1. The problem statement, all variables and given/known data Use integration by parts to find a reduction formula for the integral In = ∫pi/20 sinn(6x)dx when n is a positive integer greater than 1. 2. Relevant equations ∫udv = uv - ∫vdu 3. The attempt at a solution Let u = 6x du = 6dx ∫pi/20 sinn(u) (du/6) (1/6) ∫sinn-1(u)sinu du Let v = sinn-1(u) and dw = sinu du and dv = (n-1)sinn-2(u)cosu du and w = -cos(u) (1/6)(-cos(u)sinn-1(u) - ∫-cos2(u) (n-1) sinn-2(u) du When the left hand side of the equation is evaluated from 0 to pi/2, it is found to equal 0. (1/6)(n-1)∫cos2sinn-2(u) du (1/6)(n-1)∫(1-sin2u)sinn-2u du (1/6)(n-1)∫sinn-2u - sinnu du In = (1/6)(n-1)(In-2 -In) In = (1/6)(n-1)(In-2) -(1/6)(n-1)(In) In + (1/6)(n-1)(In)= (1/6)(n-1)(In-2) (1 + (n-1)/6)In = (1/6)(n-1)(In-2) ((n+5)/6)In = (1/6)(n-1)(In-2) In = (1/6)(n-1)(In-2)(6/(n+5)) In = ((n-1)/(n+5))(In-2) This was not one of my answer choices for my homework. Could you please help me see what I'm doing wrong?