Yep, that's correct, Dunjaaa. There is a slightly faster solution in which you make the substitution u=1/x. But all the deft moves are in your solution. First, the use of a substitution to equate the integral with a similar looking integral. Then the use of some basic properties to relate the two integrals together. In this case it was the fact that the inverse tan of a number and the inverse tan of the number's reciprocal is constant.