1. The problem statement, all variables and given/known data What is the integral of sqrt(x^2-1)/x dx? 2. Relevant equations 3. The attempt at a solution ∫ √(x^2 - 1) dx / x let x = sec u: u = sec^-1(x) and tan u = √(x^2 - 1) dx = sec u tan u du now the integral becomes ∫ √sec^2(u) - 1) sec u tan u du / sec u = ∫ tan u tan u du = ∫ tan^2(u) du = ∫ (sec^2(u) - 1) du = ∫ (sec^2(u) du - ∫ du = tan u - u + c back substitute u = sec^-1(x) and tan u = √(x^2 - 1) = √(x^2 - 1) - sec^-1(x) + c However, the correct answer should be arccot(sqrt(x^2-1))+sqrt(x^2-1) + c. Can someone help me find what went wrong?