北大版高等数学第三章积分的计算及应用答案习题3.2

1习题3.22222222222222222222111.lnlnlnln222111lnlnln.222224111122.1212212axaxaxaxaxaxaxaxaxaxaxaxxxxdxxdxxxdxxxxxxxdxxxdxxCxxedxxdexeedxxexedxaaaaaxxexdexeeedxaaaaaxea求下列不定积分：2223223222122122.1113.sin2cos2cos2cos222211cos2sin2.244.arcsinarcsinarcsinarcsin11(1)arcsin21axaxaxaxaxxxdexeeeCaaaaxexCaaaxxdxxdxxxxdxxxxCxdxxdxxxxdxxxxdxxxxx2arcsin1.xxC2222222222225.arctanarctanarctanarctan11(1)1arctanarctanln(1).2121116.cos3cos3cos3cos32221313cos3sin3cos3sin322241xxxxxxxxxdxxdxxxxdxxxxdxxxxxxCxIexdxxdeexedxexexdxexxde22222223cos3sin33cos324139cos3sin3,2444131cos3sin32cos33sin3.132413sin37.sin3sin33cos3sin33cos3sin33xxxxxxxxxxxxxxxexexexdxexexIIxxeCxxeCxIdxxdeexexdxeexxdeexecos33sin3xxexdx2sin33(cos33),1sin33cos3(sin33cos3).1010xxxxxexexIeIexexCxxC22222222118.sinsinsincos1sincos1sincossin1sincos.11sincos,1(sincoaxaxaxaxaxaxaxaxaxaxaxaxaxaxbIebxdxbxdeebxebxdxaaabebxbxdeaabebxebxbebxdxaabebxebxbIaabIebxebxbaaaeIabxbabs).bxC222222222222229.191919181921919191919,1911119ln(319)2231119ln(319).26IxdxxxxdxxxdxxxxdxxxxdxxdxxxIxIxxxxCxxxxC2222222222210.coshsinhsinhsinhsinhcosh.11.ln(1)ln(1)ln(1)ln(1)ln(1)1.1arccos12.(arccos)(arccos)21(arccos)2arccoxxdxxdxxxxdxxxxCxxdxxxxxdxxxdxxxxxxxxCxxxxdxxxdxxxx222s1(arccos)21arccos1xdxxxxxdx322(arccos)21arccos2.xxxxxC2222222222arccos1113.arccos(1)21arccos12(1)2(1)1arccos1.2(1)2114.arctanarctan2(1)1arctan.,,22122arctan,11arcxxdxxdxxxdxxxxxxCxxxdxxdxxxxxxdxxxxuxudxuduxxdxuuduuuCxu1tanarctan2(arctan)2arctan(arctan)(1)arctan.xdxxxxxCxxxxCxxxC22222222arcsin1arcsin15.arcsin1arcsin(0)1/1arcsin(1/)arcsinln|1/1/1|1/1arcsinln(11)lnarcsinln(11)ln||(0)(xxdxdxxdxxxxxxdxxxxxxdxxxxCxxxxxxCxxxxCxx原函数为偶函数424322442423442442434).1(ln)12ln16.(ln)(ln)444(ln)1(ln)1lnln4248(ln)1(ln)1lnln.482488xxxxdxxxdxxdxxxxxxxxdxxdxxxxxxxxxdxxxC223/225/225/2arctan1arctan(1)1217.arctan(1)(1)2(1)23xxdxxdxxdxxx4223/225/2arctan1.tan,(/2,/2).sec,3(1)3(1)xdxxuudxuduxx3225/23322325/223/222323/223/22cos(1sin)sin(1)11sinsin,3311arctanarctan11(1)3(1)3311arctan11.3(1)39(1)1dxuduuduxxxuuCCxxxxdxxxxCxxxxxxxCxxx222222222222222222222118.ln(1)ln(1)211ln(1)22111(1)1ln(1)221111ln(1)12221111ln(1)1ln(1)ln(1)222221ln(12xxxdxxxdxxdxxxxxxdxxxxxdxxxxxdxxxxxxxxxxxCxx22211)1ln(1).44xxxxxC