ʃ (1+x)/(x+3)(x-1) dx?
回答 (1)
2015-10-20 3:03 pm
✔ 最佳答案
設 (1+x) / ((x+3) (x-1)) = a/(x+3) + b/(x-1) = (a(x-1) + b(x+3)) / ((x+3) (x-1)) = ((a+b)x + 3b-a) / ((x+3) (x-1)) 比較分子係數得 a+b = 1 及 3b-a = 1 , 解得 a = b = 1/2.
ʃ (1+x) / ((x+3) (x-1)) dx
= ʃ ( 1/2 /(x+3) + 1/2 / (x-1) ) dx
= 1/2 ʃ 1/(x+3) d(x+3) + 1/2 ʃ 1/(x-1) d(x-1)
= 1/2 In|x+3| + 1/2 In|x-1| + C
收錄日期: 2021-04-18 13:57:54
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https://hk.answers.yahoo.com/question/index?qid=20151020063807AAG0izX