（精心整理）高中数学微积分公式大全

微積分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotxsinxdx=-cosx+Ccosxdx=sinx+Ctanxdx=ln|secx|+Ccotxdx=ln|sinx|+Csecxdx=ln|secx+tanx|+Ccscxdx=ln|cscx–cotx|+Csin-1(-x)=-sin-1xcos-1(-x)=-cos-1xtan-1(-x)=-tan-1xcot-1(-x)=-cot-1xsec-1(-x)=-sec-1xcsc-1(-x)=-csc-1xDxsin-1()=cos-1()=tan-1()=cot-1()=sec-1()=csc-1(x/a)=sin-1xdx=xsin-1x++Ccos-1xdx=xcos-1x-+Ctan-1xdx=xtan-1x-½ln(1+x2)+Ccot-1xdx=xcot-1x+½ln(1+x2)+Csec-1xdx=xsec-1x-ln|x+|+Ccsc-1xdx=xcsc-1x+ln|x+|+Csinh-1()=ln(x+)xRcosh-1()=ln(x+)x≧1tanh-1()=

ln()|x|<1coth-1()=ln()|x|>1sech-1()=ln(+)0≦x≦1csch-1()=ln(+)|x|>0Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=-csch2xsechx=-sechxtanhxcschx=-cschxcothxsinhxdx=coshx+Ccoshxdx=sinhx+Ctanhxdx=ln|coshx|+Ccothxdx=ln|sinhx|+Csechxdx=-2tan-1(e-x)+Ccschxdx=2ln||+Cduv=udv+vduduv=uv=udv+vdu→udv=uv-vducos2θ-sin2θ=cos2θcos2θ+sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θDxsinh-1()=cosh-1()=tanh-1()=coth-1()=sech-1()=csch-1(x/a)=sinh-1xdx=xsinh-1x-+Ccosh-1xdx=xcosh-1x-+Ctanh-1xdx=xtanh-1x+½ln|1-x2|+Ccoth-1xdx=xcoth-1x-½ln|1-x2|

+Csech-1xdx=xsech-1x-sin-1x+Ccsch-1xdx=xcsch-1x+sinh-1x+Csin3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθ→sin3θ=¼(3sinθ-sin3θ)→cos3θ=¼(3cosθ+cos3θ)sinx=cosx=sinhx=coshx=正弦定理:===2R餘弦定理:a2=b2+c2-2bccosαb2=a2+c2-2accosβc2=a2+b2-2abcosγsin(α±β)=sinαcosβ±cosαsinβcos(α±β)=cosαcosβsinαsinβ2sinαcosβ=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)=,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<x<1=n=½n(n+1)=n(n+1)(2n+1)=[½n(n+1)]2Γ(x)=x-1e-tdt=22x-1dt=x-1dtβ(m,n)=m-1(1-x)n-1dx=22m-1xcos2n-1xdx=dx希臘字母(GreekAlphabets)大寫小寫讀音大寫小寫讀音大寫小寫讀音ΑαalphaΙιiotaΡρrhoΒβbetaΚκkappaΣσ,ςsigmaΓγgammaΛλlambdaΤτtauΔδdeltaΜμmuΥυupsilonΕεepsilonΝνnuΦφphiΖζzetaΞξxiΧχkhiΗηetaΟοomicronΨψpsiΘθthetaΠπpiΩωomega倒數關係:sinθcscθ=1;tanθcotθ=1;cosθsecθ=1商數關係:tanθ=;cotθ=平方關係:cos2θ+sin2θ=1;tan2θ+1=sec2θ;1+cot2θ=csc2θ;順位高d順位低;0*=*==0*==;=;=順位一:對數;反三角(反雙

曲)順位二:多項函數;冪函數順位三:指數;三角(雙曲)算術平均數(Arithmeticmean)中位數(Median)取排序後中間的那位數字眾數(Mode)次數出現最多的數值幾何平均數(Geometricmean)調和平均數(Harmonicmean)平均差(AverageDeviatoin)變異數(Variance)or標準差(StandardDeviation)or分配機率函數f(x)期望值E(x)變異數V(x)動差母函數m(t)DiscreteUniform(n+1)(n2+1)ContinuousUniform(a+b)(b-a)2Bernoullipxq1-x(x=0,1)ppqq+petBinomialpxqn-xnpnpq(q+pet)nNegativeBinomialpkqxMultinomialf(x1,x2,…,xm-1)=npinpi(1-pi)三項(p1et1+p2et2+p3)nGeometricpqx-1HypergeometricnnPoissonλλNormalμσ2BetaGammaExponentChi-Squaredχ2=f(χ2)=E(χ2)=nV(χ2)=2nWeibullaγRαβcb