Find the integral of 1/(x-5) with respect to x

This question tests fundamental understanding of integration and checks that the student is not simply memorizing the simple examples for the test. Most students will remember that the integral of 1/x is ln(|x|), however real understanding of the theory is needed to see that the x-5 that replaces the x in the above example makes no difference to the overall rule as all that has been changed is the addition of a constant. The official method to answer this question would be to show the student that this is the reverse of the chain rule of differentiation and that when you differentiate ln(x-5) you would get 1/(x-5) by the chain rule. And as at A-Level, differentiation is taught to be the opposite of integration. Then we can see by comparison that the answer must be ln(|x-5|). However, I like this question as it shows me the level of intuition a student has towards this area of integration. This question can then be expanded into finding the integral of 1/(5x-3) and if the intuition from the previous example holds, the student will see that the 3 can be ignored however the 5 can not and so the answer is 1/5*ln(|5x-3|).