令x=sint,则dx=cost dt
则∫√[1-(sint)^2]/sint ·cost dt
=∫ cost/sint·cost dt
=∫ cott·cost dt
=∫ (csct-sint) dt
=∫csct dt-∫sint dt
=ln|csct-cott|+cost+C
=ln|x/[√(1x^2)+1]|+√(1-x^2)+C
注：∫cscxdx=∫1/sinx dx=ln|tanx/2|+C=ln|cscx-cotx|+C