ok. so the book says to prove the reduction formula for:

integral of cos^n x dx

the says this equals 1/n cos^(n-1) x * sin x + ((n-1)/n) * integral of cos^n-2 x dx

i tried to do this by breaking cos^n x into cos^n-1 * cos x

i let u equal cos^n-1 x and dv = cos x dx

for du i got -(n-1)(cos^n-2 x)(sin x) dx

and for v i got sin x

so the answer i got was cos^n-1 * sin x + (n-1) * the integral of cos^n-2 x * sin x dx

what did i do wrong