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fREFERENCE PAGE 7 TABLE OF INTEGRALS Forms Involving val - u', a>0 30 . Vaz - 1' du - Val - uit 2 sin

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\fREFERENCE PAGE 7 TABLE OF INTEGRALS Forms Involving val - u', a>0 30 . Vaz - 1' du - " Val - uit 2 sin " + C 31. u'vaz - 13 du = " (213 - a ) val - mita" 8 sin 1 " + C a 32. (Na - " du - Val - u - aln at va -" + c 33. Val - 13 1 2 " du = -- Vai - 18 - sin !" + c 34. w du 7 sin 1 4 + C 35. at va - 12 + c 36. du Val - 12 + C 37. (a3 - up/z du = - " (213 - 5a ) vat - 1+- 8 sin 1 4 + C a 38 . du + C Forms Involving vu? - al, a >0 39. Vuz - a du = " vuz - a - " In lu+ vu'- a|+ c 10. [uvu - a du - " (213 - a ) viz - a2 - 4 In|u+ vu - a |+ c 41. ( Yu - du - Vu - at - a cos" + C 42. du Vul - al " + Inu+ viz - a- | + c 43. du = In |u+ vuz - a? |+ c 44. u- du vu? - at + - In | u+ vuz - a= | + c 45. du - + C a u 46. du +C a vul - atTABLE OF INTEGRALS Forms Involving a + bu 47. 1 du at bu Ba (a + bu - a ln |a + bul) + C 48. u du at bu 73 [(a + bu)' - 4ala + bu) + 2a' In |a + bu| + C 19. du . + C wat bu) a+ bu du b a+ bu " (a + bu) 51. u du (a + bu)' b'(a + bu) In |a + bu | + C 52. wa + bu) In a+ bu ala + bu) + c 53. u du a z ( a + bu) at bu - a + bu - - 2a In |a + bul + c 54. uva + bu du = 2 1562 (3bu - 2a)(a + bu) ? + C 55. u du 2 a+ bu 362 (bu - 2a) va + bu + C 56. u du 2 Va+ bu 1563 (8a + 3blu - 4abu) va + bu + C 57. du . Vat bu - Va uva+ bu + C, ifa >0 va vat but va 2 - tan-1 a + bu + C. if a 0 113. 2au - u' du = " - 2au - 17 + 2 Cos-1 9 - " ) 40 114. 12au - 1- du = 24- au - 3a? 6 -2au - 1+ 2cost ( a - " ) +c 115. (V 2au - " du - 2au - 1 + a cos-1( a - " ) + c 116. V/ 2au -= - 2v2au - 12 - 505-1 (1 - ") +C 117. du V/2au - 13 - cos-1( a - ")+ C 118. u du V/2au - 12 -V2au - u'+ acos-1( 2 -") + c 119. w du (u + 3a) V2au 2 2au - 13+ 3 cos(a - ") +c 120. du /2au - 12 -+ c 1 \\/ 2au - 12TABLE OF INTEGRALS Basic Forms 1. Jude = wo - v du 11. csc u cot u du = -escu + c 2. u" du - " + C, nx-1 12. tan u du = In |sec u | + C [ant = In |u| + c 13. cot u du = In | sin a | + c 4. [ e" du = e" + C 14. sec u di = In | sec u + tan u | + c 5 . [ a" du -+C 15. csc u du = In |esca - cot u | + C In a 16. du Val - 12 = sin - + C, a>0 6. sin u du = -cos u + C 17. du 7. cos u du = sin u + C alt ul a tan -1 4 + C 18. 8. - sec-1 4 + C secu du = tan u + C 9. esc'u du = -cot u + C 19. - In a - u 2a u - a + C 10. see u tan u du = sec u + c 20. du - In 2a uta + c Forms Involving val +uz, a >0 21 . Vaz + u' di = " a 7 Va + 1 + 2 1 + " In(u + vaz + 13 ) + c 22. u' Vaz + u' di = " (a' + 2u' ) vaz + 13 - " 8 In( u + vaz + u' ) + C 23. Va' + 13 "du = vastu' - aln atvatuz + C 24. Val+ uz du = _Val+ uz "+ In(u + vaz + #? ) + c 25. du "= In(u + val + u? ) + c 26. u du Val+ 12 va'+ 12 " In(u + val+ u" ) + c du 27. - In vatuta uva+ 1 + c 28. Val+ 12 +C 29. (az+ 12)3/2 + C a val+ 2

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