令 √(1+e^x) = u, 则 e^x=u^2-1,x=ln(u^2-1),dx= 2udu/(u^2-1)I = ∫ √(1+e^x)dx = ∫ 2u^2du/(u^2-1) = 2 ∫ [1+1/(u^2-1)]du = 2u +∫ [1/(u-1)-1/(u+1)]du = 2u +ln |(u-1)/(u+1)| + C = 2√(1+e...