5.5 The Substitution Rule/1: Difference between revisions
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&= -\int{e^{u}} du \\ [2ex] | &= -\int{e^{u}} du \\ [2ex] & | ||
&= -e^{u} du \\ [2ex] | &= -e^{u} du \\ [2ex] & | ||
&= -e^{-x}+C \\ [2ex] | &= -e^{-x}+C \\ [2ex] & | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 19:46, 1 September 2022
![{\displaystyle {\begin{aligned}&\int {e^{-x}}dx,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/9f416969a5bf53a831b887d5bc218ad63a8c0290)