If\:U_1=\int cot^nxdx,\:show\:that\:U_n=\frac{-1}{n-1}cot^{n-1}x-U_{n-2} I'm going to take a while to do latex so here's a picture of my working so far instead: I don't know how to work the integral on the last step. Maybe some hints? (use spoilers) Thanks so much for the help!