5.5 The Substitution Rule/1: Difference between revisions
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\begin{align} | \begin{align} | ||
& \int{e^{-x}} dx , | & \int{e^{-x}} dx ,\\[2ex]u=-x \\[2ex] | ||
& u=-x \\ [2ex] | & u=-x \\ [2ex] | ||
Revision as of 19:44, 1 September 2022
![{\displaystyle {\begin{aligned}&\int {e^{-x}}dx,\\[2ex]u=-x\\[2ex]&u=-x\\[2ex]&du=-dx\\[2ex]&\int {e^{-x}}dx\\[2ex]&=-\int {e^{u}}du\\[2ex]&=-e^{u}du\\[2ex]&=-e^{-x}+C\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/f1d3086e5117c3b1920980927bb7d8630e9be581)