原式=∫[1-√(1-x^2)]dx/x^2//*分子分母同乘1-√(1-x^2),
设x=sint,dx=costdt,
(csct)^2=1/x^2,
(cott)^2=1/x^2-1=(1-x^2)/x^2.
cott=√(1-x^2)/x,
原式=∫(1-cost)*costdt/(sint)^2
=∫costdt/(sint)^2-∫(cost/sint)^2dt
=∫d(sint)/(sint)^2-∫(cott)^2dt
=-1/(sint)-∫[csct)^2-1]dt
=-1/(sint)+cott+t+c
=-1/x+√(1-x^2)/x+arxsinx+C.