Question: Given the decomposition

\[\frac{2{{x}^{3}}-2{{x}^{2}}+3x-4}{\left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+2 \right)}=\frac{x-2}{{{x}^{2}}-1}+\frac{x}{{{x}^{2}}+2}\]

find

\[\int{\frac{2{{x}^{3}}-2{{x}^{2}}+3x-4}{\left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+2 \right)}dx}\]