Question 1 (2 points) Consider the integral sec x dx. There are often more ways than one to solve an integral. In this and the next questions, we will explore different ways to solve this integral. (a) (1pt) Let u = tana, try a substitution. Can you solve the integral this way? Give it a try. Do not worry if you cannot get this to work. (b) (1pt) Let usecx, try a substitution. Give it a try. Do not worry if you cannot get this to work. Question 2 (5 points) Use integration by parts with u = secx, dv = sec x dx to solve the integral [sec x dr. The identity tan x + 1 = sec x might be helpful. You may use that [secx dr= = In | secx+tanx|+C Question 3 (6 points) In this problem you will use partial fractions to eval- uate the integral: J du (a) (2pts) First set up the partial fraction decomposition for: 1 A B C + + + (1-u)2 u D (1-u) 1+u (1+u) Show that B 1/4 and D = 1/4. = (b) (4pts) Assume that A = B = C = D = 1/4. Evaluate the integral S du - 1/s Question 4 (5 points) We will consider the integral sec x dx once more. Now use sec x = 1 COS X to rewrite: sec x dx = dx cos x dx Cosx Then use the substitution u = sin x. Can you use Question 3 to solve this integral? Show all your work!