Hi So lets have ∫(2x)/(4x^(2)+2) dx Without factorising the 2 from the denominator, I integrate and I get 1/4*ln(4x^(2)+2)+c which makes sense as when I differentiate it I get the original derivative. BUT when I factor the 2 from the denominator I have 2x/[2(2x^(2)+1)] simplify it down = x/(2x^(2)+1) which is the same as (2x)/(4x^(2)+2) Now when I integrate ∫x/(2x^(2)+1)dx I get 1/4*ln(2x^(2)+1)+c which is obviously different from the first integral. Why? because when I simplify it by factorisation its the same thing so Why is it different? Please, any help would be appreciated. Thanks.