(2e) 例62e2dh 于」 )dx In(2 1+ln2 1+x+x 1+(x+x 例7 x(1+x 于 x(1 ∫(2+=, 1+ +x arctan x +In x +C x4-1+1 例8 x dx (x2+1)(x2-1)+1 1+ 1+x -丁 dx- dx x-x+arctan+C 数学的也 定积分例 11  2 x e x dx = (2e )x dx ln(2 ) (2 ) e e x = +C 1 ln 2 2 + = x x e + C． ln(2 ) (2 ) e e x = +C 1 ln 2 2 + = x x e + C． 例 12  (1 ) 1 2 2 x x x x + + + dx = (1 ) 1 ( ) 2 2 x x x x + + + dx = ( 2 1 1 + x + x 1 )dx= 2 1 1 + x dx + x 1 dx = arctan x +ln | x | +C ． = 2 4 1 1 1 x x + − + dx= 2 2 2 1 ( 1)( 1) 1 x x x + + − + dx = (x 2 −1 + 2 1 1 + x )dx = x 2dx − dx + 2 1 1 + x dx = 3 1 x 3−x + arctan x + C ． e dx x x  例6 2 dx x x x x  + + + ( ) 2 2 1 1 例7 dx x x  + 2 4 1 例8 定积分