Official solution
\[\int {{{3{x^{13}} + 2{x^{11}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^4}}}} dx\]
\[\int {{{\left( {{3 \over {{x^3}}} + {2 \over {{x^5}}}} \right)dx} \over {{{\left( {2 + {3 \over {{x^2}}} + {1 \over {{x^4}}}} \right)}^4}}}} \]
Let \[\left( {2 + {3 \over {{x^2}}} + {1 \over {{x^4}}}} \right) = t\]
\[ - {1 \over 2}\int {{{dt} \over {{t^4}}}} = {1 \over {6{t^3}}} + C\]
\[ \Rightarrow {{{x^{12}}} \over {6{{\left( {2{x^4} + 3{x^2} + 1} \right)}^3}}} + C\]