令x=sint,t∈[-π/2,π/2] 则√(1-x²)=√(1-1sin²t)=cost,dx=costdt∫1/[x√(1-x²)] dx= ∫cost/(sintcost) dt=∫csctdt=ln|csct-cott|+C=ln|[2-√(1-x²)]/x|+CC为任意常数
