y'=1/(√(1 +x²))y=∫dx/(√(1 +x²),设x=tant,则:y=∫dtant/(√(1 +tan²t)=∫sec^2dt/sect=∫sectdt=∫dt/cost=∫dsint/(1-sin^2 t)=(1/2)[∫d(1+sint)/(1+sint)-∫d(1-sint)/(1-sint)]=(1/2)ln(1+sint)/(1-sint)+c=ln(x+√(1+x^2))+c.