导数微分积分基本公式对照表

导数微分积分基本公式对照表导数表微分表积分表1()为常数cc0=′()为常数cdc0=()∫∫=+=cdxacaxadx0,为常数2()()Rxx∈=′−αααα1()()Rdxxxd∈=−αααα1()1111−≠++=+∫ααααcxdxx,∫+=)(cxdx3()xxee=′()dxeedxx=∫+=cedxexx4()()10ln≠=′aaaaxx()()10ln≠=aadxaadxx()∫≠+=10ln1acaadxaxx5()xx1ln=′()dxxxd1ln=()0ln≠+=∫xcxxdx6()exxaalog1log=′()edxxxdaalog1log=7()xxcossin=′()xdxxdcossin=cxdxx+=∫sincos8()xxsincos−=′()xdxxdsincos−=cxdxx+−=∫cossin9()xtgx2sec=′()xdxtgxd2sec=ctgxdxx+=∫2sec10()xctgx2csc−=′()xdxctgxd2csc−=cctgxdxx+−=∫2csc11()tgxxx⋅=′secsec()tgxdxxxd⋅=secsec[()∫∫==⋅xxdtgxdxxsecsecsec]12()ctgxxx⋅−=′csccsc()ctgxdxxxd⋅−=csccsc13()()111arcsin2−=′xxx()()111arcsin2−=xdxxxdcxxdx+=−∫arcsin1214()()111arccos2−−=′xxx()()111arccos2−−=xdxxxd15()211xarctgx+=′()dxxarctgxd211+=carctgxxdx+=+∫2116()211xarcctgx+−=′()dxxarcctgxd211+−=∫+=−caxxadxarcsin2217()vuvu′±′=′±()dvduvud±=±caxxaxdx+±+=±∫2222ln18()vuvuuv′+′=′()udvvduuvd+=caxarctgaaxdx+=+∫12219()uccu′=′()cducud=∫++−=−caxaxaaxdxln212220()02≠′−′=′⎟⎠⎞⎜⎝⎛vvvuvuvu()02≠−=⎟⎠⎞⎜⎝⎛vvudvvduvud∫++−=−caxaxaxdxxaarcsin222222221xvuxvuyy′⋅′⋅′=′其中()()()xhvvguufy===,,()()()()()()dxxhvgufdvvgufduufdy′′′=′′=′=其中()()()xhvvguufy===,,caxxaaxxdxax+±+±±=±∫2222222ln22