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Hi danagasta, If my last instructions did not work then you need to reset your RAM. You are missing the negative sign and, I have no idea where you got the absolute value inside the brackets. Yes, the absolute value are used in books and, on integral tables but, I can asure you that the Ti 89 should not have produce them in this answer. I'll stand behind that In( -cos(x) / (sin(x)-1)) is the correct answer. You can go ahead and simplify after the calculation to get the answer you want but, that is the good answer that Ti 89 is going to give you for the integral of sec(x). Errors that do not match the suspected, I am pretty sure that Texas Instruments would have you clear the RAM. I do not like resetting the RAM but, I could not find the cause to why you got the answer you did. And so far no other expert has produced a solution to convince me otherwise. I was not able to come up with any of the 3 answers MiB8888 did on my Ti 89. I am not saying that they are not good answers, they are book and integral tables answers. You are not going to get them on the Ti 89.