x2sinx 2xcosx 2 cosxdx x2sinx 2xcosx 2sinx C. 12. te 2tdt; 解 te 2tdt
11 2t1 2t 2t
tde te edt 222
1111
te 2t e 2t C e 2t(t ) C.
2422 13. ln2xdx;
1
解 ln2xdx xln2x x 2lnx dx xln2x 2 lnxdx
x1
xln2x 2xlnx 2 x dx xln2x 2xlnx 2x C.
x
解 xsinxcosxdx
11
xcos2x sin2x C.
48 15. x2cos2 解 x2cos2
x
dx; 2
16. xln(x 1)dx; 解 xln(x 1)dx
111
x2ln(x 1) (x 1 )dx
22x 1
1111
x2ln(x 1) x2 x ln(x 1) C.
2422 17. (x2 1)sin2xdx;
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11
x3 x2sinx xcosx sinx C.
62
tt
1111
x3 x2sinx xdcosx x3 x2sinx xcosx cosxdx
6262
1121212
ln(x 1)dx xln(x 1) x dx 2 22 x 1
le
x11111
dx x2(1 cosx)dx x3 x2dsinx x3 x2sinx xsinxdx 226262
ar
n.
1111
xsin2xdx xdcos2x xcos2x cos2xdx 2 4 44
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14. xsinxcosxdx;
t