5.5 The Substitution Rule/29
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Revision as of 04:19, 4 September 2022 by Johnny C. (talk | contribs) (Created page with "<math> \int e^{tan(x)}sec^2(x)dx </math> <math> \begin{align} u &=tan(x) \\[2ex] du &= sec^2(x)dx \\[2ex] \end{align} </math> <math> \begin{align} \int e^udu \\[2ex] &= e^u+c \\[2ex] &= e^{tan(x)}+ c \end{align} </math>")
![{\displaystyle {\begin{aligned}u&=tan(x)\\[2ex]du&=sec^{2}(x)dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/f4babe8cedb3b8d0a180f477053d9d6090ee95f1)
![{\displaystyle {\begin{aligned}\int e^{u}du\\[2ex]&=e^{u}+c\\[2ex]&=e^{tan(x)}+c\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e8b3d2f3c62c125066f2cb1acf3945ce17c7910b)