Integration of e^-x = ...?

____________________________________

Answer

      -x 
    -e   + C

Explanation

We know the integration formula for exponential function. 
    /                      
    |  f(x)               f(x)
    | e     . f'(x) dx = e     + C  for base e logarithm 
    |                      
    /

Here f(x) is the function of x and f'(x) derivative of f(x) and e is exponential function.

Now we solve the above question. 

    /       
    |  -x   
    | e  dx 
    |       
    /

Here -x is function of x. Its derivative is not exist so first of all we try to make derivate of -x. Derivative of -x is -1.

      /       
      |  -x    -1 
    = | e   . ----- dx 
      |        -1
      /

         /       
         |  -x    
    = -1 | e   . -1 dx 
         |        
         /
                
            -x    
    = -1 . e    + C
         -x
    = - e   + C

____________________________________

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