微积分归纳总结 1 . 常见的等价无穷小量 x23332x0sinarcsintanarctan1ln(1),1ln(0),1cos, (1),2tan, tansin,sin326011xxxxxxxxexxaaaxxxxxxxxxxxxxxaxb( 1) 当时 :( 2) 当时 : 2 . 求导公式表 1222C011lnloglnlnsincos xcossin(9) tansec(10) cotcsc(12) secsectan1(13) csccsccot(14) arctan1(15) arcxxxxxaxxeeaaaxxaxxxxxxxxxxxxxxxx ( 1) (2)() ( 3)( 4) ( 5) ( 6)( 7)( 8)22211cot(16) arcsin1111(17) arccos(18)21xxxxxxxx 3 . 基本不定积分表 12222(1) 0(2)(3)ln1(4)(5)(6) cossinln1(7) sincos(8)sectancos(9) sectansec(10) csccot1(11)csccotsinxxxxxdxdxcx dxcxcxaa dxce dxecxdxxcaxdxxcdxxdxxcxxxdxxcxxdxcscxxdxxx 221(12)arctan11(13)arcsin1cdxxcxdxxcx 4 . 不定积分表延伸 2222222222(1)tanln cos(2) cotln sin(2) secln sectan(4) cscln csccot1111(5)arctan(6)ln2111(7)ln(8)arcsin21(9)lxdxxcxdxxcxdxxxcxdxxxcxxadxcdxcaxaaxaaxaxaxdxcdxcaxaxaaaxdxxa 22222222222222n(10)arcsin22(11)ln22xxacxaxax dxaxcaxaxa dxxaxxac 5 . 定积分题型库 1111212120002331234210021312222001ln(1)1(1)(2)(3)arcsin(4)ln(2)1(5)(ln)(6)arccos(7)(1)1(8)(9)(10)(1)(1)(1)xexxdxedxxx dxxdxxxxdxdxxxdxxxdxdxdxxxxx 4143100221arctan(11)(12)(13)1cos 2(1)(1)xxdxdxdxxxxx 112221012sin1x(14)()(15)ln(16)( 1)1xt dt dxxdxxxdxtx 222202(17)sinarctan(18)(3)4(19)cosxnxe dxxxdxnx dx 21001221001(20)sin2 (tan1)(21)(1)(22)coscosxxdxxxdxk xlx dx 101022200021440141sincos(23)arctan (cos)(24)(25)4sincos1sin...