Given that $y = 2xe^{\frac{x}{2}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Hence, find \(\displ

Question

Given that $y = 2xe^{\frac{x}{2}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Hence, find $\displaystyle\int xe^{\frac{x}{2}} \, \mathrm{d}x.$

Accepted Answer

$\displaystyle\int x\mathrm e^{x/2}\,\mathrm dx=2x\mathrm e^{x/2}-4\mathrm e^{x/2}+C$

Applications of Integration - Integration as an Inverse Process of Differentiation