数学分析数学分析数学分析 (6).pdf

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2、220()()xaxbdx?F?)0,0(?ba;?F?0)(e2Radxxax;?)(ln12R?F?pdxxxp;267?1123 2()/xdx?F;?120(ee)xxdx?F;?1140 xdx?F?ln xxdx120?F?1?esin?F205xxdxF?025cose51xdxF?025cose5251xdxxF?025sine25251xdxF?025sine25451xdxx?esin?F205xxdx295?2?ecos?F302xxdxF?032sine21xdxF?032sine23xdxx?F?032cose43xdxF?032cose4943xdxx?F?032c

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4、axa21?6?1?p1?pF?221)(ln11ln1ppxpdxxx1)2(ln11?pp?7?txtan?F?dxx2/32)1(1?F?22cos?tdt2?8?tex?120(ee)xxdx?FF?11222)1(21)1(tttdt41?9?3?1(10)?F?dxx114Cxxxxxx?)12arctan(42)12arctan(421212ln8222?F?0411dxx22?10?F?dxxx021ln?Fdxxx1021lndxxxF?121ln,?tx1?dxxxF?121lndtttF?1021ln?01ln02?F?dxxx?269?xxdx1201?F;?1121x

5、xdx?Flne;?xxdx?F112;?12101()?Fxxdx;?113211xxdxsin?F;?F20tan1?dxx;?1?xxdx1201?FF?10221)1(21xxd102)1(x?1?2?1121xxdx?FlneF?e12)(lnln11xdx?ex1)arcsin(ln2?3?tx?1?xxdx?F112F?102)1(2dtt38?4?tx?1?12101()?FxxdxF?10212tdt2?5?113211xxdxsin?FF?01231sin1dxxxF?10231sin1dxxx?F10231sin1dxxxF?1022)1(1sin21xdx102)1(c

6、os21?x?)1(cos21lim20 xx?F10231sin1dxxx?F?01231sin1dxxx?6?tx?tan?3?9?F20tan1?dxxF?0412tdt2?270?lim!nnnn?nnnn!lnlim?nknnkn1ln1limF?101lnxdx,?ennnn1!lim?(1)lncosxdx02?F;(2)xxlnsin0?Fdx?(3)F20cot?xdxx;(4)arcsin xxdx01F;(5)ln xxdx1201?F?(1)?tx?2?,?8.1.11?lncosxdx02?FF?20sinln?tdt2ln2?(2)?tx?,?F?0sinlnxdx

7、xF?0sinlntdtF?0sinlntdtt,?F?0sinlnxdxxF?0sinln2xdxF?20sinln?xdx2ln22?(3)F20cot?xdxxF?20sinln?xxddxxxxF?2020sinln)sinln(?2ln2?(4)?,?xtarcsin?F?10arcsindxxxF20cot?tdtt2ln2?271(5)F?1021lndxxxF10arcsinlnxxd10)arcsin(lnxx?F?10arcsindxxx2ln2?Cauchy?(cpv)112?Fxxdx;?(cpv)1214xdx?F;?(cpv)ln/11 22xxdxF?(1)(cp

8、v)112?Fxxdx?AAAxx)1ln(21arctanlim2?(2)(cpv)1214xdx?F?)2(ln)2(lnlim21420BBBxx2ln?(3)(cpv)ln/11 22xxdxF?)ln(ln)ln(lnlim12/1210BBBxx0?Fbadxxf)(bx?)(xf?)(xfbx?xbabt?Fbadxxf)(21)(tdttabbfabF?()$%&?F?adxxf)(?F?adxxf)(F?adxxg)(),?a?)()(xgxf.F?adxxf)(F?.adxxg)(?FAadxxf)(F.Aadxxg)(?A 272?F?adxxf)(),?ac?F?cdx

9、xf)(F?adxxf)(F?cadxxf)(F?cdxxf)(?FAadxxf)(F?cadxxf)(F?Acdxxf)(?A?xxxgxfsin)()(?F?1)(dxxfF?1)(dxxgF?1)()(dxxgxf10.?a?0F?()$%&?0lndxxxxaaxfF?()$%&?01lndxxxaaxfa?F?()$%&?0lndxxxxaaxfF?()$%&?01lndxxxaaxfadxxaxxaaxflnln0?()$%&?F?()$%&?Fdxxaxxaaxfalnln0dxxaxxaaxfalnln?()$%&?F?tax2?ax:?0:?at?xaaxtaat?dttat

10、dxxaxlnlnlnln?dxxaxxaaxfalnln?()$%&?F?dttattaatfalnln0?()$%&?F?F?()$%&?0lndxxxxaaxfF?()$%&?01lndxxxaaxfa0lnlnaxaxafdxaxx?&)?$%(F0lnln0atatafdtatt?&)?$%(F?273?F?adxxf)(Axfx?)(lim?0?A?0?A021?A1?aX?0?Xx?/AAxf21)(?Axf21)(?FBadxxf)(F?Xadxxf)(F?BXdxxf)()(21)(XBAdxxfXa?F?F?BaBdxxf)(limF?adxxf)(?0?A?0?A?)(xf),?aF?adxxf)(F?adxxf)(0)(lim?xfx?F?adxxf)(?F?axdf)()()(limafxfx?,?,?11?F?adxxf)()(limxfx?0)(lim?xfx?274

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