少少既積分問題
2011-02-16 9:59 am
圖片參考：http://imgcld.yimg.com/8/n/HA07267602/o/701102160010513873381220.jpg
點樣做到個答案出黎
可唔可以show埋個step出黎比我參考下
回答 (1)
2011-02-16 4:09 pm
✔ 最佳答案
令 x = 2tanθ則 x = 4tan²θ, dx = 2sec²θdθ 及 θ = tan⁻¹(x/2)
∫[2/(x² + 4)]dx
= ∫[2/(4²tan²θ + 4)]2sec²θdθ
= ∫[sec²θ/(tan²θ + 1)]dθ
= ∫(sec²θ/sec²θ)dθ
= ∫dθ
= θ + C
= tan⁻¹(x/2) + C
參考: miraco
收錄日期: 2021-05-03 20:18:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110216000051KK00105