xx学校试题一111高数答案.pdfVIP

8lnx8

=lim=

3x→1x−13

2x−52x−61

15．dx=dx+dx

222

x−6x+10x−6x+10x−6x+10

11

2dx

=2d(x−6x+10)+2

x−6x+10(x−3)+1

1

2

=ln|x−6x+10|+2dx(x−3)



(x−3)+1

2

=ln(x−6x+10)+arctan(x−3)+C

16．sin(lnx)dx=xsin(lnx)−xdsin(lnx)=xsin(lnx)−cos(lnx)dx



=xsin(lnx)−xcos(lnx)+xdcos(lnx)



=xsin(lnx)−xcos(lnx)−sin(lnx)dx



1

故=[xsin(lnx)−xcos(lnx)]+C

2

17．由奇、偶函数在对称区间上定积分性质知

2

1x

原式=2dx

02

1+1−x

1