Notice that all the choices are of the same form with only a difference in the trig. function used. Our antiderivative is

-7F(cot(-9r)) . Its derivative is, by chain rule, -63F'(cot(-9r)csc^2(-9r) . Looking at the original function we see that F'(r)=tanr*secr . This yields F(r)=sec(r). Thus the answer is A.