求不定积分sqrt（1+cos x)/sin x

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/11 00:42:23

求不定积分sqrt（1+cos x)/sin x
RT.还有其他解法的么
SIn不在根号里

以下 S 表示积分符号.
= = = = = = = = =
因为 1 +cos x =2 [cos (x/2) ]^2,
sin x =2 sin (x/2) cos (x/2),
所以根号(1 +cos x) /sin x
=根号2 |cos (x/2)| / [ 2 sin (x/2) cos (x/2) ]
=(根号2 /2) * sgn[ cos (x/2) ] * csc (x/2).
所以 S [ 根号(1 +cos x) /sin x ] dx
=(根号2 /2) * sgn[ cos (x/2) ] * S[ csc (x/2) ] dx
=(根号2 /2)* sgn[ cos (x/2) ] * S[ csc (x/2) ] d(x/2)
=(根号2 /2)* sgn[ cos (x/2) ] * ln | csc (x/2) -cot (x/2) | +C,
(C 为任意常数).
= = = = = = = = =
以上计算可能有误,你最好检查一下.
sgn x 是符号函数.
sgn x =1,x>0,
sgn x =0,x=0.
sgn x = -1,x

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