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Answers by Amol V.

Note that if you multiply your equation by x and rearrange the terms you can write the equation as    x*y'+2y-6x=0.    If you let M(x,y) = 2y-6x and N(x,y)=x then you have a differential equation of the following form   N(x,y)*y'+M(x,y)=0...

First guess to find a root. If you plug in x=1 you will find that this is a root. So (x-1) is a factor to your expression. Do long division on your initial expression by (x-1). Then your factors will be (x-1) and whatever you get from long division. But your answer from long division will be...

I also don't know what you mean by the golden rule for an antiderivative. However, one of the most useful formulas when taking the antiderivative of a single term of the form xn is ∫xndx = xn+1/(n+1).