∫(0,1)(arcsin√x)/(√x(1-x))dx=∫(0,1)(arcsin√x)/(√x(1-x))d(√x)^2=2∫(0,1)(arcsin√x)/(√(1-x))d(√x)=2∫(0,1)(arcsin√x)/d(arcsin√x)=(arcsin√x)^2|(0,1)=π^2/4所以积分收敛,且值=π/2....