如何证明：∫secx^3dx=1/2[secxtanx+ln|secx+tanx|]+C

呵呵！证明？
求导即可。
(1/2) [ sec x tan x +ln |sec x+tan x| ] 的导数
=(1/2) [ (sec x)' tan x +sec x (tan x)' +(sec x +tan x)' /(sec x +tan x) ]
=(1/2) [ (sec x tan x) tan x +sec x (sec x)^2 +(sec x tan x +(sec x)^2 ) /(sec x +tan x) ]
=(1/2) [ sec x (tan x)^2 +(sec x)^3 +sec x ]
=(1/2) [ sec x ( (tan x)^2 +1 ) +(sec x)^3 ]
=(sec x)^3.
= = = = = = = = =
可耻地匿了.

一：可用公式(积分符号以S代替）Ssecx^ndx=(1/n-1)tanxsecx^(n-2) + (n-2)/(n-1)Ssecx^(n-2)dx.证：Ssecx^ndx=Ssecx^(n-2) secx^2 dx=secx^(n-2) tanx — Stanx(secx^n-2)` dx =secx^(n-2) tanx—(n-2)S(1--sinx^2)/...