λ lambda Τ
τ
tau
Δ
δ delta Μ
μ
mu
Υ
υ upsilon
欢迎阅读
Ε
ε epsilon Ν
Ζ
ζ zeta
Ξ
Η
η
eta
Ο
Θ
θ theta Π
ν
nu
Φ
ξ
xi
Χ
ο omicron Ψ
π
pi
Ω
φ
phi
χ
khi
ψ
psi
ω omega
倒数关系:sinθ cscθ =1;tanθ cotθ =1;cosθ secθ =1
欢迎阅读
Dxsinh-1(
x a
)=
1 a2 x2
cosh-1( x )= 1
a
x2 a2
tanh-1(
x a
)=
a a2 x2
coth-1( x )= a
sinh-1xdx=xsinh-1x- 1 x2 +C
cosh-1xdx=xcosh-1x- x2 1 +C tanh-1xdx=xtanh-1x+?ln|1-x2|+C coth-1xdx=xcoth-1x-?ln|1-x2|+C sech-1xdx=xsech-1x-sin-1x+C csch-1xdx=xcsch-1x+sinh-1x+C
i 1
6
n
i3 =[?n(n+1)]2
i 1
Γ
(x)=

t
x-1e-tdt=2

t
2x-1
e
t2
dt=
(ln 1) x-1dt
0
0
0t
(1+x)r=1+rx+ r(r 1) x2+ r(r 1)(r 2) x3+…-1<x<1 β
2!
3!
(m,n)=
1
x
m-1(1-x)n-1dx=2
商数关系:tanθ = sin ;cotθ = cos
c os
s in
平方关系:cos2θ +sin2θ =1;tan2θ +1=sec2θ ;1+cot2θ =csc2θ
順位高 順位低
;顺位高
d
顺位低;
0*= 1 *= =0* 1 = 0 00
0 0 = e0( ) ; 0 = e 0 ;1 = e 0
2
2
sech-1( x )= a a x a2 x2
csch-1(x/a)= a x a2 x2
γ
a
R
b
α
β
c
正弦定理: a = b = c =2R sin sin sin
余弦定理:a2=b2+c2-2bccosα b2=a2+c2-2accosβ c2=a2+b2-2abcosγ

2 sin 2m-1xcos2n-1xdx=
0
0
x
m1
0 (1 x)mn dx
希腊字母(GreekAlphabets)
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,? sigma
Γ
γ gamma Λ
微积分公式
Dxsinx=cosx
cosx=-sinx tanx=sec2x cotx=-csc2x
secx=secxtanx
cscx=-cscxcotx
Dxsin-1( x )= 1
a
a2 x2
cos-1( x )= a
tan-1(
x a
)=
a a2 x2
cot-1( x )= a
sinxdx=-cosx+C cosxdx=sinx+C tanxdx=ln|secx|+C cotxdx=ln|sinx|+C secxdx=ln|secx+tanx|+C cscxdx=ln|cscx–cotx|+C sin-1xdx=xsin-1x+ 1 x2 +C cos-1xdx=xcos-1x- 1 x2 +C tan-1xdx=xtan-1x-?ln(1+x2)+C cot-1xdx=xcot-1x+?ln(1+x2)+C sec-1xdx=xsec-1x-ln|x+ x2 1 |+C csc-1xdx=xcsc-1x+ln|x+ x2 1 |+C
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)
(2n)!
ln(1+x)=x- x2 + x3 - x4 +…+ (1)n x n1 +…
2 34
(n 1)!
tan-1x=x- x3 + x5 - x7 +…+ (1)n x 2n1 +…
3 57
(2n 1)
n
1 =n
i 1
n
i =?n(n+1)
i 1
n i2 = 1 n(n+1)(2n+1)
cot cot
cot cot

ex=1+x+ x2 + x3 +…+ xn +…
2! 3!
n!
sinx=x-
x3
+
x5
-
x7
(1)n x 2n1 +…+
+…
3! 5! 7!
(2n 1)!
cosx=1- x2 + x4 - x6 +…+ (1)n x2n +…
2! 4! 6!
1 e2x
欢迎阅读
sin-1(-x)=-sin-1x cos-1(-x)=-cos-1x tan-1(-x)=-tan-1x cot-1(-x)=-cot-1x sec-1(-x)=-sec-1x csc-1(-x)=-csc-1x
sinh-1( x )=ln(x+ a2 x2 )x R a
csch-1( x )=ln( 1 +
a
x
1 x2 x2
)|x|>0
duv=udv+vdu
duv=uv=udv+vdu →udv=uv-vdu cos2θ -sin2θ =cos2θ cos2θ +sin2θ =1 cosh2θ -sinh2θ =1 cosh2θ +sinh2θ =cosh2θ
cosh-1( x )=ln(x+ x2 a2 )x≧1 a
tanh-1( x )= 1 ln( a x )|x|<1 a 2a a x
coth-1( x )= 1 ln( x a )|x|>1 a 2a x a
sech-1( x )=ln( 1 +
a
x
1 x2 x2
)0≦x≦1
2cosαsinβ=sin(α+β)-sin(α-β)
cosα-cosβ=-2sin?(α+β)sin?(α-β)
2cosαcosβ=cos(α-β)+cos(α+β) 2sinαsinβ=cos(α-β)-cos(α+β)
tan(α±β)=
tan tan
tan tan

,cot(α±β)=
sec-1( x )= a a x x2 a2
csc-1(x/a)= Dxsinhx=coshx coshx=sinhx tanhx=sech2x cothx=-csch2x sechx=-sechxtanhx cschx=-cschxcothx
sinhxdx=coshx+C coshxdx=sinhx+C tanhxdx=ln|coshx|+C cothxdx=ln|sinhx|+C sechxdx=-2tan-1(e-x)+C cschxdx=2ln| 1 ex |+C
sin3θ =3sinθ -4sin3θ cos3θ =4cos3θ -3cosθ →sin3θ =?(3sinθ -sin3θ ) →cos3θ =?(3cosθ +cos3θ )
e jx e jx
e jx e jx
sinx=
cosx=
2j
2
பைடு நூலகம்
sinhx= e x e x coshx= e x e x
sin(α±β)=sinαcosβ±cosαsinβ
sinα+sinβ=2sin?(α+β)cos?(α-β)
cos(α±β)=cosαcosβ sinαsinβ
sinα-sinβ=2cos?(α+β)sin?(α-β)
2sinαcosβ=sin(α+β)+sin(α-β)
cosα+cosβ=2cos?(α+β)cos?(α-β)