Closed form of $\int_1^2\sqrt\frac{x^6+4x^4-2x^3+1}{x^4}\ \mathrm dx$

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Find the exact value (closed form) of:

$\displaystyle\int_1^2\sqrt\frac{x^6+4x^4-2x^3+1}{x^4}\ \mathrm dx$

I do not really know where to start, so please forgive me for not showing my attempt.

Wolfram alpha gives $2.27986$.