la) Find this antiderivative. Use a Formula from pages 510-511 if you like. 5 (81+x2)3/2 dx b) Check your answer by differentiating.2) Find this definite integral. Use a Formula from pages 510-511 if you like. 2 xv5 + 2xdx\f4) Use Trapezoid Rule and Simpson's Rule to find an approximation for the integral in problem #2. Use 16 subdivisions, show all work.7.2 Integration Using Tables of Integrals A Table of Integrals We have studied several techniques for finding an antiderivative of a function. How- ever, useful as they are, these techniques are not always applicable. There are numer- ous other methods for finding an antiderivative of a function. Extensive lists of integration formulas have been compiled based on these methods. A small sample of the integration formulas that can be found in many mathematic cal handbooks is given in the following table of integrals. The formulas are grouped according to the basic form of the integrand. Note that it may be necessary to modify the integrand of the integral to be evaluated in order to use one of these formulas. TABLE OF INTEGRALS Forms Involving a + bu Jath " (a+ bu - alaja + bul) + c 2 - [(a + bu) - data + bu) + 2a' Inja + bul] + C *+ lola + bul + c (a + buy "bathu 4. wVa + bu du - Tsy (3bw - 20)(a + bu)"+ c 5du - 7 ( bu - 20) Va + hi + C 6.du I Vathi- Vo+ c (ifa>0) "Vat hu Va Va+ buy + Val Forms Involving Va' + #'.120 7. Vato du - " Vato + 5 lou + Va + wl + c 8. ( w Va to du = " (a' + 2 ) Va +w - - Inju + Vatw|+c 2172-In|+ Vo+rl+c7.2 INTEGRATION USING TABLES OF INTEGRALS 511 TABLE OF INTEGRALS (continued) Forms Involving Va' + ', a > 0 (continued) 10. Vatta+c I1. Vo + + C + C Forms Involving Va' - 4..>0 14. J WV r - adu - " (2 - 8)V/7 -4- -lu + Vr-al+c 15. -du = Vi - " + Inla + Vr-al+c 16. - Is + Vr -al+c 17. +C Forms Involving Va' - 8.a>0 20. a+ Ve- + c 21. Va -w + C 22. ( 6 - ) 7Ver Forms Involving " and In a 23. for du = - (au - 1) + c 25. 26. In udu = winn- utc 17. ' In a du = (m + 1) [(a+ 1)in m - I] + c (n*=1) 28. ar In a - In| In a| + c 29. (In u) du - w(In m) - m (In my du