- #1
FurryLemon
- 2
- 0
Hi
So let's 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.
So let's 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.