5.5 The Substitution Rule/1: Difference between revisions
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\begin{align} | \begin{align} | ||
& \int{e^{-x}} dx , u=-x \\[2ex] | & \int{e^{-x}} dx , u=-x \\[2ex] &= | ||
& u=-x \\ [2ex] | &= u=-x \\ [2ex] | ||
& du=-dx\\ [2ex] | &= du=-dx\\ [2ex] | ||
& \int{e^{-x}} dx \\ [2ex] | &= \int{e^{-x}} dx \\ [2ex] | ||
& -\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 19:42, 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/c6dfe847d3047205ca983965deabc03c04a2f43b)