Evaluate the following integral. \( \int \frac{x}{\sqrt{x-3}} d x \) Click to view the table of general integration formulas. \( \int \frac{x}{\sqrt{x-3}} d x=\square \)

Calculate the integral \( \int \frac{x}{\sqrt{x-3}} d x \). Evaluate the integral by following steps: - step0: Evaluate using partial integration formula: \(\int \frac{x}{\sqrt{x-3}} dx\) - step1: Evaluate the integral: \(\int \left(\sqrt{x-3}\right)^{-1}x dx\) - step2: Prepare for integration by parts: \(\begin{align}&u=x\\&dv=\frac{1}{\sqrt{x-3}}dx\end{align}\) - step3: Calculate the derivative: \(\begin{align}&du=dx\\&dv=\frac{1}{\sqrt{x-3}}dx\end{align}\) - step4: Evaluate the integral: \(\begin{align}&du=dx\\&v=2\left(x-3\right)^{\frac{1}{2}}\end{align}\) - step5: Substitute the values into formula: \(x\times 2\left(x-3\right)^{\frac{1}{2}}-\int 1\times 2\left(x-3\right)^{\frac{1}{2}} dx\) - step6: Calculate: \(2x\left(x-3\right)^{\frac{1}{2}}-\int 2\left(x-3\right)^{\frac{1}{2}} dx\) - step7: Evaluate the integral: \(2x\left(x-3\right)^{\frac{1}{2}}-\frac{4\left(x-3\right)^{\frac{3}{2}}}{3}\) - step8: Simplify: \(2x\sqrt{x-3}-\frac{4\left(x-3\right)^{\frac{3}{2}}}{3}\) - step9: Simplify: \(2x\sqrt{x-3}-\frac{4\sqrt{\left(x-3\right)^{3}}}{3}\) - step10: Expand the expression: \(2x\sqrt{x-3}-\frac{\left(4x-12\right)\sqrt{x-3}}{3}\) - step11: Add the constant of integral C: \(2x\sqrt{x-3}-\frac{\left(4x-12\right)\sqrt{x-3}}{3} + C, C \in \mathbb{R}\) The integral \( \int \frac{x}{\sqrt{x-3}} d x \) is equal to \( 2x\sqrt{x-3} - \frac{(4x-12)\sqrt{x-3}}{3} + C \), where \( C \) is an arbitrary constant.