推 j0958322080 :太感謝了 12/21 12:39
推 a016258 :push 12/21 16:09
※ 引述《MathforPhy (Wakka)》之銘言：
: a(cscx)^2 dx
: -------------------
: [1-(acscx)^2]^(1/2)
: 有試過tan(x/2) = y ，不過還是積不出來
(Note that, since |csc x|≧1, |a| should be less than 1)
a csc^2 x a csc^2 x
∫-------------------dx = ∫-----------------------dx
√(1 - a^2 csc^2 x) √(1-a^2 - a^2 cot^2 x )
( t = a cot x, dt = -a csc^2(x)dx )
1
= -∫--------------dt
√(1-a^2 - t^2)
t
= -arcsin--------- + C
√(1-a^2)
a cot x
= -arcsin--------- + C
√(1-a^2)
--
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