文档介绍：第六章不定积分
§1 不定积分的概念
:
R √
5 3 x
(1) (x + x − 4 )dx;
R
(2) (5 − x)3 dx;
R √√
( ) 3 √3 √2 ;
3 ( x + x + x + 3 x )dx
R dx
(4) x4(1+x2) ;
R 3x2
(5) 1+x2 dx;
R
( ) x√+1 ;
6 x dx
R
(7) (2 sin x − 4 cos x)dx;
R
(8) (3 − sec2 x)dx;
R
(9) (tan2 x + 3)dx;
R 2+sin2 x
(10) cos2 x dx;
R tan x
(11) 2 x 2 x dx;
cos 2 −sin 2
R cos 2x
(12) cos x−sin x dx;
R dx
(13) 1+cos 2x ;
R
(14) (5x + 1)2dx;
R x
x 1 x e
(15) (2 + ( 3 ) − 5 )dx;
R −x
( ) x e√;
16 e (1 − x )dx
1
R
(17) (cos x − 2 −√ 1 )dx;
1+x2 4 1−x2
R p √
(18) x xdx;
R
(19) 22x3xdx;
R
(20) ( √ 3 + sin x)dx.
4−4x2
= f(x),它在点(x, f(x))处的切线的斜率为2x ,且通过
点(2, 5).
(x)满足给定的关系式,试求f(x):
(1) xf 0(x) = 1(x > 0);
f 0(x)
(2) x = 1(x > 0);
(3) f(x)f 0(x) = 1(x > 0);
f 0(x)
(4) f(x) = 1(f(x) > 0).
§2 换元积分法与分部积分法
:
R 1
(1) 5x−6 dx;
R 1
(2) x(1+2x) dx;
R
(3) √ 1 √ dx;
x+1+ x−1
R
(4) ( √ 1 + √ 1 )dx;
3−x2 1−3x2
R 1
(5) 2+3x2 dx;
R
− x
(6) e 2 dx;
2
R 2
(7) xe−x dx;
R ex
(8) 1+ex dx;
R dx
(9) ex+e−x+2 ;
R dx
(10) ex+e−x ;
R
(11) tan xdx;
R
(12) tan5 x sec2 xdx;
R 1−2 sin x
(13) cos2 x dx;
R
(14) dx ;
A sin2 x+B cos2 x
R
(15) cos5 xdx;
R dx
(16) 1+sin x ;
R cos 2x
(17) sin x cos x dx;
R
(18) sin x cos x dx;
1+sin4 x
R x
(19) 4+x2 dx;
R x
(20) 4+x4 d