第1个回答 2019-03-06
微积分公式
Dxsinx=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
Dxsin-1()=
cos-1()=
tan-1()=
cot-1()=
sec-1()=
csc-1(x/a)=
sin-1xdx=xsin-1x++C
cos-1xdx=xcos-1x-+C
tan-1xdx=xtan-1x-ln(1+x2)+C
cot-1xdx=xcot-1x+ln(1+x2)+C
sec-1xdx=xsec-1x-ln|x+|+C
csc-1xdx=xcsc-1x+ln|x+|+C
sinh-1()=ln(x+)xR
cosh-1()=ln(x+)x≥1
tanh-1()=ln()|x|1
sech-1()=ln(+)0≤x≤1
csch-1()=ln(+)|x|>0
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||+C
duv=udv+vdu
duv=uv=udv+vdu
→udv=uv-vdu
cos2θ-sin2θ=cos2θ
cos2θ+sin2θ=1
cosh2θ-sinh2θ=1
cosh2θ+sinh2θ=cosh2θ
Dxsinh-1()=
cosh-1()=
tanh-1()=
coth-1()=
sech-1()=
csch-1(x/a)=
sinh-1xdx=xsinh-1x-+C
cosh-1xdx=xcosh-1x-+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
sin3θ=3sinθ-4sin3θ
cos3θ=4cos3θ-3cosθ
→sin3θ=(3sinθ-sin3θ)
→cos3θ=(3cosθ+cos3θ)
sinx=cosx=
sinhx=coshx=
正弦定理:===2R
余弦定理:a2=b2+c2-2bccosα
b2=a2+c2-2accosβ
c2=a2+b2-2abcosγ
sin(α±β)=sinαcosβ±cosαsinβ
cos(α±β)=cosαcosβsinαsinβ
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=2sin(α+β)cos(α-β)
sinα-sinβ=2cos(α+β)sin(α-β)
cosα+cosβ=2cos(α+β)cos(α-β)
cosα-cosβ=-2sin(α+β)sin(α-β)
tan(α±β)=,cot(α±β)=
ex=1+x+++…++…
sinx=x-+-+…++…
cosx=1-+-+++
ln(1+x)=x-+-+++
tan-1x=x-+-+++
(1+x)r=1+rx+x2+x3+-1=n
=n(n+1)
=n(n+1)(2n+1)
=[n(n+1)]2
Γ(x)=x-1e-tdt=22x-1dt=x-1dt
β(m,n)=m-1(1-x)n-1dx=22m-1xcos2n-1xdx=dx