Evans, Lawrence C. (1998). Partial Differential Equations. Providence, Rhode Island: American Mathematical Society. ISBN0-8218-0772-2.
Arbogast, Todd; Bona, Jerry (2005). Methods of Applied Mathematics(PDF).
Horowitz, David (September 1990). "Tabular Integration by Parts". The College Mathematics Journal. 21 (4): 307–311. doi:10.2307/2686368. JSTOR 2686368.
การหาปร, นธ, ละส, วน, ในแคลค, และในคณ, ตว, เคราะห, งกฤษ, integration, parts, หร, partial, integration, เป, นทฤษฎ, บทท, เช, อมโยงระหว, างปร, นธ, ของผลค, ณฟ, งก, นค, หน, บปร, นธ, ของอน, นธ, และปฏ, ยาน, นธ, ของฟ, งก, นค, การหาปร, นธ, อย, างบ, อยคร, โดยการแปลงร, ป. inaekhlkhuls aelainkhnitwiekhraah karhapriphnththilaswn xngkvs Integration by parts hrux Partial Integration epnthvsdibththiechuxmoyngrahwangpriphnthkhxngphlkhunfngkchnkhuhnung kbpriphnthkhxngxnuphnthaelaptiyanuphnthkhxngfngkchnkhunn mikarhapriphnthwithinixyangbxykhrng odykaraeplngrupfngkchnthihaptiyanuphnthyak aelwhaptiyanuphnthkhxngfngkchnthihaidngaykwa kdnisamarthaeplngihxyuinrupxyangngayinhnungbrrthdodykarhapriphnthkhxngkdphlkhunxnuphnthkahndih u u x aela du u x dx aelakahndih v v x aela dv v x dx sahrbkarhapriphnththilaswn caidwa u x v x d x u x v x v x u x d x displaystyle int u x v x dx u x v x int v x u x dx hruxinrupthikrathdrdkwa u d v u v v d u displaystyle int u dv uv int v du enuxha 1 thvsdibth 1 1 phlkhunkhxngsxngfngkchn 2 kartikhwamodyichkraf 3 xangxing 4 aehlngkhxmulxunthvsdibth aekikhphlkhunkhxngsxngfngkchn aekikh thvsdibthniaesdngiddngsmkarkhanglangni smmtiwa u x aela v x epnfngkchnthihaxnuphnthid cakkdphlkhun insykrnkhxngilbnis d d x u x v x v x d d x u x u x d d x v x displaystyle frac d dx Big u x v x Big v x frac d dx left u x right u x frac d dx left v x right hapriphnththngsxngkhangethiybkb x d d x u x v x d x u x v x d x u x v x d x displaystyle int frac d dx left u x v x right dx int u x v x dx int u x v x dx caknnichniyamkhxngpriphnthimcakdekht u x v x u x v x d x u x v x d x displaystyle u x v x int u x v x dx int u x v x dx u x v x d x u x v x u x v x d x displaystyle int u x v x dx u x v x int u x v x dx caidsutrsahrbkarhapriphnththilaswnemux du aela dv epnphltangxnuphththkhxngfngkchnkhxngtwaepr x d u u x d x d v v x d x displaystyle du u x dx quad dv v x dx u x d v u x v x v x d u displaystyle int u x dv u x v x int v x du priphnththangsaykhxngsmkar uv dx prakxbdwy v xnuphnthkhxng v ephuxthicaichthvsdibthniidnn txnghakha v ptiyanuphnthkhxng v kxn aelwcunghapriphnththangkhwa vu dxkartikhwamodyichkraf aekikh kartikhwamthvsdibthniodyichkraf esnokhnginphaphkhunxyukbtwaepr t kahndesnokhngpharaemtrik x y f t g t smmtiwaesnokhngniepnfngkchnhnungtxhnung eracasamarthkahndidwa x y f g 1 y displaystyle x y f g 1 y y x g f 1 x displaystyle y x g f 1 x phunthikhxngbriewnsinaenginkhux A 1 y 1 y 2 x y d y displaystyle A 1 int y 1 y 2 x y dy inthanxngediywkn phunthikhxngbriewnsiaedng khux A 2 x 1 x 2 y x d x displaystyle A 2 int x 1 x 2 y x dx phunthirwm A1 A2 mikhaethakbphunthikhxngrupsiehliymihy x2y2 lbdwyphunthikhxngrupelk x1y1 y 1 y 2 x y d y A 1 x 1 x 2 y x d x A 2 x y x x 1 x 2 y x y y 1 y 2 displaystyle overbrace int y 1 y 2 x y dy A 1 overbrace int x 1 x 2 y x dx A 2 biggl x y x biggl x1 x2 biggl y x y biggl y1 y2 smmtiwaesnokhngnieriybinbriewniklekhiyng thaihklawthungpriphnthimcakdekht x d y y d x x y displaystyle int xdy int ydx xy cdrupihm x d y x y y d x displaystyle int xdy xy int ydx ephraachann karhapriphnththilaswnsamarthphicarnaidwaphunthisinaenginmacakphunthirwmlbdwyphunthisiaedngkartikhwamihehnphaphniyngxthibayidwathaimkarhapriphnththilaswnsamarthhapriphnthkhxngfngkchnphkphn f 1 x id emuxthrabpriphnthkhxngfngkchn f xv xnthicringaelw fngkchn x y aela y x epnswnklbkn aelapriphnth x dy samarthkhanwniddngkhangbn emuxthrabpriphnth y dxxangxing aekikhEvans Lawrence C 1998 Partial Differential Equations Providence Rhode Island American Mathematical Society ISBN 0 8218 0772 2 Arbogast Todd Bona Jerry 2005 Methods of Applied Mathematics PDF Horowitz David September 1990 Tabular Integration by Parts The College Mathematics Journal 21 4 307 311 doi 10 2307 2686368 JSTOR 2686368 aehlngkhxmulxun aekikh wikitara miethkhnikhkarhapriphnth karhapriphnththilaswn aekhlkhuls Hazewinkel Michiel b k 2001 Integration by parts Encyclopedia of Mathematics Springer ISBN 978 1 55608 010 4 Integration by parts from MathWorld bthkhwamekiywkbkhnitsastrniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy khnitsastrekhathungcak https th wikipedia org w index php title karhapriphnththilaswn amp oldid 6917557, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,