Evaluate the indefinite integral. $($Use $C$ for the constant of integration.$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2\sqrt[\phantom{2}]{5+x}dx$

Evaluate the indefinite integral. $($Use $C$ for the constant of integration.$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x-\frac{1}{x^2})(x^2+\frac{2}{x}{)}^{4}dx$

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