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\begin{equation*}

\begin{split}

\int_{1}^{9} \frac{3x-2}{\sqrt{x}}dx &= \int_{1}^{9}\frac{3x}{x^{\frac{1}{2}}}dx - \int_{1}^{9}\frac{2}{x^{\frac{1}{2}}}dx \\ \\

&= 3\int_{1}^{9}x^{\frac{1}{2}}dx - 2\int_{1}^{9}x^{\frac{-1}{2}}dx \\ \\

&= 3 \left[ \frac{2}{3}(x^{\frac{3}{2}}) \right]_{1}^{9} - 2 \left[ 2x^{\frac{1}{2}} \right]_{1}^{9} \\ \\

&= 2 \left[9^{\frac{3}{2}} - 1 \right] - 4 \left[ 9^{\frac{1}{2}} - 1 \right] \\ \\

&= 2 \left[27 - 1 \right] - 4 \left[ 3 - 1 \right] \\ \\

&= 2*26 - 4*2 \\ \\

&= 44 \\

\end{split}

\end{equation*}

[/tex]