.
令y = arcsin√x、x = sin²y、dx = (2siny)(cosy) dy
x = 1/2 ==> y = π/4
x = 1 ==> y = π/2
∫(1/2→1) (arcsin√x)/√[x(1 - x)] dx
= ∫(π/4→π/2) y/(sinycosy) * (2sinycosy dy)
= ∫(π/4→π/2) 2y dy
= y² |(π/4→π/2)
= π²/4 - π²/16
= 3π²/16
请多加几个括号，标清运算顺序，或者发图片。
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