微积分公式大全Word版

微积分公式

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

sin -1 x dx = x sin -1 x+2

1x -+C cos -1 x dx = x cos -1 x-2

1x -+C

tan -1 x dx = x tan -1 x-½ln (1+x 2

)+C cot -1 x dx = x cot -1 x+½ln (1+x 2)+C sec -1 x dx = x sec -1

x- ln

|x+12

-x |+C

csc -1 x dx = x csc -1 x+ ln |x+12-x |+C

tanh coth 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 |

x

x e e 211---+| + C

d uv = u d v + v d u

d uv = uv = u d v + v d u → u d v = uv - v d u cos 2θ-sin 2θ=cos2θ cos 2θ+ sin 2θ=1 cosh 2θ-sinh 2θ=1 cosh 2θ+sinh 2θ=cosh2θ

sinh -1 x dx = x sinh -1 x-2

1x ++ C

cosh -1 x dx = x cosh -1

x-12-x + C

tanh -1 x dx = x tanh -1 x+ ½ ln | 1-x 2

|+ C

coth -1 x dx = x coth -1 x- ½ ln | 1-x 2|+ 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 a b

c α β γ R

tan -1

x = x-33x +55x -7

7

x +…+)12()1(12+-+n x n n + …

(1+x)r

=1+r x+!2)1(-r r x 2+!

3)2)(1(--r r r x 3+… -1

(ln t

x-1 d t

β(m , n ) =⎰10x m -1(1-x)n -1

d x =2⎰20sin π2m -1x cos 2n -1x d x

= ⎰

∞

+-+0

1

)1(n

m m x x d x

希腊字母 (Greek Alphabets)

大写 小写

读音 大写 小写

读音 大写 小写 读音

Α α alpha Ι ι iota Ρ ρ

rho Β β beta Κ κ kappa Σ σ, ς sigma

Γ γ gamma Λ λ lambda Τ τ

tau Δ δ delta Μ μ mu Υ υ upsilon

Ε ε epsilon Ν ν nu Φ φ

phi Ζ ζ zeta Ξ ξ xi Χ χ

khi Η η eta Ο ο omicron Ψ ψ

psi Θ

θ theta

Π

π pi

Ω

ω omega

倒数关系: sin θcsc θ=1; tan θcot θ=1; cos θsec θ=1 商数关系: tan θ=

θθcos sin ; cot θ= θ

θ

sin cos 平方关系: cos 2θ+ sin 2θ=1; tan 2θ+ 1= sec 2θ; 1+ cot 2θ= csc 2θ

順位低順位高

;

顺位高d 顺位低 ; 0*

=

∞

1

* =

∞∞ = 0*01 = 0

0 00 = )(0-∞e ; 0∞ = ∞⋅0e ; ∞1 = ∞⋅0e

顺位一: 对数; 反三角(反双曲) 顺位二: 多项函数; 幂函数 顺位三: 指数; 三角(双曲)

算术平均数(Arithmetic mean) n

X X X X n

+++=

(21)

中位数(Median) 取排序后中间的那位数字 众数(Mode)

次数出现最多的数值

几何平均数(Geometric mean) n n X X X G ⋅⋅⋅= (21)

调和平均数(Harmonic mean)

)1...11(11

21n

x x x n H +++=