练习4(2-3x V2+3x 2-3x 3x x 4-9x 4-(3x) 练习5 = x-Vx+1 =」xxyx2+1)x=x2dx-」yx2+1xtc 练习6 1+2= e dx 2x 202//30 e^(+e 16
2021/1/30 16 ? 2 3 2 3 4 = + − dx x x 练习 ? 1 5 2 = − + dx x x x 练习 ? 1 1 6 2 = + dx e 练习 x dx x x dx x dx x x − − − = − − = 2 2 2 4 (3 ) 3 4 9 2 4 9 2 3 x x x dx x dx x xdx = − ( + + 1) = − − + 1 2 2 2 + = dx e e e dx x x x (1 ) 2
[例9求1= dx 令c2-2=t 2t d x 即x=lm(2+2, t2+2 dt t t+2 =2.arctan -s+c 2-2 =v2 arctan 2+C 202//30
2021/1/30 17 − = dx e I x 2 1 [例9] 求 [解] 2 e 2 t x 令 − = ln( 2), 2 即 x = t + dt t t dx 2 2 2 + = + = dt t t t I 2 1 2 2 + = dt t 2 1 2 2 C t = + 2 arctan 2 1 2 C e x + − = 2 2 2 arctan
例0求=4-xh 丌 丌 令x=2sit(,<< 4-x=2v1-sin't=2vcos't=2cos 2cost dx=2cos tdt Ⅰ=4[cos2t 1+ cos 2t 2(t+-sin2t)+C 202//30
2021/1/30 18 I = − x dx 2 [例10] 求 4 [解] 令 x = 2sint ) 2 2 ( − t t x t t t 2cos 4 2 1 sin 2 cos 2cos 2 2 2 = − = − = = I = tdt 2 4 cos + = dt t 2 1 cos 2 4 = t + sin2t) + C 2 1 2( dx = 2costdt
为了作变量回代,将政改写为 I=2(t+ sint cost)+C 根据代换函数x=in,作一个 直角三角形 Ⅰ=V4-x2t 2arcsin-+=.4-x +c 202//30
2021/1/30 19 为了作变量回代,将I改写为 I = 2(t + sint cost) + C 直角三角形 根据代换函数 x = 2sint, 作一个 x 2 2 4 − x t I = − x dx 2 4 x C x x = + − + 2 4 2 2 2arcsin
求/=/ Vx2+9 令x=3tant x2+9=tant+1=3v sect=sect d x= 3sec tdt 3sec t d t=sect dt vx t 9 sect Insect+ tant+C 202//30
2021/1/30 20 + = 9 [ 11] 2 x dx 例 求 I [解] 令 x = 3tan t x 9 3 tan t 1 3 sec t 3sec t 2 2 2 + = + = = = ln sec t + tan t + C = = + dt t dt t t x dx sec 3sec 3sec 9 2 2 dx tdt 2 = 3sec