高等数学A上册习题解答 至微分中值定理(17)

华中师范大学专用

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1.¦e ؽȩ:

(1) xln(x 1)dx

ln(x 1)d

x2

=2

=x22ln(x 1) x2

dln(x 1)x2

2

x2=2ln(x 1) 2(x 1)

dx=x2

1 2ln(x 1)

2[x+1+1x 1]dxx2=2ln(x 1) x24 x2 12ln(x 1)+C.(2)

(x2 1)sin2xdx

= 1

2

(x2 1)dcos2x= 12

2

(x 1)cos2x+cos2xxdx

= 12

1 2(x 1)cos2x+2

xdsin2x

= 1

2(x2 1)cos2x+12xsin2x 12

sin2xdx

= 1

2(x2 1)cos2x+112xsin2x+4cos2x+C.

(3)

coslnxdx

=xcoslnx+

sinlnxdx

=xcoslnx+xsinlnx

coslnxdx

l §

coslnxdx=

1

2

x[coslnx+sinlnx]+C.17

(0.43)

(0.44)

(0.45)

(0.46)