Note: he initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{6x^3+10x^2+20x+24}{x^4+4x^2}dx$

Then the integrand has partial fractions decomposition

$\frac{a}{x^2}+\frac{b}{x}+\frac{cx+d}{x^2+4}$

where

$a=$

$b=$

$c=$

$d=$

Integrating term by term, we obtain that

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{6x^3+10x^2+20x+24}{x^4+4x^2}dx=$