8. Consider the indenite integral fan/a: 1 dm. a. At first glance, this integrand may not seem suited to substitution due to the presence ofa: in separate locations in the integrand. Nonetheless, using the composite function Va: 1 as a guide, let u. = a: 1. Determine expressions for both a: and 03:1: in terms of u. b. Convert the given integral in a: to a new integral in u. c. Evaluate the integral in (b) by noting that = 111/2 and observing that it is now possible to rewrite the integrand in u by expanding through multiplication. d. Evaluate each of the integrals [x/a: Ida: and fan/2:2 1 dm. Write a paragraph to discuss the similarities among the three indenite integrals in this problem and the role of substitution and algebraic rearrangement in each. 9. Consider the indenite integral fsin3(a:)da:. a. Explain why the substitution 1:. = sin(m) will not work to help evaluate the given integral. b. Recall the Fundamental Trigonometric Identity, which states that sin2(m) + cos2 (11:) = 1. By observing that sin3(m) = sin(:r:) - sin2(m), use the Fundamental Trigonometric Identity to rewrite the integrand as the product of sin(a:) with another function. c. Explain why the substitution 1:. = cos(m) now provides a possible way to evaluate the integral in (b). d. Use your work in (a)(c) to evaluate the indenite integral fsin3(m) dm. e. Use a similar approach to evaluate fcos3(m) do