\[\displaystyle\int_0^{2} \left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\right) \ dx\]

If the above integral can be expressed as \[2_2 F_1\left(\frac{-1}{a},\frac{1}{b};\frac{4}{3};c\right)+\frac{18}{5}-\dfrac{3\Gamma({\frac{1}{\lambda}})\Gamma({\frac{\mu}{3}})}{10\sqrt[\nu]{\pi}}\]

Evaluate \[\lfloor{a+b+c+\mu+\nu+\lambda \rfloor}\]

\(\rightarrow\) \(_2 F_1(a',b';c';d')\) is the Hypergeometric function

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