微积分公式大全

微积分公式

sec x = sec x tan cot 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-1x dx = x sin-1x+2

-+C

1x cos-1x dx = x cos-1x-2

1x

-+C tan-1 x dx = x tan-1 x-½ln (1+x2)+C

cot-1 x dx = x cot-1 x+½ln (1+x2)+C

sec-1 x dx = x sec-1 x- ln |x+1

2-

x|+C

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

2-

x|+C

sech x = -sech x csch x = -csch 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 |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-21x ++ 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

γR

-1

β(m , n ) =⎰1

0x

m -1

(1-x)n -1

d x =2

⎰

2

sin

π

2m -1

x

cos 2n -1

x 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

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 +++=