How do you integrate #(x^(3)+5) / (x^(2)+5x+6) dx# using partial fractions?
Firstly, note that the degree on the numerator is higher than the degree on the denominator.
Thus, we can use polynomial long division to get it into a form where the degree on the numerator is lower than the denominator. From that, we can use partial fractions to simplify.
So, now, we consider the fractional bit, namely,
And by the comparison of coefficients on both sides, we have
Which yields the solution
Thus, we can finally write the integrand as...