高等数学积分公式大全1.docx

1、高等数学积分公式大全1（一）含有ax+ b的积分（山一王丄1心+ax+ b = ab+ C2.J (站十“吐 召(“ + )(+可(“工-1)ax+ b- bin ax+ Z?|) + C3.x24.-X ax+ b(ax+ b)2 - 2b(ax+ b)+ b1 n ax+ b + C a 2 d.yb)-Inb甲+CX6A(Inax+a7b)9ax+ b)2(ax+ b) 二 T(ax+ b)2耳 + -) + C ax+ bax+ ) + C1 bJ f心&(ax+ by 丄(自b- 2 bln 护（二）含有h的积分 2 ax + bdx io.j xyfax+bdxii. (3ax-

2、2b)J(ax+ bV + C15护ax+ b+4inbx b dAx(ax+ b)2ax+ b12dxax +15bax +%J日 x+ bdx (15a2x2 - 2abx+ Sb2 ) J(ax+ b)3 + C105 才 vJ / dx -2l_qx_ 2b)yjax+ b + C 13. y/ax+ b _ 3iTJ / X 血14.yhx+ b (3a2x1 一 4abx+ Sb2)fa x+ b + C 15/Jax+ b - b+ C (b 0)!=ln2 ax+ b - f 心. arctan J + C (d 0) y -bbx16Xb17dx；Y +X2x18dx20.d

3、AIn3(lxxff-i2(adxax + b7 X2(/7ax+ ba2召jv十b1)7X +1 )a In 2a（三）含有汽的积分+ CI x.= 十arctan 19. J+矿=a ax+ a2 方x!&x+ bdx220）bxCabxdxb23.AXAxbax24In2bbb)25.Iadxab)bxbbAaxx1At ax2(b 0)（四）含有宀* M的积分ac + b + CUlnln2a1 a 小.arctan x+ Cslab b27.28.dA(a A2 + b)ax1 + bx2dA(ax1 + b)2dT2b( ax + b) 2b J ax2 +（五）含有八-八一29.

4、； +C4ac- b1(b2 4ac)dxax + bx+ cd-v2a J ax + bx+ c30. In ax + bx+ c- 2a六 含有 x2 + a2（六）含有c32dxX33Xdxxa3435x2a17a22、 a )=dx2ln( ap +231.ln( -T +arsh + Ga2a362dxa377Xax383932ln( x +Cx27 矿Ja2a2dx32) +2、 a )y/ x2 + a2=dx2ln( x+x47T7+4- + ln(A +2 2j j x + a2 )3dx40. =(2jv2 + 532)V x2 + a2 82 2+ c24228dxx43

5、2adx44a2Xx2a1a2a22dx2 + 52az)Vf xy x2 + 41. * = x2 + a2)3 + C的积分七含有Q丘-孑（七）含有V+ a2 + a Ina45X46ax47XdxCx48X49x1X2日2a2X+ J/ _ 召2+ C二 archG In In2x +22a50X2a2dxaxa5115222d.va53X222dxa54x+x2X2a2ya2a2In+ C+x + In2x +(2x2 - 5召冷 Jx - + a4 In8 8+ C1 aarccos 3xX2- a2）3 + CX .一（28+ C57.58.a arccos2 2X 3 QX2 2

6、x _ a + InX（3 0）的积分arcsiii - + Ca60.dAX261.62.64.arcsin-+ C2X662d.v67Xadx682369270a282 aa2X2dxx2 dx2 Y2 a arcsin2+ Carcsin8+ C (5a2 _ 2x2)Va2 -8頁+ 0罰仝+C8 a717273In742ax+b+2ax+ b4ac- b1 In2二cU的积分2-x22ax + bx +SA2 + bx +（九）含有2 2 arcsin x a) 2X2- x2 + aln - 2ax+ b I2 ；+ 加+cd” rrHza757677.78ax + bx+ cx

7、J ax2 + bx+ c2 jx +b+ 2jayJ ax1 + byj c+ bx- ax1 . 2ax-byarcsin f + C Q a b1 + 4 召clax- by/c+ bx- ax1 + arcsin = + Ca 2 a yj b2 + 4同 cJc+ bx- ax2 dxY b + 4&c+ bx - ax + 1=8存, lax- b arcs 1 门 f + Cyj b2 + 4ac. X =dx Vc+ bx-lax- b或x- a)(b- x的积分(b-x- a + A80.X-方)J - + (b- a)arcsin b- Xdx+ C81.2 arcsinX

8、- 3)(b- x) k- a _ + Cb- x (a b)82.x- a)(b- x)dx2x- a - b4J(x- a)(b- x) +(a b2)106.a+ bcosx1abbarctanf tan x)+ C108.2 ? f 2J COS x- b“sin212abIn/)tan x+ a + Cbtdn x- aJ xsin axdx1 . 1 sin ax- xcosax +a110.1 . 2 2 x cos ax a xsin?x+ -cosax+ C _a a a111.XCOSZYdx 丄 COSEX+ 丄 xsizx+C矿 ax cos axdx112. 2 2s

9、in ax+ xcos ax sin ax+ C Ja a（十二）含有反三角函数的积分（其中113.114.arcsina.xx xarcsin +axarcsin dxa2 - x2 + C2 - x2 + C寸)arcsin + 4 a 42xarccos22x22a1ax aa2 - x2 + C乂a咖in亠丄&+ 2刊J3 a 9x arccos dx119.” arctan aZk Cf 1 Jxarctan - ln(a + x ) + Ca 2x arcsinarccosxarccos-x2 + C3 iX X 1丄arccos (x +3 a 9115.116.117.23、

10、X)arccos4 a118.120.1 # 2 _(目2x .arctan dxa2 x ax )arctan x+ Ca 2x2121.3Xarctan dxax a 2arctan - x +3 a 63ln(a6（十三）含有指数函数的积分1 .a dx a122.In a123.(ax- l)eJA +124.z-1c ax126.127. aIn a1In a 3(In盯In a/i-1 x x a axI e;M sin bxdx128. = cJA(a sin bx- bcosbx) + C 矿+扩129.rJcos bxdx cJA(dsin bx+ a cos bx) + C

11、/ +扩* H f Ie sm bxax130. ei/A sin 1 bx(a sin bx- nbcos bx)a + b ir*哗卓 ”卄还a + bHax ne cos bxax131. c cos 1 6x(z? cos bx+ nbsin bx)+ bFn( n - V)b2a2 + b2 n2盘耳 n2 t te cos bxdx（十四）含有对数函数的积分132.133.xln x134.135.136.1沙nxdx -占+CJ (In x)ndxx(ln x)n - nJ( In x)j x(ln x)/7dxnJ+1 ii 门x (In x) 功+ 1；J-I dxX（1口旷

12、 dx（十五）含有双曲函数的积分137.shdxchx+ C138.chxd 忑shA+ C139.J thdxIn chx+ Cx 1 （ 小fsh：Adx _T+ sh2x+ C140. =-chAdx + sh2x+ C141. = - i（十六）定积分1st* cos nxdxsin nxdx142.-n -71=0cos n?Asin nxdx143.=00? m nji 斗* cos mxcos nxdx7T, m- n144.-n=i145.sin mAsin nxdx-HIitJ sin z?Asin nxdxji146.0, m 羊 n147. =n- 211 - 1n_ 2m丰nm- n mxcos nxdxxdxC为大于i的正奇数），712n- 1nn-3门一 231 7T4一（”为正偶数），I =ac ta nv4ac- b2