Question

can someone help me with integral of 1/sqrt(x^2+1)? I have looked at the solution and I understand the substitutions but I don't see where they are coming from

Answer 1

This you memorize, arctan(x) if I'm correct

Answer 2

i dont believe in memorization, also thats not the right answer

Answer 3

i think you are thinking of 1/sqrt(x^2-1)

Answer 4

pretty sure its the sinh^-1(x). I dont understand what you mean by you dont know where they are coming from though

Answer 5

I know that you can get the answet by subsituting x = tan y and then dx = sec^2 y dy and then you just integrate secy dy but I dont understand what initial thought drives those substitutions. You can tell me that it works so it must right but I would like to understand the thought process behind it

Answer 6

I really dont have an explanation for that either. My professor used to tell me that if you work with integrals for a certain period of time, you'll begin to recognize what fits into certain situations. You see the problem, and you immediately recognize the integral, or something to substitute with. This is a classic case.

Answer 7

yeah, i get you, I was just hoping for something more satisfying