∫ e − x d x , u = − x u = − x d u = − 1 d x ∫ e − x d x − ∫ e u d u − e u d u − e − x + C {\displaystyle {\begin{aligned}&\int {e^{-x}}dx,u=-x\\[2ex]u=-x\\[2ex]du=-1dx\\[2ex]&\int {e^{-x}}dx\\[2ex]&-\int {e^{u}}du\\[2ex]&-e^{u}du\\[2ex]&-e^{-x}+C\end{aligned}}}
![{\displaystyle {\begin{aligned}&\int {e^{-x}}dx,u=-x\\[2ex]u=-x\\[2ex]du=-1dx\\[2ex]&\int {e^{-x}}dx\\[2ex]&-\int {e^{u}}du\\[2ex]&-e^{u}du\\[2ex]&-e^{-x}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3dd22954039b1ac40da399329457968948d7f605)