∫ e − x d x , u = − x u = − x d u = − 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=-dx\\[2ex]&\int {e^{-x}}dx\\[2ex]=&=-\int {e^{u}}du\\[2ex]=&=-e^{u}du\\[2ex]=&=-e^{-x}+C\\[2ex]\end{aligned}}}
![{\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/276c0a96a0578b9d752b38073b19a72ec65e7fd5)