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1、习题 3.2 2222222222222222222111.lnlnlnln222111lnlnln.222224111122.1212212axaxaxaxaxaxaxaxaxaxaxaxxxxdxxdxxx dxxxxxxxdxxxdxxCxx e dxx dex ee dxx exe dxaaaaaxx exdex eee dxaaaaax eag求下列不定积分：2223223222122122.1113.sin2cos2cos2cos222211cos2sin2.244. arcsinarcsinarcsinarcsin11(1)arcsin21axaxaxaxaxxxdex eeeC
2、aaaaxexCaaaxxdxxdxxxxdxxxxCxdxxdxxxxdxxxxdxxxxx2arcsin1.xxC2222222222225. arctanarctanarctanarctan11(1)1arctanarctanln(1).2121116.cos3cos3cos3cos32221313cos3sin3cos3sin 322241xxxxxxxxxdxxdxxxxdxxxxdxxxxxxCxIexdxxdeexe dxexexdxexxde22222223cos3sin 33cos324139cos3sin 3,2444131cos3sin 32cos33sin 3.1324
3、13sin 37.sin3sin 33cos3sin33 cos3sin33xxxxxxxxxxxxxxxexexexdxexexIIxx eCxx eCxIdxxdeexexdxeexxdeexecos33sin 3xxexdx精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 4 页sin33(cos33 ),1sin33cos3(sin33cos3 ).1010 xxxxxexexIeIexexCxxC22222222118.sinsinsincos1sincos1sincossin1sincos.11sincos,1(sincoax
4、axaxaxaxaxaxaxaxaxaxaxaxaxbIebxdxbxdeebxebxdxaaabebxbxdeaabebxebxb ebxdxaabebxebxbIaabIebxebxbaaaeIabxbabs).bxC222222222222229.19191918192 1919191919,1911 119ln(319)22 31119ln(319).26Ix dxxxxdxxxdxxxxdxxxx dxxdxxxIxIxxxxCxxxxCgg2222222222210.coshsinhsinhsinhsinhcosh.11. ln(1)ln(1)ln(1)ln(1)ln(1)1.1a
5、rccos12. (arccos )(arccos )21(arccos )2 arccoxxdxxdxxxxdxxxxCxx dxxxxxdxxxdxxxxxxxxCxxxx dxxxdxxxx222s1(arccos )21arccos1xdxxxxxdx精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 4 页22(arccos )2 1arccos2.xxxxxC2222222222arccos1113.arccos(1)21arccos12(1)2(1) 1arccos1.2(1)2114. arctanarctan2(1)1ar
6、ctan.,22122arctan,11arcxxdxxdxxxdxxxxxxCxxxdxxdxxxxxxdxxxxu xudxuduxxdxu uduuuCxu1tanarctan2(arctan)2arctan(arctan)(1)arctan.xdxxxxxCxxxxCxxxCg22222222arcsin1arcsin15.arcsin1arcsin(0)1/1arcsin(1/)arcsinln |1/1/1 |1/1arcsinln(11)lnarcsinln(11)ln |(0)(xxdxdxxdxxxxxxdxxxxxxdxxxxCxxxxxxCxxxxC xx原函数为偶函数4
7、24322442423442442434).1(ln)12ln16.(ln)(ln)444(ln)1(ln)1lnln4248(ln)1(ln)1lnln.482488xxxxdxxxdxxdxxxxxxxxdxxdxxxxxxxxx dxxxCg223/ 225/ 225/2arctan1arctan(1)1217.arctan(1)(1)2(1)23xxdxxdxxdxxxg精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 4 页223/ 225/ 2arctan1.tan ,(/2,/ 2).sec,3(1)3(1)xdxxu ud
8、xuduxx3225/ 23322325/223/ 222323/ 223/ 22cos(1sin)sin(1)11sinsin,3311arctanarctan11(1)3(1)3311arctan11.3(1)39 (1)1dxuduu duxxxuuCCxxxxdxxxxCxxxxxxxCxxx222222222222222222222118.ln(1)ln(1)211ln(1)22111(1) 1ln(1)221111ln(1)12221111ln(1)1ln(1)ln(1)222221ln(12xxxdxxxdxx dxxxxxxdxxxxxdxxxxx dxxxxxxxxxxxCxx22211)1ln(1).44xxxxxC精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 4 页