s12基本积分公式 F"(x)=f(x) f(x)dx= F(x)+C +1 例如:(x,)=x(≠-1) + +1 →|xar A+1+C
§1.2 基本积分公式 f x dx = F x +C ( ) ( ) F (x)=f(x) 例如: = + + ) 1 ( 1 x x C x x dx + + = + 1 1 ( −1)
基本积分表 (1)0x=C ( 2) dx=x+C (3)x4dx= -b4 H+1C(≠-1) (4)1x=ln|x|+C(x≠0) (5)ex=e2+C
基本积分表 dx = x +C (2) C x x dx + + = + 1 (3) 1 dx = C (1) 0 ( −1) dx x C x = + ln | | 1 (4) ( x 0) e dx e C x x = + (5)
(6)ax=+C(a>0,a≠1) (7I cos xdx=sinx+C (8) sin xd=-cosx+C ) sec xdx=」∫3d=nx+C (10) csc2xdx= 1dx =-cotx+c sin x
C a a a dx x x = + ln (6) (a >0, a 1) xdx = x +C (7) cos sin xdx = − x +C (8) sin cos dx x C x xdx = = + tan cos 1 (9) sec 2 2 dx x C x xdx = = − + cot sin 1 (10) csc 2 2
(Dlsecxtan xdx=secx+C (12 )cscxcot xdx=-cscx+C (13 dx arcsin x+c arccos+C 14)「,12k= arctan x+C 1+x -arccot+C
x xdx = x +C (11) sec tan sec x xdx = − x +C (12) csc cot csc dx x C x = + − arcsin 1 1 (13) 2 = −arccosx+C dx x C x = + + arctan 1 1 (14) 2 = −arccotx+C
例1求积分x2√xdx 解:」x rax xide A+l 根据积分公式「xdx=x,;+ + x2√xdx= x52 +C=2x2+C
例1 求积分 x xdx 2 解: x xdx 2 = x dx 2 5 C x x dx + + = + 1 1 根据积分公式 x xdx 2 C x + + = + 1 2 5 1 2 5 = x 2 +C 7 7 2