令t=√(x^2-9),t^2=x^2-9,2tdt=2xdx tdt=xdx积分号下：√(x^2-9)dx/x=√(x^2-9) xdx/x^2 （分子分母同乘以x）=t *tdt/(t^2+9)=t^2dt/(t^2+9)=[1-9/(t^2+9)]dt∫[1-9/(t^2+9)]dt=t-3arctan(t/3)+C=√(x^2-9)-3arctan[√(x^2-9)/3]+C
