Answer
$ -e^{-x}+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 $\quad u=-x$
(2)$ \quad du=-dx\ \ \Rightarrow\ \ dx=-du$
$(3)$
$\displaystyle \int e^{-x}dx=\int e^{u}(-du)$= ... constant multiple
$=-\displaystyle \int e^{u}du$
$=-e^{u}+C$ = ... bring back x
$= -e^{-x}+C$
