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兩題積分的問題 20點
2014-05-20 8:08 am
回答 (13)
2014-05-20 2:57 pm
✔ 最佳答案
(1) ∫dx/(2x^2+8x+25)=∫dx/[2(x^2+4x+4)+17]=∫d(x+2)/[2(x+2)^2+17]=∫dy/(2y^2+17)......y=x+2=∫0.5dy/(y^2+a^2)......a^2=8.5=(1/2a)∫d(y/a)/[(y/a)^2+1].....a=√8.5=(1/2a)∫du/(1+u^2).....u=y/a=atan(u)/2a+c=atan(y/a)/2a+c=atan[(x+2)/√8.5]/2√8.5+c=atan[(x+2)/√(17/2)]/√34+c2014-05-20 07:05:49 補充：
(2) w2=∫(x+1)dx/√(4-9x^2)
3x=2*siny => dx=2cosy*dy/3
4-9x^2=4-4sin^2y=4*cos^2y
w2=∫(2siny/3+1)2cosy*dy/(2*2cosy)
=∫(2siny/3+1)dy/2
=∫(2siny+3)dy/6
=∫siny*dy/3+∫dy/2
=-cosy/3+y/2+c
=-√(4-9x^2)/2+atan[3x/√(4-9x^2)]/2+c
or
w2=-√(4-9x^2)/2+asin(3x/2)/2+c
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140520000015KK00121