you started out well. see here and match up with your work to see where you went wrong
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