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thank you jared to wrap up first thing i want to do is im going to factor and then im going to multiply by dx on both sides so that would be my first step so ill have d y is equal to a factor out an x and im left with a 1 plus y squared times dx i can divide by 1 plus y squared so i have 1 over 1 plus y squared d y equals x dx and again looking at this i dont have a quotient rule for anti-differentiation right so immediately whenever i see a den whenever i see a denominator i see like that squared automatically i think of arc sine arc cosine and the anti-derivative of this is going to be tan uh tan inverse so its gonna be tan inverse and therefore uh thats gonna be plus c so what did i write that right in there sorry i just wanted to make sure i had so i have tan inverse of y because thats in terms of y and then this is going to be one half x squared and then plus big c right and now heres the important heres the one i want to get to so again pattern recognition make sure yo