2. FIRST REDUCTION FORMULA For any n a positive integer, it is always true that [ xedx = x"ex -n ( 2"-ledx We will first attempt to understand the recursion formula. (1) When n = 1 this becomes. . . (a) Work: substituting 1 in for n on both sides, we obtain (since the function f (x) = 20 is interpreted as the constant function f (x) = 1) fredx = re -1 / x'-ledx xedx = me" - ( edx (b) Answer: xel dx = rez - / edx (2) Verify the statement for n = 1 by using integration by parts. (Stop when you reproduce your answer in part a.) (a) Work: We let u = a and dy = edx so that 1 = I dv = edx du = de U = er (b) Work, cont'd: Performing integration by parts, we have and we stop here, since the formula is equal to the answer in part 1b. (3) When n = 2 this becomes ... (substitute 2 in for n on both sides of the formula above) (4) Verify the statement for n = 2 by using integration by parts (once). Note that you can stop integrating when it is of the form given in part 3. (5) Use integration by parts to prove this recursion formula for all positive integers n. (Don't pick a specific n...., just leave n as n.)3. INTEGRATING CSC r Compute fescardr by following the work of / sec3 xda in https://en. wikipedia.org/wiki/Integral_of_secant_cubed. Recall that 1 + cot r = cscr and dx CSC = - cscr cot r and d cotr = - cscr dx