Given that $y=2x{{\text{e}}^{\frac{x}{2}}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Hence, find

Question

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

Accepted Answer

$\dfrac{\mathrm dy}{\mathrm dx}=(x+2)\mathrm e^{\frac{x}{2}}$. $\displaystyle\int x\mathrm e^{\frac{x}{2}}\,\mathrm dx=2(x-2)\mathrm e^{\frac{x}{2}}+C$.

Applications of Integration - Integration as an Inverse Process of Differentiation

Applications of Integration - Integration as an Inverse Process of Differentiation

Solution:

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