∫ e t a n ( x ) s e c 2 ( x ) d x {\displaystyle \int e^{tan(x)}sec^{2}(x)dx}
u = t a n ( x ) d u = s e c 2 ( x ) d x {\displaystyle {\begin{aligned}u&=tan(x)\\[2ex]du&=sec^{2}(x)dx\\[2ex]\end{aligned}}}
∫ e u d u = e u + c = e t a n ( x ) + c {\displaystyle {\begin{aligned}\int e^{u}du\\[2ex]&=e^{u}+c\\[2ex]&=e^{tan(x)}+c\end{aligned}}}
![{\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)