Integration of e^(-x)

 Here's the step-by-step solution of the integral of $e^{-x}$ using the substitution method:

Step 1:

Start by identifying the function you want to integrate, in this case e^(-x).

$\int e^{-x}dx$

Step 2:

Identify the substitution that can be used to make the integral easier to solve. In this case, we can substitute , 

u = -x

so ,  dx = -du

 

Step 3:

Replace dx and x in the original integral with the derivative of the substitution 

$\int e^{u}(-du)$

on integrating we would have

= $-e^{u}$ + C

Step 4:

Replace u with -x in the final result:

$-e^{-x}$ + C

Note : C is a constant of integration.