高中数学 积分公式表

微积分公式
Dx sin x=cos x
cos x = -sin x
tan x = sec2 x
cot x = -csc2 x
sec x = sec x tan x
csc x = -csc x cot x ? sin x dx = -cos x + C
? cos x dx = sin x + C
? tan x dx = ln |sec x | + C
? cot x dx = ln |sin x | + C
? sec x dx = ln |sec x + tan x | + C
? csc x dx = ln |csc x – cot x | + C sin-1(-x) = -sin-1 x
cos-1(-x) = ? - cos-1 x
tan-1(-x) = -tan-1 x
cot-1(-x) = ? - cot-1 x
sec-1(-x) = ? - sec-1 x
csc-1(-x) = - csc-1 x
Dx sin-1 ( )=
cos-1 ( )=
tan-1 ( )=
cot-1 ( )=
sec-1 ( )=
csc-1 (x/a)= ? sin-1 x dx = x sin-1 x+ +C
? cos-1 x dx = x cos-1 x- +C
? tan-1 x dx = x tan-1 x-?ln (1+x2)+C
? cot-1 x dx = x cot-1 x+?ln (1+x2)+C
? sec-1 x dx = x sec-1 x- ln |x+ |+C
? csc-1 x dx = x csc-1 x+ ln |x+ |+C
sinh-1 ( )= ln (x+ ) x R
cosh-1 ( )=ln (x+ ) x≥1
tanh-1 ( )= ln ( ) |x| 1
sech-1( )=ln( + )0≤x≤1
csch-1 ( )=ln( + ) |x| >0

Dx sinh x = cosh x
cosh x = sinh x
tanh x = sech2 x
coth x = -csch2 x
sech x = -sech x tanh x
csch x = -csch x coth x ? sinh x dx = cosh x + C
? cosh x dx = sinh x + C
? tanh x dx = ln | cosh x |+ C
? coth x dx = ln | sinh x | + C
? sech x dx = -2tan-1 (e-x) + C
? csch x dx = 2 ln | | + C
duv = udv + vdu
? duv = uv = ? udv + ? vdu
→? udv = uv - ? vdu
cos2θ-sin2θ=cos2θ
cos2θ+ sin2θ=1
cosh2θ-sinh2θ=1
cosh2θ+sinh2θ=cosh2θ
Dx sinh-1( )=
cosh-1( )=
tanh-1( )=
coth-1( )=
sech-1( )=
csch-1(x/a)=
? sinh-1 x dx = x sinh-1 x- + C
? cosh-1 x dx = x cosh-1 x- + C
? tanh-1 x dx = x tanh-1 x+ ? ln | 1-x2|+ C
? coth-1 x dx = x coth-1 x- ? ln | 1-x2|+ C
? sech-1 x dx = x sech-1 x- sin-1 x + C
? csch-1 x dx = x csch-1 x+ sinh-1 x + C

sin 3θ=3sinθ-4sin3θ
cos3θ=4cos3θ-3cosθ
→sin3θ= ? (3sinθ-sin3θ)
→cos3θ=?(3cosθ+cos3θ)
sin x = cos x =
sinh x = cosh x =
正弦定理: = = =2R
余弦定理: a2=b2+c2-2bc cosα
b2=a2+c2-2ac cosβ
c2=a2+b2-2ab cosγ

sin (α±β)=sin α cos β ± cos α sin β
cos (α±β)=cos α cos β sin α sin β
2 sin α cos β = sin (α+β) + sin (α-β)
2 cos α sin β = sin (α+β) - sin (α-β)
2 cos α cos β = cos (α-β) + cos (α+β)
2 sin α sin β = cos (α-β) - cos (α+β) sin α + sin β = 2 sin ?(α+β) cos ?(α-β)
sin α - sin β = 2 cos ?(α+β) sin ?(α-β)
cos α + cos β = 2 cos ?(α+β) cos ?(α-β)
cos α - cos β = -2 sin ?(α+β) sin ?(α-β)
tan (α±β)= , cot (α±β)=

ex=1+x+ + +…+ + …
sin x = x- + - +…+ + …
cos x = 1- + - +…+ + …
ln (1+x) = x- + - +…+ + …
tan-1 x = x- + - +…+ + …
(1+x)r =1+rx+ x2+ x3+… -1