2.1第一类换元积分法ppt课件

1、一一. .第一类换元积分法第一类换元积分法( (凑微分法凑微分法) )二二. .第二类换元积分法第二类换元积分法1.1.积分形式的不变性：积分形式的不变性：CuFduuf)()(则cxFdxxf)()(若的函数为xu2.2.积分形式不变性下的积分形式不变性下的 基本积分公式：基本积分公式：ckukducuduu111cudxuln1caadxauuln1cedxeuucuudusincoscuuducossincuudutansec2cuuducotcsc2cuuduusectanseccuuduucsccotcsccuduuarcsin112cudxuarctan112cudu)(3132c

2、xddxxxddxxln1xddxx112)(ceddxexxxddxx21xdxdxcossinxdxdxsincosxdxdxxsectansecxdxdxxcsccotcscxdxdxtansec2xdxdxcotcsc2xddxxarcsin112xddxxarctan112)(1baxdadx)(212cxdxdx3.常见的凑微分常见的凑微分习题处理习题处理例例:求下列不定积分求下列不定积分)0() 1 (22axadx).(arctan1122公式caxadxxadxxa221解：dxaxa22111)(1112axdaxacaxaarctan1cuduuarctan112)(1a

3、xdadx 一一. .第一类换元积分法第一类换元积分法( (凑微分法凑微分法) )dxx291dxx2311913311312xdxcx3arctan31cx52arctan101dxx24251dxx25211251525211252512xdxcuduuarctan112Caxxxaarcsind122dxxa221)2(dxaxa2111axdaxaa2111cax arcsincuduuarcsin112dxxa221解：dxx291dxx23113133113312xdxcx3arcsindxx29251dxx253115153531135512xdxcx53arcsin31cudu

4、uarcsin11222)3(xadxdxxa221解：dxxaxaa1121)(121xadxaaCxaxaaln21dxxa221Cxaxaaln21221xa )(1xaxaxaxa11a21)(121xadxaadxx2491dxxx)213151（)23(51xdxxdxCxx32ln5162xxdxdxxx)23)(23(1dxxx23123161)23(23121)23(2312161xdxxdxcxx2323ln121Cxxsin1sin1ln21xdxsec)4(xdxcosdxxx2coscosxxd2sin1)(sinCxxtanseclnCxxxdxcotcsclncscxdxsec1：解xdxsecCxxtanseclndxxa221Cxaxaaln21xdxseccxxtansecln解解2 2 .dxxxxxxtansec)tan(secsec)tan(sectansec1xxdxx_)tan(secsecddxxxx)tan(secxx 4.2 换元积分法换元积分法作业作业 习题习题4 教材教材P982单号题；单号题；3双号题双号题 2. 2. 补充题补充题 Cxxdxxfsin)(知知 ,求求.) 1(d