積分 √4-x² / x dx
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謝謝
很急 積分 √4-x² / x dx
2011-05-06 5:42 pm
回答 (2)
2011-05-06 6:13 pm
✔ 最佳答案
∫√(4－x^2)/x dxSol
Set x=2Siny
dx=2Cosydy
√(4－x^2)=2Cosy (不考慮負)
∫√(4－x^2)/x dx
=∫2Cosy/(2Siny)2Cosydy
=2∫Cos^2 y/Sinydy
=2∫(1－Sin^2 y)/Sinydy
=2∫Cscydy－2∫Sinydy
=2ln｜Cscy－Coty｜+2Cosy+c
=2ln｜(2/x)－√(4－x^2)/x｜+√(4－x^2)+c
2011-05-06 8:15 pm
http://www.wolframalpha.com/input/?i=y%3D%E2%88%AB%28%E2%88%9A4-x%C2%B2%29+%2F+x+dx
y=∫(√4-x²) / x dx
y = 2 log(x)-x^2/2
http://www.wolframalpha.com/input/?i=y%3D%E2%88%AB%5B%E2%88%9A%284-x%C2%B2%29%5D+%2F+x+dx
y=∫[√(4-x²)] / x dx
y == Sqrt[4 - x^2] + 2 Log[2 x] - 2 Log[2 + Sqrt[4 - x^2]]
y=∫(√4-x²) / x dx
y = 2 log(x)-x^2/2
http://www.wolframalpha.com/input/?i=y%3D%E2%88%AB%5B%E2%88%9A%284-x%C2%B2%29%5D+%2F+x+dx
y=∫[√(4-x²)] / x dx
y == Sqrt[4 - x^2] + 2 Log[2 x] - 2 Log[2 + Sqrt[4 - x^2]]
收錄日期: 2021-05-02 10:38:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110506000010KK01650