清華大學(xué)微積分高等數(shù)學(xué)課件第15講不定積分三-文庫(kù)吧資料
2025-01-22 06:19本頁(yè)面
【正文】 CxBqpxxCxBkk)()()()4(22222211???????????????項(xiàng)重因式對(duì)應(yīng)二次2022/2/13 10 分解為最簡(jiǎn)分式的和將例435]1[23 ???xxx將分母分解因式)1(223 )2)(1(43 ????? xxxx將真分式分解)2(223 )2(21435?????????xCxBxAxxx[解 ] CBA ,)3( 用比較系數(shù)法確定常數(shù))24()4()()1()2)(1()2(522CBAxCBAxBAxCxxBxAx?????????????????2022/2/13 11 ????????????????524140CBACBABA1,32,32 ?????? CBA223 )2(121321132435?????????????xxxxxx? ?? ?? dxxx x 43 523??? ??????? 2)2(232132 x dxx dxx dxCxxx ??????2112ln322022/2/13 12 ? ????? ??? dxxxxxx xxI 122 1]2[ 23453求積分例將分母分解因式)1(222345 )1)(1(122 ???????? xxxxxxx將真分式分解)2(22223453)1(111221???????????????xEDxxCBxxAxxxxxxx[解 ] 用比較系數(shù)法確定常數(shù))3()()()2()()()1)(()1)(1)(()1(12342223ECAxEDCBxDCBAxBCxBAxEDxxxCBxxAxx???????????????????????????2022/2/13 13 23,21,43,41,41????????EDCBA???????????????????????????110210ECAEDCBDCBABCBAdxxxdxxxdxxI ???????????? 222)1(32113411141?? ??????? 1431 )1(811ln41 222xdxxxdx?? ??? ?? 22222)1(23)1()1(41xdxxxd2022/2/13 14 xxx ar c tan43)1l n (811ln41 2 ??????? ??????? 1431 )1(811ln41 222xdxxxdxI?? ??? ?? 22222)1(23)1()1(41xdxxxdCxx xx ???????? ]ar c tan21121[231141 22CxxxxI ??????? ]113
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