高等数学公式

( arcctg ) x = - a x ln a 2 1+ x 基本积分表： 三角函数的有理式积分： tgxdx = - ln cos x + C dx = 2 sec2 xdx = tgx + C cos x ctgxdx = ln sin x + C dx = 2 csc2 xdx = - ctgx + C sec xdx = ln sec x + tgx + C sin x csc xdx = ln csc x - ctgx + C sec x tg dx x = sec x + C dx 1 x csc x ctgxdx = -csc x + C = arctg C + 2 2 x a + x a a 1 - ax = a dx + C dx x a ln a = ln + C x 2 - a 2 2 a x + a shxdx = chx + C dx 1 a + x = ln + C a 2 - x 2 2 a a - x chxdx = shx + C dx x = arcsin + C dx = ln( x + x 2 a 2 )+ C 2 - 2 a a x x 2 a 2 p p 2 2 1 I = sin cos n n xdx = n n - xdx = In - n 2 0 0 2 x 2 + a 2 = x dx x 2 + 2 + a a ln( x + x 2 + a 2 ) + C 2 2 2 x 2 - a 2 = x dx x 2 - 2 - a a ln x + x 2 - a 2 + C 2 2 2 a 2 - x 2 = x dx a 2 - x 2 + a x arcsin + C 2 2 a 2 2 u 1- u x 2 du sin x = co ， s x = ， u = tg ， dx = 2 2 2 1+ u 1+ u 2 1+ u 一些初等函数： 两个重要极限： 1 - e x - e x sin x 双曲正弦 : shx = lim = 1 x 0 x 2 x - x 1 e + e 双曲余弦 x : chx = lim 1 ( + ) = e = 2.718281828 5 4 904 ... 5 x 2 x x - x shx e - e 双曲正切: thx = = x - ......