常用不定积分计算公式
04-16
常用不定积分公式 ⎰cot 2x dx =⎰(csc 2x -1)dx =-cot x -x +C ⎰dx 1d (a a 2+x 2=)a ⎰1+x a 2=1a arctan ⎛ x ⎫
⎝a ⎪⎭+C
⎰dx d (x a )a 2-x 2=⎰-x =arcsin ⎛ x ⎫
a 2⎝a ⎪⎭+C
⎰tan xdx =⎰sin x
cos x dx =-⎰d cos x
cos x =-ln cos x +C =ln sec x +C
⎰cot xdx =⎰cos x d sin
sin x dx =⎰x
sin x =ln sin x +C =-ln cos x +C
⎰sec xdx =⎰sec x (sec x +tan x )d (sec x
sec x +tan x dx =⎰+tan x )
sec x +tan x =ln (sec x +tan x )+C
⎰csc
xdx =⎰csc x (csc x -cot x )
csc x -cot x dx =⎰d (csc x -cot x )
csc x -cot x =ln (csc x -cot x )+C
(1)
(2)
(3) .