作者LuisSantos (^______^)
看板trans_math
标题Re: [积分]
时间Fri Mar 23 20:01:43 2007
※ 引述《topractise ()》之铭言：
: arcsinx
: ∫ ---------------- dx = ?
: (1-x^2)^3/2
-1 1
令 y = sin x , 则 dy = ------------- dx
√(1 - x^2)
siny = x
-1
sin x
∫----------------- dx
(1 - x^2)^(3/2)
-1
sin x 1
= ∫(---------)(-------------) dx
1 - x^2 √(1 - x^2)
y
= ∫(--------------) dy
1 - (siny)^2
y
= ∫---------- dy
(cosy)^2
= ∫(y)((secy)^2) dy
= (y)(tany) - ∫tany dy
(令 u = y , dv = (secy)^2 dy , 则 du = dy , v = tany)
= (y)(tany) - ln|secy| + c
= (y)(tany) + ln|cosy| + c
= (sinx)(tan(sinx)) + ln|cos(sinx)| + c
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 61.216.4.116
1F：推 topractise:感谢＠＠ 59.113.183.211 03/23 20:25