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} | &= -e^{u} \\[2ex] | ||
&= -e^{-x}+C \\ [2ex] | &= -e^{-x}+C \\ [2ex] | ||
Revision as of 19:52, 1 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\int {e^{-x}}dx,\quad u=-x\\[2ex]&u=-x\\[2ex]&du=-dx\\[2ex]&\int {e^{-x}}dx\\[2ex]&=-\int {e^{u}}du\\[2ex]&=-e^{u}\\[2ex]&=-e^{-x}+C\\[2ex]\end{aligned}}}