设x=tant=>dx=d(tant)=sec²tdt∴∫(1/√(1+x^2))dx=∫(1/sect)sec²tdt=∫sectdt=∫cost/(cost)^2 dt＝∫1/(cost)^2 dsint＝∫1/(1-(sint)^2) dsint令sint = θ化为∫1/(1-θ^2)dθ=(ln|1+x|-ln|1-x|)/2+C=...