人气:315 ℃ 时间:2020-04-16 17:56:52
解答
1/[√(x + 1) + √(x - 1)] * [√(x + 1) - √(x - 1)]/[√(x + 1) - √(x - 1)],分母有理化= [√(x + 1) - √(x - 1)]/[(x + 1) - (x - 1)]= (1/2)[√(x + 1) - √(x - 1)]∫ dx/[√(x + 1) + √(x - 1)] = (1/2)∫...第一题不对啊是么,那你的答案是什么?标准答案是1/3[(X+1)√(X+1)-(X-1)√(X-1)]+C(x + 1)^(3/2) = (x + 1)^(1 + 1/2) = (x + 1) * (x + 1)^(1/2) = (x + 1)√(x + 1)(x - 1)^(3/2) = (x - 1)^(1 + 1/2) = (x - 1) * (x - 1)^(1/2) = (x - 1)√(x - 1)(1/3)(x + 1)^(3/2) - (1/3)(x - 1)^(3/2) + C= (1/3)[(x + 1)^(3/2) - (x - 1)^(3/2)] + C= (1/3)[(x + 1)√(x + 1) - (x - 1)√(x - 1)] + C感觉这题目不是你的功课- -
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