1、 1常 用 积 分 公 式 g708g980g709g2559g7389ax b+ g11352g12227g2010( 0a )g31g714 dxax b+ g729 1 ln ax b Ca + + 2g714 ( ) dax b x+ g729 11 ( )( 1) ax b Ca + + g708 1 g709 3g714 dx xax b+ g729 21 ( ln )ax b b ax b Ca + + + 4g7142dx xax b+ g729 2 231 1 ( ) 2 ( ) ln2 ax b b ax b b ax b Ca + + + + + 5g714 d( )xx
2、 ax b+ g729 1 ln ax b Cb x+ + 6g714 2 d( )xx ax b+ g729 21 lna ax b Cbx b x+ + + 7g714 2 d( )x xax b+ g729 21 (ln )bax b Ca ax b+ + + 8g71422 d( )x xax b+ g729231 ( 2 ln )bax b b ax b Ca ax b+ + + 9g714 2d( )xx ax b+ g729 21 1 ln( ) ax b Cb ax b b x+ + g708g1120g709g2559g7389 ax b+ g11352g12227g2010
3、g3g20g19g714 dax b x+ g729 32 ( )3 ax b Ca + + g3g20g20g714 dx ax b x+ g729 322 (3 2 ) ( )15 ax b ax b Ca + + g3g20g21g714 2 dx ax b x+ g729 2 2 2 332 (15 12 8 ) ( )105 a x abx b ax b Ca + + + g3g20g22g714 dx xax b+ g729 22 ( 2 )3 ax b ax b Ca + + g32g20g23g7142dx xax b+ g729 2 2 232 (3 4 8 )15 a x
4、abx b ax b Ca + + + g3g20g24g714 dxx ax b+ g7291 ln ( 0)2 arctan ( 0)ax b b C bb ax b bax b C bbb + + + + + + g11352g12227g2010 22g714 2dxax b+ g7291 arctan ( 0)1 ln ( 0)2a x C bbabax b C bab ax b + + g11352g12227g2010 29g714 2 dxax bx c+ + g72922 2222 22 2arctan ( 4 )4 41 2 4ln ( 4 )4 2 4ax b C b a
5、cac b ac bax b b ac C b acb ac ax b b ac+ + + + 30g714 2 dx xax bx c+ + g729 2 21 dln2 2b xax bx ca a ax bx c+ + + + g708g1857g709g2559g7389 2 2x a+ ( 0)a g11352g12227g2010 31g714 2 2dxx a+g729 1arsh x Ca + g729 2 2ln( )x x a C+ + + 32g714 2 2 3d( )xx a+g729 2 2 2x Ca x a+33g714 2 2 dx xx a+g729 2 2
6、x a C+ + 34g714 2 2 3 d( )x xx a+g729 2 21 Cx a +435g71422 2 dx xx a+g72922 2 2 2ln( )2 2x ax a x x a C+ + + + 36g71422 2 3 d( )x xx a+g729 2 22 2 ln( )x x x a Cx a + + + +37g714 2 2dxx x a+g7292 21ln x a a Ca x+ + 38g714 2 2 2dxx x a+g7292 22x a Ca x+ + 39g714 2 2dx a x+ g72922 2 2 2ln( )2 2x ax a
7、x x a C+ + + + + 40g714 2 2 3( ) dx a x+ g729 2 2 2 2 4 2 23(2 5 ) ln( )8 8x x a x a a x x a C+ + + + + + 41g714 2 2dx x a x+ g729 2 2 31 ( )3 x a C+ + 42g714 2 2 2 dx x a x+ g72942 2 2 2 2 2(2 ) ln( )8 8x ax a x a x x a C+ + + + + 43g7142 2dx a xx+ g7292 22 2 ln x a ax a a Cx+ + + + 44g7142 22 dx a
8、 xx+ g729 2 2 2 2ln( )x a x x a Cx+ + + + + g708g983g709g2559g7389 2 2x a ( 0)a g11352g12227g2010 45g714 2 2dxx ag729 1arch xx Cx a + = 2 2ln x x a C+ + 46g714 2 2 3d( )xx ag729 2 2 2x Ca x a +47g714 2 2 dx xx ag729 2 2x a C + 548g714 2 2 3 d( )x xx ag729 2 21 Cx a +49g71422 2 dx xx ag72922 2 2 2ln2
9、 2x ax a x x a C + + + 50g71422 2 3 d( )x xx ag729 2 22 2 lnx x x a Cx a + + +51g714 2 2dxx x ag729 1 arccos a Ca x + 52g714 2 2 2dxx x ag7292 22x a Ca x + 53g714 2 2 dx a x g72922 2 2 2ln2 2x ax a x x a C + + 54g714 2 2 3( ) dx a x g729 2 2 2 2 4 2 23(2 5 ) ln8 8x x a x a a x x a C + + + 55g714 2 2
10、dx x a x g729 2 2 31 ( )3 x a C + 56g714 2 2 2 dx x a x g72942 2 2 2 2 2(2 ) ln8 8x ax a x a x x a C + + 57g7142 2dx a xx g729 2 2 arccos ax a a Cx + 58g7142 22 dx a xx g729 2 2 2 2lnx a x x a Cx + + + g708g1855g709g2559g7389 2 2a x ( 0)a g11352g12227g2010 59g714 2 2dxa xg729arcsin x Ca + 60g714 2 2
11、 3d( )xa xg729 2 2 2x Ca a x+661g714 2 2 dx xa xg729 2 2a x C + 62g714 2 2 3 d( )x xa xg729 2 21 Ca x+63g71422 2 dx xa xg72922 2 arcsin2 2x a xa x Ca + + 64g71422 2 3 d( )x xa xg729 2 2 arcsinx x Caa x +65g714 2 2dxx a xg7292 21ln a a x Ca x + 66g714 2 2 2dxx a xg7292 22a x Ca x + 67g714 2 2 da x x
12、g72922 2 arcsin2 2x a xa x Ca + + 68g714 2 2 3( ) da x x g729 2 2 2 2 43(5 2 ) arcsin8 8x xa x a x a Ca + + 69g714 2 2dx a x x g729 2 2 31 ( )3 a x C + 70g714 2 2 2 dx a x x g72942 2 2 2(2 ) arcsin8 8x a xx a a x Ca + + 71g7142 2da x xx g7292 22 2 ln a a xa x a Cx + + 72g7142 22 da x xx g729 2 2 arc
13、sina x x Cx a + g708g1073g709g2559g7389 2ax bx c + + ( 0)a g11352g12227g2010 73g714 2 dxax bx c+ +g729 21 ln 2 2ax b a ax bx c Ca + + + + + 774g714 2 dax bx c x+ + g729 22 4ax b ax bx ca+ + + 2234 ln 2 28ac b ax b a ax bx c Ca+ + + + + + 75g714 2 dx xax bx c+ +g729 21 ax bx ca + + 23 ln 2 22b ax b a
14、 ax bx c Ca + + + + + 76g714 2dxc bx ax+ g729 21 2arcsin4ax b Ca b ac +77g714 2 dc bx ax x+ g729223 22 4 2arcsin4 8 4ax b b ac ax bc bx ax Ca a b ac + + + +78g714 2 dx xc bx ax+ g729 2 3 21 2arcsin2 4b ax bc bx ax Ca a b ac + + +g708g2325g709g2559g7389 x ax b g6122 ( )( )x a b x g11352g12227g2010 79
15、g714 dx a xx b g729( ) ( )ln( )x ax b b a x a x b Cx b + + + 80g714 dx a xb x g729( ) ( )arcsinx a x ax b b a Cb x b x + + 81g714 d( )( )xx a b x g7292arcsin x a Cb x + ( )a b 104g714 dsinxa b x+ g7292 22 2 2 2tan1 2lntan 2xa b b aCxb a a b b a+ + + + 2 2( )a b 106g714 dcosxa b x+ g729tan1 2lntan 2x
16、 a ba b b a Ca b b a x a bb a+ + +2 2( )a b g709 113g714 arcsin dx xa g729 2 2arcsin xx a x Ca + + 10 114g714 arcsin dxx xa g7292 22 2( )arcsin2 4 4x a x x a x Ca + + 115g714 2 arcsin dxx xa g72932 2 2 21arcsin ( 2 )3 9x x x a a x Ca + + + 116g714 arccos dx xa g729 2 2arccos xx a x Ca + 117g714 arcc
17、os dxx xa g7292 22 2( )arccos2 4 4x a x x a x Ca + 118g714 2 arccos dxx xa g72932 2 2 21arccos ( 2 )3 9x x x a a x Ca + + 119g714 arctan dx xa g729 2 2arctan ln( )2x ax a x Ca + + 120g714 arctan dxx xa g729 2 21 ( )arctan2 2x aa x x Ca+ + 121g714 2 arctan dxx xa g7293 32 2 2arctan ln( )3 6 6x x a ax
18、 a x Ca + + + g708g2325g989g709g2559g7389g6363g6980g2001g6980g11352g12227g2010 122g714 dxa x g729 1ln xa Ca + 123g714 e dax x g729 1 eax Ca + 124g714 e daxx x g729 21 ( 1)eaxax Ca + 125g714 e dn axx x g729 11 e e dn ax n axnx x xa a 126g714 dxxa x g729 21ln (ln )x xx a a Ca a + 127g714 dn xx a x g72
19、9 11 dln lnn x n xnx a x a xa a 128g714 e sin dax bx x g729 2 21 e ( sin cos )ax a bx b bx Ca b + 129g714 e cos dax bx x g729 2 21 e ( sin cos )ax b bx a bx Ca b + + 11 130g714 e sin dax n bx x g729 12 2 21 e sin ( sin cos )ax n bx a bx nb bxa b n + 222 2 2( 1) e sin dax nn n b bx xa b n+ 131g714 e
20、cos dax n bx x g729 12 2 21 e cos ( cos sin )ax n bx a bx nb bxa b n + 222 2 2( 1) e cos dax nn n b bx xa b n+ g708g2325g3247g709g2559g7389g4557g6980g2001g6980g11352g12227g2010 132g714 ln dx x g729 lnx x x C + 133g714 dlnxx x g729ln ln x C+ 134g714 ln dnx x x g729 11 1(ln )1 1nx x Cn n+ + + 135g714
21、(ln ) dnx x g729 1(ln ) (ln ) dnnx x n x x 136g714 (ln ) dm nx x x g729 1 11 (ln ) (ln ) d1 1m n m nnx x x x xm m+ + + g708g2325g1128g709g2559g7389g2464g7366g2001g6980g11352g12227g2010 137g714 sh dx x g729chx C+ 138g714 ch dx x g729shx C+ 139g714 th dx x g729ln chx C+ 140g714 2sh dx x g729 1 sh22 4x
22、 x C + + 141g714 2ch dx x g729 1 sh22 4x x C+ + g708g2325g1857g709g4462g12227g2010 142g714 cos dnx xpipig729 sin dnx xpipig7290 143g714 cos sin dmx nx xpipig7290 144g714 cos cos dmx nx xpipig729 0, m nm npi =12 145g714 sin sin dmx nx xpipig729 0, m nm npi =146g7140sin sin dmx nx xpi g7290cos cos dmx
23、 nx xpi g7290,2m nm n pi =147g714 nI g729 20sin dn x xpi g729 20 cos dn x xpi nI g729 21 nn In 1 3 4 22 5 3n n nI n n = L g708ng1038g3835g1122 1 g11352g8503g3867g6980g709g712 1I g7291 1 3 3 12 4 2 2nn nIn n pi= L g708ng1038g8503g1610g6980g709g712 0I g729 2pi g8296g2529: 932e26e6-4daf-48d7-8321-ff10a
24、1ec16c8.doc g11458g18648: D:hweer_xiongMy Documents g12696g7424: C:Documents and Settingshweer_xiongApplication DataMicrosoftTemplatesNormal.dot g8173g20000: g12227g2010g15932 g1039g7100: g1328g13785: liu g19376g18761g4395: g16399g16311: g5326g12447g7097g7411: 2007/2/20 12:35:00 PM g1474g16342g10268
25、g13244g15411: 3 g2081g8437g7368g7044g7097g7411: 2007/2/20 12:35:00 PM g2081g8437g4396g8296g1166g2741: Information Technology and Telecommunications g13244g17667g13329g7190g19303: 1 g2010g18924 g7380g5472g2027g2372g3324: 2007/9/26 1:34:00 PM g7380g5472g2027g2372g11352g4395g6988 g19925g6988: 12 g4395g6988: 1,531 (g13016) g4395g1815g6988: 8,732 (g13016)
