5求积分a+20+r血 4 2 1 解n+2+在-j+ "5dx 2 1+x =号1+2w)-10+5+ (()+arctan.x+C
例5 求积分 解 . (1 2 )(1 ) 1 2 + + dx x x dx x x dx x + − + + + = 2 1 5 1 5 2 1 2 5 4 + + dx (1 2x)(1 x ) 1 2 dx x dx x x x + + + = + − 2 2 1 1 5 1 1 2 5 1 ln(1 2 ) 5 2 arctan . 5 1 ln(1 ) 5 1 ln(1 2 ) 5 2 2 = + x − + x + x + C
1 例6求积分∫ dx. xx 1+e2+e3+e6 解 令t=e6→x=6lnt, d= 6达， 1+e2+e3+e6 =a+=度》
例6 求积分 解 . 1 1 2 3 6 dx e e e x x x + + + 令 6 x t = e x = 6lnt, , 6 dt t dx = dx e e e x x x + + + 2 3 6 1 1 dt t t t t 6 1 1 3 2 + + + = dt t t t + + = (1 )(1 ) 1 6 2 dt t t t t + + − + = − 2 1 3 3 1 6 3