Verified answer

Try integration by parts with u = csc^6 x and dv = cot x dx

f(x)=xcscx - x/cotx cscx=1/sinx cotx=cosx/sinx f(x)=xsinx - xsinx/cosx f(x)=xsinx(1-1/cosx) Then do the product rule or do whatever else. Remember that 1/cosx = secx.