高等數(shù)學(xué)(同濟(jì)六版)上冊(cè)期末總復(fù)習(xí)

1、 附錄 I基本求導(dǎo)公式： (1(C = 0， C為常數(shù)； (5(a x = a x ln a; (7(sin x = cos x; (2( x = x 1， 為常數(shù); (3(e x = e x ; 1 (4(ln | x | = ; x (10(cot x = csc2 x; 1 ; (11(sec x = sec x tan x; (12(csc x = csc x cot x; (13(arcsin x = 1 x2 1 1 1 (14(arccos x = ;(15(arctan x = ; (16(arccot x = ; 2 1+ x 1 + x2 1 x2 (17(sh x = c

2、h x; (18(ch x = sh x. 附錄 II基本積分公式： (1 kdx = kx + C，k為常數(shù)； x +1 (2 x dx = + C，常數(shù) 1; +1 1 ; (常數(shù)a > 0且a 1 x ln a (8(cos x = sin x; (9(tan x = sec2 x; (6(log a x = (4 e x dx = e x + C ; (6 sin xdx = cos x + C ; (8 sec 2 xdx = tan x + C ; (10 sec x tan xdx = sec x + C ; (12 tan xdx = ln | cos x | +C ;

3、1 1 (3 dx = ln | x | +C ; x ax (5 a x dx = + C，常數(shù)a > 0且a 1; ln a (7 cos xdx = sin x + C ; (9 csc 2 xdx = cot x + C ; (11 csc x cot xdx = csc x + C ; (13 cot xdx = ln | sin x | +C ; (15 csc xdx = ln | csc x cot x | +C ; 1 dx = arcsin x + C; a (14 sec xdx = ln | sec x + tan x | +C ; (16 dx = arcsin

4、 x + C ; a2 x2 1 x2 1 1 1 x dx = arctan x + C ; (18 (19 2 dx = arctan + C ; 2 2 1+ x a +x a a 1 1 xa (20 2 dx = ln + C; 2 x a 2a x + a 1 1 (21 dx = ln( x + x 2 + a 2 + C ; (22 dx = ln | x + x 2 a 2 | +C ; 2 2 2 2 x +a x a (23 sh xdx = ch x + C ; (17 (24 ch xdx = sh x + C. 3 1 n 1 n 3 , n為正偶數(shù)； n n2 4 2 2 n n 2 2 I