subintervals) to approximate 1+ x2 dx. 27. x 8. Use Simpson's rule with n = 2 (so there are 2n = 4 29. Use the . 10 x 2 subintervals) to approximate dx. and use J2 In x value o Use Table 1 on pages 547-549 to find each indefinite integral in 30. Use the Problems 9-22. and us value 9 . dx 10. dx 31. Use S x(1 +x) x2 ( 1 + x ) interv X 11. dx 12. dx (3 + x) 2(5 + 2x) (5 + 2x ) 2 ( 2 + x ) theor integ 1000 1 32. Use 13. dx 14. inter V 16 + x x V 16 + xAppendix C Tables Table 1 Integration Formulas Integrals Involving u" 1. of du = 1't Enti " * - 1 2. ( u' du = 1 du = Injul Integrals Involving a + bu, a # 0 and b + 0 3. at bu du = - Inla + bul 4. du u a + bu b 2 In a + bul 5 . 12 (a + bu)2 2a(a + bu) a2 at bu - du 263 63 53 In a + bul 6. (at bu) ? du = 2 ( Inla + bul + -a ) at bu 7. (a + bu) (at bu) ? du 63 b' ( a + bu ) 20 Inla + bul 8. u ( a + bu) " du = ( a + bu ) " + 2 a ( a + bu ) nti (n + 2) 62 (n + 1) 62 , " * -1, -2 9. 1 u ( a + bu ) du = - In 4 a" la + bu 10. du = 1 b a + bu 12 ( a + bu ) au In a2 11. u(a + bu) 2 du = In a(a + bu) a2 la + bu 12 . u(a + bu) ? du = a + 2bu 2b a + bu au(a + bu) In 3 Integrals Involving a2 - u2, a > 0 13 . 12 - a 2 du = 1 4 - a 2a" "lut a 2 2 - 12 du = uta za u - a Integrals Involving (a + bu) and (c + du), b # 0, d # 0, and ad - bc # 0 15 . (at bu) (c + du) du = - Inc + du ad - be la + bul 16. (a + bu) (c + du) du = ad - be ( In a + bul - " inlc + dul ) 17 . ( a + bu ) ( c + du ) -du = 1 "bd " - ad - be (1 2 Inla + bul - Inle + dul ) [Note: The constant of integration is omitted for each integral, but must be included in any particular application of a formula. The variable i is the variable of integration; all other symbols represent constants.] 709