高等数学积分表大全

高等数学积分公式表

常 用 积 分 公 式

（一）含有ax?b的积分(a?0)

1．?1dx＝lnax?b?C ax?ba2．?(ax?b)?dx＝3．?1(ax?b)??1?C（???1）

a(??1)x1dx＝2(ax?b?blnax?b)?C ax?bax21?1?dx＝3?(ax?b)2?2b(ax?b)?b2lnax?b??C 4．?ax?ba?2?5．?6．?7．?dx1ax?b＝?ln?C

x(ax?b)bxdx1aax?b＝??ln?C

x2(ax?b)bxb2x1bx(lnax?b?)?C dx＝a2ax?b(ax?b)21b2x2)?C 8．?dx＝3(ax?b?2blnax?b?aax?b(ax?b)29．?dx11ax?b＝?ln?C 22x(ax?b)b(ax?b)bx（二）含有ax?b的积分

2(ax?b)3?C 3a23(3ax?2b)(ax?b)?C 11．?xax?bdx＝215a22223(15ax?12abx?8b)(ax?b)?C 12．?x2ax?bdx＝

105a310．?ax?bdx＝13．?2xdx＝2(ax?2b)ax?b?C

3aax?b高等数学积分公式表

14．?2x2222(3ax?4abx?8b)ax?b?C dx＝315aax?b1b2?blnax?b?bax?b?barctanax?b?b?C?C(b?0)??dx?15．?＝?xax?b???16．?17．?18．?

(b?0)x2dxax?badx＝? ??bx2bxax?bax?bdxax?b dx＝2ax?b?b?xxax?bax?bax?badx＝ dx??2?xx2xax?b（三）含有x2?a2的积分

19．?21．?dx1xdx1x?aarctan?C= 20．=ln?x2?a22ax?a?C x2?a2aadxx2n?3dx?= 22n222n?12?22n?1(x?a)2(n?1)a(x?a)2(n?1)a(x?a)（四）含有ax2?b(a?0)的积分

?1arctan?abdx?22．?2＝?ax?b?1ln?2?ab?ax?Cb(b?0)

ax??b?C(b?0)ax??bx1xbdxx22dx＝lnax?b?C 24．?2dx＝??223．?2 ax?b2aaaax?bax?b1x21adxdxdxln?C??25．?＝ 26．＝?x2(ax2?b)bxb?ax2?b x(ax2?b)2bax2?b高等数学积分公式表

ax2?bdxa127．?32＝2ln??C

x(ax?b)2bx22bx228．?dxx1dx＝ ?2222?(ax?b)2b(ax?b)2bax?b（五）含有ax2?bx?c(a?0)的积分

22ax?b?arctan?C?22dx4ac?b29．＝?4ac?b2ax?bx?c?12ax?b?b2?4ac?ln?C2?b2?4ac2ax?b?b?4ac?(b2?4ac)?

(b2?4ac)30．?x1bdx2dxlnax?bx?c?＝ 22?ax?bx?c2a2aax?bx?c（六）含有31．?32．?34．?35．?36．?dxx2?a2x2?a2(a?0)的积分

x?C1＝ln(x?x2?a2)?C a＝arshdx(x2?a2)3x(x?a)x2223＝xa2x2?a21x?a2?C 33．??C

xx2?a2dx＝x2?a2?C

dx＝?2x2a22x?a?ln(x?x2?a2)?C dx＝22x2?a2x2(x2?a2)3dx＝?xx2?a2?ln(x?x2?a2)?C

1x2?a2?ax2?a2dx?C 38．?37．?＝ln＝??C 222222axaxxx?axx?adx39．?x2a22x?a?ln(x?x2?a2)?C x?adx＝2222x340．?(x2?a2)3dx＝(2x2?5a2)x2?a2?a4ln(x?x2?a2)?C

88高等数学积分公式表

41．?xx2?a2dx＝42．?x43．?44．?2221(x2?a2)3?C 3xa42222x?adx＝(2x?a)x?a?ln(x?x2?a2)?C

88x2?a2?ax2?a222?C dx＝x?a?alnxxx2?a2x2?a2dx＝??ln(x?x2?a2)?C 2xx（七）含有45．?46．?48．?49．?50．?x2?a2(a?0)的积分 xxarch?C1=lnx?x2?a2?C xa＝?xa2x2?a21x?a22dxx2?a2＝

dx(x2?a2)3x(x?a)x2223?C 47．??C

xx2?a2dx＝x2?a2?C

dx＝?x2a22x?a?lnx?x2?a2?C dx＝22x2?a2x2(x2?a2)3dx＝?xx2?a2?lnx?x2?a2?C

1ax2?a2dx51．?＝arccos?C 52．?＝?C 222222axaxxx?axx?adx53．?x2a22x?a?lnx?x2?a2?C x?adx＝2222x354．?(x2?a2)3dx＝(2x2?5a2)x2?a2?a4lnx?x2?a2?C

881(x2?a2)3?C 55．?xx2?a2dx＝356．?x2xa42222x?adx＝(2x?a)x?a?lnx?x2?a2?C

8822高等数学积分公式表

57．?58．?ax2?a2dx＝x2?a2?aarccos?C

xxx2?a2x2?a2dx＝??lnx?x2?a2?C 2xx（八）含有59．?61．?63．?64．?dxa2?x2xa?x22a2?x2(a?0)的积分

xxdx?C 60．?＝?C

222223aaa?x(a?x)＝arcsindx＝?a2?x2?C 62．?x(a?x)223dx＝1a?x22?C

x2a2x2a?x?arcsin?C dx＝?22aa2?x2x2x2(a2?x2)3dx＝xa2?x2?arcsinx?C a1a?a2?x2a2?x2dx?C 66．?65．?＝ln＝??C 222222axaxxa?xxa?xdx67．?x2a2x2a?x?arcsin?C a?xdx＝22a22x3x68．?(a2?x2)3dx＝(5a2?2x2)a2?x2?a4arcsin?C

88a1(a2?x2)3?C 69．?xa2?x2dx＝?370．?x71．?72．?2xa4x2222a?xdx＝(2x?a)a?x?arcsin?C

88a22a?a2?x2a2?x222?C dx＝a?x?alnxxa2?x2a2?x2x＝dx??arcsin?C

x2xa（九）含有?ax2?bx?c(a?0)的积分

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