partial fractions with numerator and denominator of the same degree

Question

I tried using partial fractions but wasn't sure what to do with the ${x^2}$: $$\int \frac{x^2}{3x^2 - 4} dx$$

Answer 1

First step is to do long division (when numerator and denominator have the same degree):

$$\frac {x^2}{3x^2-4} = \frac 1 3 + \frac{4}{3} \frac {1}{3x^2-4}.$$

Now you can do partial fractions on the second term (you should factor the denominator into two linear terms).