TABLEofINTEGRALS_referencepages.pdf

TABLEofINTEGRALS_referencepages.pdf - REFERENCE PAGES TABLE...

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Unformatted text preview: REFERENCE PAGES TABLE OF INTEGRALS BASICFORMS l.j.1¢dv=uv-J.udu I!.Jcscuwtudum—cscu+c Z-JMW’u: “n+1 +C, n%——1 . l2.j‘tanudu=1n[sccuf+C . n+1 3. %=1u]u[+0 l3.jcotudu=1n|sinu]+c l4. Isacuduz=ln|secu+tanu]+ C 4. je“du=e"+C n I5. Icsc:du=1n]cscu—cotu]+c 5.Ia”dum-£~+C Ina “‘u+C I6.J. mfg—“2:513 a 6.!sinudu=—cosu+c d 1 I7. I 2:: =2 mn"-:-+C a 1.!cosudu=sinu+C ~ 1 u - law! —--sec”‘—+C 8.Isec’udu=tanu+C Hvuzu—az a a 1 n+0 9.!csczudu=—cotu+0 ‘9' Iain“ ”gm “-0 +C lD.Isecutanudu=secu+C HI 2=—-1n ”fa +C V2 "-1122 u-I-a FORMS INVOLVING «In: + u: a > 0 2:. {map —m+—m(u+m)+ rt 22. Ina/:13 + Meta =%(a2 + max/a? + H2 -%In(u + «faz + H2) + C 2+ 2 + 2+ 2‘ 23.j—Wduax—aw2—amiww “guys a . d2 f2+ 2 (2+ 2 24. j—a—Jw-duwm¥+ln(u+da2+u2)+c 25. d“ ='—In(u+«/a’+u2:)+C 4m uzdu u a2 . —~—=— 1 2—— +q/2+ 1 + ZGIW 2.a+u 21n(u! a u) C [2 2+ 27.I——§i—=—im “Jr“ a +C : uv‘az+u2 a ll REFERENCE PAGES TABLE OF INTEGRALS FORMS INVOLVING «4/113 — 113. a > 0 2 30. J‘q/a'2 — uidu=%\/a2 H 1:2 + %sin”1-Ii+ C a 4 3|. [M2Wdu=%(2u2 — a2)m+%—sin“£+ C a a + Jag - u2 u +C l2... 2 32. I#d¢t=3/az—u9ham u Jazz—u: 1 u 33. ————-2————du=~-—- a2—u1—sin“‘-—+C u u a 1d 34. J—i= —5—m+isin-Ii+ C azmuz 2 2 a 35. --~—= ~——1n 7-: 36. —‘Ii~w—= —%./a2 — at + C 4 37. I (a2 — air/2 du = —% (2n2 — Suzy/a2 — u“ + 3%sin“ 1‘- + c a u 33 J—du———w~m—+C ' (chm/2 am FORMS INVOLVING «mi — a2, a > 0 2 39. fouz—azdu=%mw%miu+‘fuz~02]+ C 4 40. Ina/u? '- a’du=%(2u2— aghhfi ~ :12 —%1nIu + «fuz— a1|+ C «fag-“a: - ' __1 a 4!.Jleu=‘/u2—a2—acos —-—+C IHI 2“ 2 2... 2 42. —Wu=——M+Iulu+~/M——53I+C M It 43. —d‘-‘—--=1n[u+./u2—a=[+c uzdu u a:2 44. w=3m+3hlu+Ju3—azl+ c du = «In: —_a2 ”2",”; — a2 a2“ 45.‘ +C It 45 IL__.__ - (LP-"a2?“ azm +C REFERENCE PAGES TABLE OF INTEGRALS FORMS iNVOLVING a + bu udu l .41. Jaw“ —?(a+bu~aln|a+bu|)+C uzdu 1 2 2 45.] =-—[(a+bu) —4a(a+bu)+.2a lnfa+buil+C a+bu 2323 49.!‘u(a+”buj=;ll—ln 62:15:: +C 5°“!fi33=_¢7:+%m “:17" +C 3|. fimm+ +~1—1nla+buf+C SLIfium—fim “:5“ +C uzdu 1 a2 53. (n+bu)2H-§(a+bu a+bu—2aln|a+bui)-ITC 54. SIM/a + bu du— —— 1523’; (31):! w 2a)(a + bu?” + C udu m= 3—:2 (bu H 2a)‘!a + bu + C 56 SSJ—MZ = (8412 + 3b: 2 . 4abu)\/a + bu + C I x/a + bu 15b3 51 IWdu:1-— a+bu—J— +C ifa>0 uJa-i-bu flu Ja+bu+f ' a + bu . ,_..,. + C iffl;< 0 «a + bu du 58. “NI—d =24“? +b + V}— J‘ H u a u a uala + bu 59. J'N/a + bu du = _‘/au + bu+ bJ du 112 +2 ”1/0 + bu 60. “I u’k/a + bu du “A E121}? [u"(a + but)”2 .. naI u"‘1 w: + bu du] u ”du 2u’k/a + bu 2m: J‘ u’Hdu m = ban + 1) ‘ 1762:: +1) «[111 —+ bu 62 J‘ du \la + bu b(2u — 3) du u’R/a + but (201 — 1W" 2001 ~ 1) arkfa + bu REFERENCE PAGES TABLE OF IrxTTEGRALs TRIGONOM ETREC FORMS 63. Isinzudu=%u—%sin2u+ c 64. Icos’udu = éu + §sin 2n + C 65. Itmzudu=tanu—H+C 66. J‘Vcotzu du = -c0t u — u + C 67. IsinBy d1£*—‘-%(2+sin2u;)cosu+ C 68. Icosau du =§(2 + coszu)‘sinu -E- C 69. Itmz’udumétan’u-Flnlcosuf-LC 10. Jcot3udu= ~21cot2u — misinul + C 7|. Issfiuduwfiecutanu+§1nlsecu+tanuI+C. 72. Jcscaudu= —%cseu cotu+§1nfcscu -— cotu] + C s 1 — I ‘13. [Siam du § —-—- sin’Hu cos u‘+ n I sin’Hb: du n n 1 _1 , n —' 1 _2 74. cos"u du = Ems" u 5111 u + n cos" :4 du n 1 -l n-Z 75. tan u dit =*~ 1 tan" 1: — tan u du n _ INVERSE TRIGONOMETRIC FO RM5 87. f5in"‘z:du 2 usin'lu + ml} - u2 + C 88. Ices—Maia =.u cos”1u - 111 ~ u2 ~l- C 89. Itan”‘u du = Man—‘14 — % 111(1 + 141) + C 2___ f1_ 2 90. In sin—11¢ du = %_sin"u + ”—4—3- + C 2.. l _ 2 9|. Iacos“udu=%cos"lu — %~E-+ C -1 16. J CW“ d ” cot"“‘u " Icotmu du n — 1 — 2 71' I seen" d“ = 1 tanusecHu + n I360"’2:£du n _ 1 n — I 73. I csc”u du -= cot u cscHu + n cscHu du 11 — 1 n - 1 . . '- sin(a ~ b)u sin(a + b)u 79. g m ._ _._. m + Ismausmbudu 2(a—b) 2(a+b) C sin(a — b)u sin(a + b)u 30, m w WW— .1. Ices cm cos bu du 20: __ b) 201 + b) C 2-". cos(a — b)u .. cos(a + 15):: 3|. ‘ .3 a” Ism at; cos bu du 2(a ._ b) 2(a + b) 82. Insinudu=sinuwucosu+€ 83. Incosudu=cosu+ usinu+ C 84. Ju"sinudu= —u"cosu +nju’flcosudu 85. J‘u"cosudu= u“sinu —nJu""sinudu ‘ -1 n+1 . sm" 1: cos 1: n — 1 , _ 86. J. sm"u cos’"u du = ———~——--—- 5m” 11 + m n + m _ sin"+‘u cos“”‘u m — 1 n+m n+m u2+1 u t“—— 2 anu 2-[-C 92. I u tan”‘u du = ' 1 11+} 0‘ 93. In" 3111—51! (in m n + 1 [u"“sin"u —' Iii—:3]; 94- I u” cos”‘u dz: = 95. In” tan“u du = +C 2:: cosmu du J. sin"u cosm‘zu du REFERENCE PAGES TABLE OF INTEGRALS EXFONENTFAL AND LOGARITHMIC FORMS .96.J.ue“"du=iz(au—1)e“+C |00.Imudu=MMu-M+C' a 91 Iu”e""du=lu”e‘“"£Ju“”le°"du [0| Imlnudu— “”1 [( +1)1n¢—1]+C '. a a ' ' (n+1)2 {I z 93 I b d — 8“ (asinbu—b b)+C [MI I d —1n|1uu}+c . 3 sm 1: u £12sz cos I: . uinu u ea“ I . 99. Jewcosbudu= a2+b2 (acosbu+bsmbu) + C HYPERBOLIC FORMS 103. Isinhudu=coshu+ c ,Lus. Jcschudu=lnftanhéul + c lO4.IC05hudu=Si1fl1M~¥C l09. Iswhzudu=tanhu+c IBS. Itaphudu=lncoshu+c ‘ HO. Icsch’udu=—cothu+c l06. Icothudu=1n§sinhu|+c ‘ III. j‘sechutanhuduumsechu+c IDT. Iscchudu =tan"[sinhu] + C [12. fcschucothudu= -cschu + C FORMS INVOLVENG 122m: - 1:3, a > 0 _. 2 _ _ II3.I1/2au~u2duflu a«/20u—u2+-a—COS'E(Q ")+C 2 2 if _ 2 ._. ‘ 2a—uE‘-—-du=\/2aw---u3+acos”1(a 14)“? C u . a H8. J—iég—m —\/2au — u2+ aces—‘(a _ u) + C «flan—H2 0 11de (n+3a) 3a2 _(a'-u) ll . m=—-———\/2au—u2+~—~cosl +C 9 «flan—:42 2 2 a f _ 2 120. IJL_=___2M+C m/Qau—uz an ...
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