高等数学常用导数积分公式查询表好
高等数学常用导数积分公式查询表好 08070141常用导数和积分公式导数公式： ? (1) (C)?0 ? (3) (sinx)?cosx?1?(x)?x (2)? (4) (cosx)?sinx (5) (tanx)?sec2x (7) (secx)?secxtanx (9) (ax)?axlna (log1 (11)ax)?xlna (arcsinx)?1 (13) 1?x2 (arctanx)?1 (15) 1?x2 (cotx)?csc2x (cscx)?cscxcotx(ex)?ex(lnx)?1x，(arccosx)?11?x2(arccotx)?11?x2(6)(8) (10) (12)(14) (16)08070141常用导数和积分公式根本积分表?tgxdx?lncosx?C?ctgxdx?lnsinx?C?secxdx?lnsecx?tgx?C?cscxdx?lncscx?ctgx?Cdx1x?arctg?C?a2?x2aadx1x?a?ln?x2?a22ax?a?Cdx1a?x?a2?x22alna?x?Cdxx?arcsin?C?a2?x2a?2ndx2?cos2x?secxdx?tgx?Cdx2?sin2x?cscxdx?ctgx?C?secx?tgxdx?secx?C?cscx?ctgxdx?cscx?Cax?adx?lna?Cx?shxdx?chx?C?chxdx?shx?C?dxx2?a2?ln(x?x2?a2)?C?2In?sinxdx?cosnxdx?00n?1In?2n?x2a22x?adx?x?a?ln(x?x2?a2)?C22x2a2222x?adx?x?a?lnx?x2?a2?C22x2a2x222a?xdx?a?x?arcsin?C22a22三角函数的有理式积分：2u1?u2x2dusinx?，cosx?，u?tg，dx? 22221?u1?u1?u一含有ax?b的积分(a1?0)dx1?ax?balnax?b?C?(ax?b)dx21(ax?b)?1?C?1a(?1)08070141常用导数和积分公式3x1dx?ax?ba2(ax?b?blnax?b)?Cx21?1?dx3?(ax?b)2?2b(ax?b)?b2lnax?b?C 4?ax?ba?2?5dx?x(ax?b)?1ax?bln?C bx6?dx1aax?b?ln?C 22x(ax?b)bxbx71bx(lnax?b?)?C dx2?(ax?b)2aax?b1b2x2)?C 8?dx3(ax?b?2blnax?b?2aax?b(ax?b)9?dx11ax?b?ln?Cx(ax?b)2b(ax?b)b2x二含有10ax?b的积分23(ax?b)?C ?3a2(3ax?2b)(ax?b)3?C 11?xax?bdx215a22(15a2x2?12abx?8b2)(ax?b)3?C ax?bdx12?x3105aax?bdx13?2xdx2(ax?2b)ax?b?C3aax?b2x2(3a2x2?4abx?8b2)ax?b?C dx315aax?b14?dx?15?xax?b?1lnbax?b?b?C(b?0)ax?b?b2ax?barctan?C(b?0)?b?b08070141常用导数和积分公式16?x2dxax?badx?bx2bxax?bax?b17?dxax?b dx2ax?b?b?xxax?b18ax?bax?badxdx?x2x2?xax?b2 三含有x19?a2的积分=dx?x2?a21xarctan?C aa20dxx2n?3dx?=?(x2?a2)n2(n?1)a2(x2?a2)n?12(n?1)a2?(x2?a2)n?121?dx1x?a=ln?Cx2?a22ax?a2四含有ax?b(a?0)的积分ax?Cb(b?0)?1arctan?dx?ab22?ax2?b?1ln?2?ab?23ax?b?C(b?0)ax?bx12dx?ax2?b2alnax?b?Cxbdxx2?dx24? aa?ax2?bax2?b25?1x2dxln?C x(ax2?b)2bax2?b261adxdx?x2(ax2?b)bxb?ax2?b08070141常用导数和积分公式27?dxaax2?b1x3(ax2?b)2b2lnx2?2bx2?C 28?dxdx(ax2?b)2x12b(ax2?b)?2b?ax2?b 五含有ax2?bx?c(a?0)的积分?22ax?b?dx?4ac?b2arctan4ac?b2?C29ax2?bx?c?12ax?b?2?b2?4aclnb?4ac2ax?b?b2?4ac?C30?xax2?bx?cdx12alnax2?bx?c?bdx2a?ax2?bx?c六含有x2?a2(a?0)的积分31?dxarshxx2?a2a?C1ln(x?x2?a2)?C 32?dxx(x2?a2)3a2x2?a2?C33?xx2?a2dxx2?a2?C34?x?1(x2?a2)3dxx2?a2?C35?x2x2x2?a2dx2x2?a2?a2ln(x?x2?a2)?C 36?x2(x2?a2)3dx?xx2?a2?ln(x?x2?a2)?C37?dx1x2?a2?axx2?a2alnx?C (b2?4ac)(b2?4ac) 08070141常用导数和积分公式103dx?a?bsinxdx?a?bsinx2a2?b2atanarctanx?b2?C22a?b(a2?b2)104x22?b?b?a12ln?C22x22b?aatan?b?b?a2atan(a2?b2)105dx2a?ba?bxarctan(tan)?C?a?bcosxa?ba?ba?b2(a2?b2)x?dx1a?b2106?lna?bcosxa?bb?axtan?2tan107a?bb?a?Ca?bb?a(a2?b2)dx1barctan(tanx)?C ?a2cos2x?b2sin2xabadx1btanx?aln?a2cos2x?b2sin2x2abbtanx?a?C10811sinax?xcosax?C 2aa12222110?xsinaxdx?xcosax?2xsinax?3cosax?Caaa11111?xcosaxdx2cosax?xsinax?Caa12222112?xcosaxdxxsinax?2xcosax?3sinax?Caaa十二含有反三角函数的积分其中a?0xx22113?arcsindxxarcsin?a?x?Caa109?xsinaxdxxx2a2xx2?)arcsin?a?x2?C 114?xarcsindx(a24a4xx3x1arcsin?(x2?2a2)a2?x2?C 115?xarcsindxa3a9208070141常用导数和积分公式116xxarccosdxxarccos?a2?x2?C ?aaxx2a2xx2?)arccos?a?x2?C 117?xarccosdx(a24a4xx3x1arccos?(x2?2a2)a2?x2?C 118?xarccosdxa3a92xxa22arctandxxarctan?ln(a?x)?C ?aa2x12xa2120?xarctandx(a?x)arctan?x?Ca2a2119xx3xa2a3arctan?x?ln(a2?x2)?C 121?xarctandxa3a662十三含有指数函数的积分1xa?C lna1axax123?edxe?Ca1axax124?xedx2(ax?1)e?Ca1naxnn?1axnax125?xedxxe?xedxaa122xa?dx126x?xadxxx1a?ax?C 2lna(lna)1nxnxa?xn?1axdx ?lnalna1axaxe(asinbx?bcosbx)?C 128?esinbxdx22a?b1axeax(bsinbx?acosbx)?C 129?ecosbxdx22a?b1axneaxsinn?1bx(asinbx?nbcosbx) 130?esinbxdx222a?bn127nx?xadx n(n?1)b2axn?2?2esinbxdx a?b2n2?08070141常用导数和积分公式131axn?ecosbxdx1eaxcosn?1bx(acosbx?nbsinbx) 222a?bnn(n?1)b2ax?2ecosn?2bxdx 22?a?bn十四含有对数函数的积分 132133?lnxdxxlnx?x?Cdx?xlnxlnlnx?C1n?11nx(lnx?)?C 134?xlnxdxn?1n?1135136nn(lnx)dxx(lnx)?n?(lnx)dx ?mn?x(lnx)dxn?11nmn?1xm?1(lnx)n?x(lnx)dx ?m?1m?1十五含有双曲函数的积分 137138139140?shxdxchx?C ?chxdxshx?C ?thxdxlnchx?C2sh?xdx?x1?sh2x?C 24x12141?chxdx?sh2x?C24十六定积分 142143?cosnxdx?sinnxdx0?cosmxsinnxdx0?0,m?n144?cosmxcosnxdx?,m?n?145?0,m?nsinmxsinnxdx ?,m?n?08070141常用导数和积分公式?0,m?n?146?sinmxsinnxdx?cosmxcosnxdx?00,m?n?2?147In?sinxdx?cosnxdxn?1In?2 nn?1n?342In? n为大于1的正奇数，I11nn?253?n?1n?331?In?n为正偶数，I02nn?2422?20n?20In 本文来源：网络收集与整理，如有侵权，请联系作者删除，谢谢！第9页 共9页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页第 9 页 共 9 页
