北大版高等数学第三章积分的计算及应用答案习题3.1

习题3.13/222222222223/23/22/33/22/33/23/22/33111.1212(12)(12).2331332.(1).(1)2(1)2(1)113.2727(27)(27).4624.(21)(21)321(21)(232xdxxdxxCxdxdxCxxxxxdxxdxxCxxdxxdxxdx求下列不定积分：/23/25/31/1/1/2100100992222211)(21).55.(1/).(2)16..(2)(2)99(2)1135/3157.arctan.3531[(5/3)]3531[5/3]15173/78.3773713/771xxxxCedxedxeCxdxdxCxxxdxdxdxxCxxxdxdxdxxx22222213arcsin.733/79.22arctan.(1)(1)1110.arctan.22211.arcsin.11()11112.1(1)(1)211111ln21xxxxxxxxxxxxxxCxdxdxxCxxxedxdeeCeedxdeeCeedxdedudueeeuuuuuCu22221ln.21lnlnlnln113.lnlnlnlnln(lnln).lnln2214.cot.1cos22sinsin22xxeCexxdxdxxdxxCxxxxddxdxxCxxx214102555454422442234412215.cot.1sin241cos21116.()(1)5(1)5(1)1111(1)(1)5(1)512112551153dxdxxCxxxxudxdxduuxxxuuvdudvvuuvvvdvvvvdvvvvv3515253214555511(1)(1)(1).531117.()11111111(ln|1|)(ln|1|).1118.()(2)(2)5(2)11152nnnnnnnnCxxxCxxudxdxduuxxnxnuduuuCxxCnunndxxdxduuxxxxxuu2arctan22111ln||ln|2|ln.210102ln(1)ln1119.(ln(1)ln)(1)1(ln(1)ln)(lnln(1)(ln(1)ln)(ln(1)ln)11ln.2ln(1)20.1xuduuuCCuuuxxdxxxdxxxxxxxdxxxxdxxxCxexxdxxarctan222arctan22arctan22ln(1)111arctanln(1)ln(1)21ln(1).4xxxexxdxdxxxedxxdxexC2223222221121.sin2cos2sin2sin2sin2.24222.sincos2sinsinsin.22223211123.sin5sin6(coscos11)sinsin11.2211212124.111(1)arcs1xxdxxdxxCxxxxxdxdCxxdxxxdxxxCxxdxdxdxxxxdxx233222222222222223/22223/2223/2in21arcsin.25.11111(1)22111111(1)12211(1)21.326.(0)()sin,(/2,/2),cos,()xCxxCxxxxdxdxdxxxxxdxdxxxxdxdxxxxxCdxaaxxattdxatdtax33223/222222222cos,1tan()cos1/.1(/)atdxdtdxtCaxataxaxCCaxaaax2222222222220,,0,arccosarccosarccosarccos.xxyyyaxaadxdyyaaCxyyaaxaaCxaaCxxaxaaCx时令22222222222227.(0).0,sec,(0,/2).tansec,tan,tan(sec1)(tan)(sec1arccos)(1arccos)arccos.xadxaxxattxdxattdtxaatxadxatdtatdtattCxaxaatCaCxaxaxaaCx时令2222222222222223/23/23/2333333328.1arcsinarcsin221arcsin.222229.ln(1)3311122(11)(1ln(11)ln33xxxxxxxxxxdxdxaxdxaaxaxaxxxaxaCaaaxxaxCadxedxdeeeCeeeeeexC333448822481)112ln(11).31130.()4411111ln(1)ln(1).44xxxxCeexCxdxdudxuxxxuuuCxxC222627242221/21/23/21/21/25312225312222211131.()2211111(1)121(1)221(2)2122222531121111153dxdxdxuduuxuxxxxxxvvvdvdvvuvvvvvdxvvvxxx25322253111.53CxxxCxxx2333333522435/32/332.()(1,1)111133()352133(1)(1).52xxxxxxxxeeudxdeduueuvuvueeuvvvduvdvvvdvCvueeC2221233.311131324421212arcsinarcsin.13132dxdxdxxxxxxxCC2222211291134.7724422111291292arcsin224282922129217arcsin.4829xxdxxdxxdxxxxCxxxxC2235.,11,1(1),2(1),11,11,1(1),2(1),112(1)2(ln)2(11)ln(11))1121ln(11)).dxxuxudxuduxdxxuxudxuduxdxuduuuCxxCuxxxC