The integral of sec x is ln|sec x + tan x| + c. That's what the internet is telling me. Now, I am having trouble understanding the modulus sign. I understand that the ln operator gives real numbers for positive values of the argument and complex numbers for negative values of the argument. So, if the ln operator is defined for negative values, why incorporate the modulus sign? Also, I differentiated ln |sec x + tan x| + c and I get |sec x|. Doesn't that mean that the integral of sec x is only defined for positive values of sec x? But that contradicts common sense when we have a look at the graph of sec x (google 'graph sec x' for a display of the graph). It's clear the function does have an integral for negative values of sec x, right?