# Thread: Integrals of Partial Fractions

1. ## Integrals of Partial Fractions

https://gyazo.com/41c1b70dc12d3d2124ceda11eb184f5f

Could someone please walk me through exactly how 1/4 turns into 1/12 and how the 3 and -3 appear in the numerators?

2. ## Re: Integrals of Partial Fractions

they multiplied top and bottom by 3

3. ## Re: Integrals of Partial Fractions

Okay, but why?

4. ## Re: Integrals of Partial Fractions

to make the numerator match the coefficient of $x$ in the denominator so that the form matched the integral template of a $\ln$ function

5. ## Re: Integrals of Partial Fractions

Originally Posted by MrJank
Okay, but why?
Do this derivative: ${D_x}\left( {\frac{1}{{12}}\log (2 + 3x)} \right)$