Since the derivative of tan(x) is sec²(x), ∫tan(x) sec²(x) dx = (1/2)tan²(x) + C ---- Update: the reason that you are getting so many different looking answers below is because 1+tan²(x) = sec²(x). In particular, suppose that C = 1/2 + D Then the answer would be (1/2)tan²(x) + 1/2 + D = (1/2)(tan²(x) + 1) + D = (1/2)sec²(x) + D = (1/2)(1/cos²(x)) + D These answers are all equivalent. It's one of the few cases where that constant you always tack on after integration affects what the result looks like. So in general, to check if two integrations of the same function are equivalent, you should subtract the two results and if the difference is a constant, you know that both answers are just as valid (or just as wrong, for that matter).