Find the indefinite integral

By definition, if the function  F(x) is the antiderivative of f(x) then we follow

the indefinite integral as

 where: f(x) as the integrand

           F(x) as the anti-derivative function 

           C  as the arbitrary constant known as constant of integration

 For the problem we may apply u-substitution then basic formula for exponential function.

Using u-substitution, we let  then .

By dividing both sides by -1 in , we get .

Applying u-substitution using and dx=-1 du in 

, we get:  

Applying the basic integration formula for exponential function: 

where a is a constant.

  Then 

To express  it in terms of x, we plug-in u=-x to get:

Recall . It can be also be written as:

Recall the logarithm property: then

It becomes 

 The final answer can be or   .