推 a2156700:i can't...i can't... 122.118.11.53 04/21 18:43
推 GBRS:I'm sorry for Helios! ~ ORZ 211.76.58.233 04/21 23:34
→ stillboy:最後一題的最後一項寫錯 cos在外面才對@@ 59.126.193.136 04/22 00:28
推 GBRS:第三題真的很簡單~對不起原PO~ORZ 211.76.58.233 04/22 00:57
plz use arc sin..no body use that sign,sin-1<x>
※ 引述《Helios (冷風醉月)》之銘言：
: sin-1(x)
: 1.∫────── dx
: (1-x^2)^2/3
arc sin<x> 1
=∫-------------- d<------------>
x <1-x^2>^(1/2>
arc sin<x> 1 1
=------------* ------------ - ∫ ------------ dx
x <1-x^2>^<1/2> x <1-x^2>
x
= < ........ > - ∫-------------- dx
: x^2 <1-x^2>
1
=< ......... > - ∫ -------------d<x^2>
x^2<1-x^2>
1
=< ......... > - ∫------------d<u> u=x^2
u<1-u>
u can finish it by urself :)
x
: 2.∫sin-1(─────)^1/2 dx
: x + a
x x <1+a>^1/2
= arc sin < ----------->1/2 * x - ∫ ------------ dx
x + a a^<1/2>
1
=<....................> - --- ∫ (u^2 -a> * u du if u=(x+a)^(1/2)
a^1/2
u can finish it by urself :)
: e^tan-1(x)
: 3.∫────────dx
: (1 + x^2)^3/2
:
arc tan x
=∫ ------------ d <arctan>
<1+x^2>^1/2
if u=arc tanx then tan u =x so
e^u
=∫ ----------------- du bcz <tanu>^2=<secu>^2-1
<1+(tanu)^2>^1/2
e^u
∫ -------------- du
sec u
∫ e^u d<cosx>
u can finish this esy intergal by ur self
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