Answer
$ 2e^{x/2}+C$
Work Step by Step
see Substitution RuIe, p.962:
1. Write $u$ a{\it s} a function of x.
2. Take the derivative $du/dx$ and solve for the quantity $dx$ in terms of $du$.
3. Use the expression you obtain in step 2 to substitute for $dx$ in the given integral and substitute $u$ for its defining expression.
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(1) Given $\displaystyle \quad u=\frac{x}{2}$
(2)$ \displaystyle \quad du=\frac{1}{2}dx\ \ \Rightarrow\ \ dx=2du$
$(3)$
$\displaystyle \int e^{x/2}dx=\int e^{u}(2du)$= ... constant multiple
$=2\displaystyle \int e^{u}du$
$=2e^{u}+C$ = ... bring back x
$= 2e^{x/2}+C$
