高等数学部分公式手册

高等数学复习公式高等数学公式导数公式：1 =(arcsin x)(tgx) = sec x21- x2(ctgx) = -csc x21(arccos x) = -(sec x) = sec xtgx1- x2(csc x) = -csc xctgx1(arctgx) =(ax) = a ln ax1+ x2111+ x(log x) = = -(arcctgx)axln a2基本积分表：tgxdx = -ln cos x +Cctgxdx = ln sin x +Cdx= sec2xdx = tgx + Ccosdx2x= csc2xdx = -ctgx +Csecxdx= ln sec x +tgx C+sin x2sec xtgxdx = sec x + Ccsc xdx = ln csc x -ctgx +Ccsc xctgxdx = -csc x +Cdx+ xdx1x= arctg +Caxa2222aax - aaxadx =+ Cx1ln a=ln+C+C- a2a x + ashxdx = chx + Cdx- xdx1a + xlnchxdx = shx + C222a a - xdxx22= ln( x + x a ) + C= arcsin +C2 a2a2-x2axpp22n -1I = sinnxdx = cosnxdx =In-2nn00xa2xxa2+ a- a- x222dx =dx =dx =xxa222+ a222+-+ln( x + x2+ a- a2) + C+ C2x2x22a222- a- xln x + x222a2xarcsin + C2a三角函数的有理式积分：2u1+ u1-u1+ u22x2dusin x =， cos x =，u = tg ，dx =221+ u2第 1 页 共 2 页 高等数学复习公式一些初等函数：两个重要极限：eexx- e-xxsin x双曲正弦 : shx =双曲余弦 :chx =双曲正切 :thx =lim=12+ e-x0x1xlim(1+ ) = e = 2.718281828459045.2xxshxchxex- e-+ e-xx=exarshx = ln( x + x2+1）-1)archx = ln( x + x211+ x1- xarthx = ln2三角函数公式：诱导公式：函数角 Asincostgctg-sin cos -tg -ctgcos sin ctg tgcos -sin -ctg -tg90-90+180-180+270-270+360-360+sin-cos -tg -ctgctg-sin -cos tg-cos -sin ctg tg-cos sin -ctg -tg-sin cos -tg -ctgsincos tgctg和差角公式：和差化积公式：a + b2a - b2a - bsin(a b) = sin a cos b cosa sin bcos(a b) = cosa cos b m sin a sin btga tgbsin a +sin b = 2 sincossina + bsin a -sin b = 2 coscosa + cos b = 2 coscosa -cos b = 2 sintg(a b) =221m tga tgbctga ctgb m1ctgb ctgaa + ba - bcos22a - b2ctg(a b) =a + b2sin第 2 页 共 2 页