微積分公式大全

1、微積分公式Dxsinx=cosxcosx=sinxtanx=sec2xcotx=csc2xsecx=secxtanxcscx=cscxcotx?sinxdx=cosxC?cosxdx=sinxC?tanxdx=ln|secx|C?cotxdx=ln|sinx|C?secxdx=ln|secxtanx|C?cscxdx=ln|cscx–cotx|Csin1(x)=sin1xcos1(x)=?cos1xtan1(x)=tan1xcot1(x

2、)=?cot1xsec1(x)=?sec1xcsc1(x)=csc1xDxsin1()=ax221xa??cos1()=axtan1()=ax22xaa??cot1()=axsec1()=ax22axxa??csc1(xa)=?sin1xdx=xsin1xC21x??cos1xdx=xcos1xC21x??tan1xdx=xtan1xln(1x2)C?cot1xdx=xcot1xln(1x2)C?sec1xdx=xsec1xln|x|C

3、12?x?csc1xdx=xcsc1xln|x|C12?xsinh1()=ln(x)xRax22xa??cosh1()=ln(x)x≧1ax22ax?tanh1()=ln()|x|1axa21axax??sech1()=ln()0≦x≦1axx1?221xx?csch1()=ln()|x|0axx1221xx?Dxsinhx=coshxcoshx=sinhxtanhx=sech2xcothx=csch2xsechx=sechxtanhx

4、cschx=cschxcothx?sinhxdx=coshxC?coshxdx=sinhxC?tanhxdx=ln|coshx|C?cothxdx=ln|sinhx|C?sechxdx=2tan1(ex)C?cschxdx=2ln||Cxxee211????duv=udvvdu?duv=uv=?udv?vdu→?udv=uv?vducos2θsin2θ=cos2θcos2θsin2θ=1cosh2θsinh2θ=1cosh2θsinh2

5、θ=cosh2θDxsinh1()=ax221xa?cosh1()=ax221ax?tanh1()=ax22xaa??coth1()=axsech1()=ax22xaxa??csch1(xa)=22xaxa???sinh1xdx=xsinh1xC21x??cosh1xdx=xcosh1xC12?x?tanh1xdx=xtanh1xln|1x2|C?coth1xdx=xcoth1xln|1x2|C?sech1xdx=xsech1xsin1

6、xC?csch1xdx=xcsch1xsinh1xCsin3θ=3sinθ4sin3θcos3θ=4cos3θ3cosθ→sin3θ=(3sinθsin3θ)→cos3θ=(3cosθcos3θ)sinx=cosx=jeejxjx2??2jxjxee??sinhx=coshx=2xxee??2xxee??正弦定理:===2R?sina?sinb?sinc余弦定理:a2=b2c22bccosαb2=a2c22accosβc2=a2b22a