求解以下問題 1/a^2+x^2dx的積分?
回答 (2)
2019-07-28 6:53 am
✔ 最佳答案
SolSet x=aTanw
Tanw=x/a
w=arcTan(x/a)
a^2+x^2
=a^2+a^2Tan^2 w
=a^2Sec^2w
dx=aSec^2 wdw
∫1/(a^2+x^2)dx
=∫aSec^2 w/(a^2Sec^2 w)dw
=(1/a)∫1dw
=w/a+c
=arcTan(x/a)/a+c
2019-07-27 8:02 pm
∫ 1 / a² + x² dx
= x³ / 3 + x / a² #
= x³ / 3 + x / a² #
收錄日期: 2021-04-30 22:52:29
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https://hk.answers.yahoo.com/question/index?qid=20190727085326AAIyxwE