微积分公式Dxsinx=cosxcosx=-sinxtanx=sec2xcotx=-csc2xsecx=secxtanxcscx=-cscxcotx1xDxsin-1()=2aax21xcos()=2aax2-1∫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+1x2+C∫cos-1xdx=xcos-1x-1x2+C∫tanxdx=xtanx-ln(1+x)+C-1-12sin-1(-x)=-sin-1xcos-1(-x)=π-cos-1xtan-1(-x)=-tan-1xcot-1(-x)=π-cot-1xsec-1(-x)=π-sec-1xcsc-1(-x)=-csc-1xxsinh-1()=ln(x+a2+x2)x∈Raxcosh-1()=ln(x+x2a2)x?1ax1a+xtanh-1()=ln()|x|<1a2aaxaxtan-1()=2aa+x2axcot()=2aa+x2-1∫cot-1xdx=xcot-1x+ln(1+x2)+C∫sec-1xdx=xsec-1x-ln|x+x21|+C-1-12x1x+acoth-1()=ln()|x|>1a2axa∫cscxdx=xcscx+ln|x+x1|+Csech-1(1x2x1)=ln(+)0?x?1x2ax1+x2x1)=ln(+)|x|>0x2axxsec()=ax-1ax2a2ax2a2csch-1(csc-1(x)=axDxsinhx=coshxcoshx=sinhxtanhx=sechxcothx=-csch2x2∫sinhxdx=coshx+C∫coshxdx=sinhx+C∫tanhxdx=ln|coshx|+Cduv=udv+vdu∫cothxdx=ln|sinhx|+Csechx=-sechxtanhx∫sechxdx=-2tan-1(e-x)+Ccschx=-cschxcothx1+ex∫cschxdx=2ln||+C1e2xx1Dxsinh-1()=∫sinh-1xdx=xsinh-1x-1+x2+Caa2+x2x1cosh-1()=∫cosh-1xdx=xcosh-1x-x21+Cax2a2axtanh()=2aax2-1-1∫duv=uv=∫udv+∫vdu→∫udv=uv-∫vducos2θ-sin2θ=cos2θcos2θ+sin2θ=1cosh2θ-sinh2θ=1cosh2θ+sinh2θ=cosh2θsin3θ=3sinθ-4sin3θcos3θ=4cos3θ-3cosθ→sin3θ=(3sinθ-sin3θ)→cos3θ=(3cosθ+cos3θ)ejxejxejx+ejxsinx=cosx=2j2∫coth-1xdx=xcoth-1x-ln|1-x2|+C∫tanh-1xdx=xtanh-1x+ln|1-x2|+Cexexex+excoshx=22abc正弦定理:===2Rsinαsinβsinγsinhx=∫sech-1xdx=xsech-1x-sin-1x+Caxcoth()=2aax2∫csch-1xdx=xcsch-1x+sinh-1x+Cxaγsech-1()=aaxa2x2Rbxacsch-1()=axa2+x2βαc余弦定理: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)ex=1+x+x2x3xn+…++…+2!3!n!xxx(1)x+-+…++…3!5!7!(2n+1)!357sinα+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)=tanα±tanβcotαcotβ,cot(α±β)=tanαtanβcotα±cotβ∑1=ni=1nnn2n+1sinx=xcosx=1-∑i=i=1nn(n+1)