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$$ OSCALC$17\mathrm{.}1\mathrm{.}051.$

Integrate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}2x\sqrt[\phantom{2}]{2x-3}dx$ using two methods. $($Use $C$ for the constant of integration.$)$

$($a$)$ Integrate using parts, letting $dv=\sqrt[\phantom{2}]{2x-3}dx.$

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$($b$)$ Integrate using substitution, letting $u=2x-3.$

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