文档介绍：- 1 - 高等数学公式 导数公式: 基本积分表: 三角函数的有理式积分: 2 2 2 2 1 2 2 1 1 cos 1 2 sin u du dx x tg u u u x u u x + = = + ?= + = , , , a x x a a a ctgx x x tgx x x x ctgx x tgx a x x ln 1 ) (log ln ) ( csc ) (csc sec ) (sec csc ) ( sec ) ( 2 2 = ′= ′??= ′?= ′?= ′= ′ 2 2 2 2 1 1 ) ( 1 1 ) ( 1 1 ) (os 1 1 ) (arcsin x tgx x arctgx x x x x + ?= ′+ = ′??= ′?= ′∫∫∫∫∫∫∫∫∫∫+ ± + = ± + = + = + = + ?= ?+ = ?+ ?= = + = = C a x x a x dx C shx chxdx C chx shxdx C a a dx a C x ctgxdx x C x dx tgx x C ctgx xdx x dx C tgx xdx x dx x x ) ln( ln csc csc sec sec csc sin sec cos 2 2 2 2 2 2 2 2 C a x x a dx C x a x a a x a dx C a x a x a a x dx C a x arctg a x a dx C ctgx x xdx C tgx x xdx C x ctgxdx C x tgxdx + = ?+ ?+ = ?+ + ?= ?+ = + + ?= + + = + = + ?= ∫∫∫∫∫∫∫∫ arcsin ln 2 1 ln 2 1 1 csc ln csc sec ln sec sin ln cos ln 2 2 2 2 2 2 2 2 ∫∫∫∫∫+ + ?= ?+ ?+ ??= ?+ + + + + = + ?= = = ? C a x a x a x dx x a C a x x a a x x dx a x C a x x a a x x dx a x I n n xdx xdx I n n n n arcsin 2 2 ln 2 2 ) ln( 2 2 1 cos sin 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 ππ - 2 - 一些初等函数: 两个重要极限: 三角函数公式: ·诱导公式: 函数角 A sin cos tg ctg - α -sin α cos α-tg α -ctg α 90°- α cos α sin α ctg α tg α 90°+ α cos α-sin α-ctg α-tg α 180°- α sin α -cos α-tg α -ctg α 180°+ α -sin α-cos α tg α ctg α 270°- α -cos α-sin α ctg α tg α 270°+ α -cos α sin α -ctg α-tg α 360°- α -sin α cos α-tg α -ctg α 360°+ α sin α cos α tg α ctg α·和差角公式: ·和差化积公式: 2 sin 2 sin 2 cos cos 2 cos 2 cos 2 cos cos 2 sin 2 cos 2 sin sin 2 cos 2 sin 2 sin sin βαβαβαβαβαβαβαβαβαβαβαβα?+ = ??+ = + ?+ = ??+ = + αββαβαβαβαβαβαβαβαβαβαβα ctg ctg ctg ctg ctg tg tg tg tg tg ± ?= ± ?± = ± = ± ± = ± 1 ) ( 1 ) ( sin sin cos cos ) cos( sin cos cos sin ) sin( m m m x x arthx x x archx x x arshx e e e e chx shx thx e e chx e e shx x x x x x x x x ?+ = ?+ ± = + + = + ?= = + = ?= ???? 1 1 ln 2 1 ) 1 ln( 1 ln( : 2 : 2 : 2 2 ) 双