tan积分

tan积分

-

2023年3月4日发(作者：游戏符号)

微积分公式

D

x

sinx=cosx

cosx=-sinx

tanx=sec2x

cotx=-csc2x

secx=secxtanx

cscx=-cscxcotx

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-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

D

x

sin-1(

a

x

)=

22

1

xa



cos-1(

a

x

)=

tan-1(

a

x

)=

22xa

a





cot-1(

a

x

)=

sec-1(

a

x

)=

22axx

a





csc-1(x/a)=

sin-1xdx=xsin-1x+21x+C

cos-1xdx=xcos-1x-21x+C

tan-1xdx=xtan-1x-½ln(1+x2)+C

cot-1xdx=xcot-1x+½ln(1+x2)+C

sec-1xdx=xsec-1x-ln|x+12x|+C

csc-1xdx=xcsc-1x+ln|x+12x|+C

sinh-1(

a

x

)=ln(x+22xa)xR

cosh-1(

a

x

)=ln(x+22ax)x≧1

tanh-1(

a

x

)=

a2

1

ln(

xa

xa





)|x|<1

coth-1(

a

x

)=

a2

1

ln(

ax

ax





)|x|>1

sech-1(

a

x

)=ln(

x

1

+

2

21

x

x

)0≦x≦1

csch-1(

a

x

)=ln(

x

1

+

2

21

x

x

)|x|>0

D

x

sinhx=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|

x

x

e

e

21

1









|+C

duv=udv+vdu

duv=uv=udv+vdu

→udv=uv-vdu

cos2θ-sin2θ=cos2θ

cos2θ+sin2θ=1

cosh2θ-sinh2θ=1

cosh2θ+sinh2θ=cosh2θ

D

x

sinh-1(

a

x

)=

22

1

xa

cosh-1(

a

x

)=

22

1

ax

tanh-1(

a

x

)=

22xa

a





coth-1(

a

x

)=

sech-1(

a

x

)=

22xax

a





csch-1(x/a)=

22xax

a





sinh-1xdx=xsinh-1x-21x+C

cosh-1xdx=xcosh-1x-12x+C

tanh-1xdx=xtanh-1x+½ln|1-x2|+C

coth-1xdx=xcoth-1x-½ln|1-x2|+C

sech-1xdx=xsech-1x-sin-1x+C

csch-1xdx=xcsch-1x+sinh-1x+C

sin3θ=3sinθ-4sin3θ

cos3θ=4cos3θ-3cosθ

→sin3θ=¼(3sinθ-sin3θ)

→cos3θ=¼(3cosθ+cos3θ)

sinx=

j

eejxjx

2



cosx=

2

jxjxee

sinhx=

2

xxee

coshx=

2

xxee

正弦定理:

sin

a

=

sin

b

=

sin

c

=2R

余弦定理:a2=b2+c2-2bccosα

b2=a2+c2-2accosβ

c2=a2+b2-2abcosγ

a

b

c

α

β

γ

R

sin(α±β)=sinαcosβ±cosαsinβ

cos(α±β)=cosαcosβsinαsinβ

2sinαcosβ=sin(α+β)+sin(α-β)

2cosαsinβ=sin(α+β)-sin(α-β)

2cosαcosβ=cos(α-β)+cos(α+β)

2sinαsinβ=cos(α-β)-cos(α+β)

sinα+sinβ=2sin½(α+β)cos½(α-β)

sinα-sinβ=2cos½(α+β)sin½(α-β)

cosα+cosβ=2cos½(α+β)cos½(α-β)

cosα-cosβ=-2sin½(α+β)sin½(α-β)

tan(α±β)=





tantan

tantan





,cot(α±β)=





cotcot

cotcot





ex=1+x+

!2

2x

+

!3

3x

+…+

!n

xn

+…

sinx=x-

!3

3x

+

!5

5x

-

!7

7x

+…+

)!12(

)1(12





n

xnn

+…

cosx=1-

!2

2x

+

!4

4x

-

!6

6x

+…+

)!2(

)1(2

n

xnn

+…

ln(1+x)=x-

2

2x

+

3

3x

-

4

4x

+…+

)!1(

)1(1





n

xnn

+…

tan-1x=x-

3

3x

+

5

5x

-

7

7x

+…+

)12(

)1(12





n

xnn

+…

(1+x)r=1+rx+

!2

)1(rr

x2+

!3

)2)(1(rrr

x3+…-1





n

i1

1=n





n

i

i

1

=½n(n+1)





n

i

i

1

2=

6

1

n(n+1)(2n+1)





n

i

i

1

3=[½n(n+1)]2

Γ(x)=

0

tx-1e-tdt=2

0

t2x-12tedt=

0

)

1

(ln

t

x-1dt

β(m,n)=1

0

xm-1(1-x)n-1dx=22

0

sin



2m-1xcos2n-1xdx

=





0

1

)1(nm

m

x

x

dx

希腊字母

大写小写读音大写小写读音大写小写读音

Α

α

alphaΙ

ι

iotaΡ

ρ

rho

Β

β

betaΚ

κ

kappaΣ

σ,ς

sigma

Γ

γ

gammaΛ

λ

lambdaΤ

τ

tau

Δ

δ

deltaΜ

μ

muΥ

υ

upsilon

Ε

ε

epsilonΝ

ν

nuΦ

φ

phi

Ζ

ζ

zetaΞ

ξ

xiΧ

χ

khi

Η

η

etaΟ

ο

omicronΨ

ψ

psi

Θ

θ

thetaΠ

π

piΩ

ω

omega

倒数关系:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1

商数关系:tanθ=





cos

sin

;cotθ=





sin

cos

平方关系:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ

順位低

順位高

;顺位高d顺位低;

0*=



1

*=





=0*

0

1

=

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)