高等数学积分表(同济6版).pdf

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1、()¹kax+bÈ©Zdx11.=ln

2、ax+b

3、+Cax+baZµ1µ+12.(ax+b)dx=(ax+b)+C(µ6=−1)a(µ+1)Zx13.dx=(ax+b−bln

4、(x+b)

5、)+Cax+ba2Zx21h1i224.dx=(ax+b)−2b(ax+b)+bln

6、ax+b

7、+Cax+ba32Zdx1ax+b5.=−ln+Cx(ax+b)bxZdx1aax+b6.=−+ln+Cx2(ax+b)bxb2xZx1b7.dx=ln

8、ax+b

9、++C(ax+b)2a2ax+bZx21b28.dx=ax+b−2bln

10、ax+b

11、−+C(ax+b)2a3ax+bZdx11ax+b9

12、.=−ln+Cx(a+b)2b(ax+b)b2x√()¹kax+bÈ©Z√q210.ax+bdx=(ax+b)3+C3aZ√2q11.xax+bdx=(3ax−2b)(ax+b)3+C15a2Z√2q12.x2ax+bdx=(15a2x2−12abx+8b2)(ax+b)3+C105a3Zx2√13.√dx=(ax−2b)ax+b+Cax+b3a2Zx22√√22214.dx=(2ax−4abx+8b)ax+b+Cax+b15a21√√Zdx√1ln√ax+b−√b+C(b>0)15.√=bax+b+qbxax+b√2arctanax+b+C(b<0)−−b−b√ZZdxax+

13、badx16.√=−−√x2ax+bbx2bxax+bZ√ax+b√Zdx17.dx=2ax+b+b√xxax+b√Z√Zax+bax+badx18.dx=−+√x2x2xax+b(n)¹kx2±aÈ©Zdx1x19.=arctan+Cx2+a2aaZZdxx2n−3dx20.=+(x2+a2)n2(n−1)a2(x2+a2)n−12(n−1)a2(x2+a2)n−1Zdx1x−a21.=ln+Cx2−a22ax+a(o)¹kax2+bÈ©qZdx√1arctanax+C(b>0)22.=ab√b√ax2+b√1ln√ax−√−b+C(b<0)2−abax+−bZx1223.d

14、x=ln

15、ax+b

16、+Cax2+b2aZ2Zxxbdx24.dx=−ax2+baaax2+bZ2dx1x25.=ln+Cx(ax2+b)2b

17、ax2+b

18、ZZdx1adx26.=−−x2(ax2+b)bxbax2+bZ2dxa

19、ax+b

20、127.=ln−+Cx3(ax2+b)2b2x22bx22ZZdxx1dx28.=+(ax2+b)22b(ax2+b)2bax2+b(Ê)¹kax2+bx+cÈ©Zdx√2arctan√2ax+b+C(b2<4ac)29.dx=4ac−b2√4ac−b22√12ax+b−√b2−4ac2ax+bx+cln+C(b>4ac)b2−4ac2ax+b+

21、b2−4acZZx12bdx30.dx=ln

22、ax+bx+c

23、−ax2+bx+c2a2aax2+bx+c√(8)¹kx2+a2(a>0)È©Zdxx√31.√=arsh+C1=ln(x+x2+a2)+Cx2+a2aZdxx32.q=√+C(x2+a2)3a2x2+a2Zx√33.√dx=x2+a2+Cx2+a2Zx134.qdx=−√+C(x2+a2)3x2+a2Zx2x√a2√35.√dx=x2+a2−ln(x+x2+a2)+Cx2+a222Zx2x√36.qdx=−√+ln(x+x2+a2)+C(x2+a2)3x2+a2√Zdx1x2+a2−a37.√=ln+Cxx2+a2a

24、x

25、

26、√Zdxx2+a238.√=−+Cx2x2+a2a2xZ√x√a2√39.x2+a2dx=x2+a2+ln(x+x2+a2)+C22Zqx√3√40.(x2+a2)3dx=(2x2+5a2)x2+a2+a4ln(x+x2+a2)+C883Z√1q41.xx2+a2dx=(x2+a2)3+C3Z√x√a4√42.x2x2+a2dx=(2x2+a2)x2+a2−ln(x+x2+a2)+C88√Z√x2+a2√x2+a2−a43.dx=x2+a2+aln+Cx

27、x

28、√Z√x2+a2x2+a2√44.dx=−+ln(x+x2+a2)+Cx2x√(Ô)¹kx2−a2(a>0)È©Zdxx

29、x

30、√

31、45.√=arch+C1=ln

32、x+x2−a2

33、+Cx2−a2

34、x

35、aZdxx46.q=−√+C(x2−a2)3a2x2−a2Zx√47.√dx=x2−a2+Cx2−a2Zx148.qdx=−√+C(x2−a2)3x2−a2Zx2x√a2√49.√dx=x2−a2+ln

36、x+x2−a2

37、+Cx2−a222Zx2x√50.qdx=−√+ln

38、x+x2−a2

39、+C(x2−a2)3x2−a2Zdx1a51.√=arccos+Cxx2−a2