# How do you integrate # e^(-x)dx#?

##### 1 Answer

Apr 26, 2016

#### Explanation:

We will use the following integral rule:

#inte^udu=e^u+C#

Thus, to integrate

#inte^-xdx#

We set

#color(red)(u=-x)" "=>" "(du)/dx=-1" "=>" "color(blue)(du=-dx)#

Since we have only

#inte^-xdx=-inte^color(red)(-x)color(blue)((-1)dx)=-inte^color(red)ucolor(blue)(du)#

This is the rule we knew originally. Don't forget that the integral is multiplied by

#-inte^udu=-e^u+C=barul|color(white)(a/a)-e^-x+Ccolor(white)(a/a)|#