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Integration of e^x = e^x / ln e is true of false...?

____________________________________

Answer
    True
Explanation
We know the integration formula "a raise to power x". 
    /             x
    |  x        a
    | a  dx = ------  + C  for base 10 logarithm ..........(i)
    |          log a  
    /

Similarly for "e raise to power x". 

    /            x
    |  x        e
    | e  dx = ------ + C  for base e logarithm  ......... (ii)
    |          ln e
    /

We should memorize the formulas (i) & (ii) because it clear the basic concept and logical result are same and easy to remember.

Here ln e = 1 (because e^0 = 1 and by use logarithm property we get ln e = 1 )

When simplify the (ii) we get
         x        x
        e        e       x
    = ------ = ------ = e
       ln e       1

    /  x       x           
    | e  dx = e  + C       ......... (iii)   
    /

Integration formulas (ii) & (iii) are same formula and we mostly use (iii). 

____________________________________

Note

(e = 2.7182818284 5904523536 0287471352 6624977572 4709369995 9574966967 6277240766 3035354759 4571382178 5251664274 ...)

                    1/n
    e = lim  (1 + n)
        n->0
                   1  n
    e = lim  (1 + ---)
        n->∞       n 

        ∞    1
    e = ∑   ---
        n=0  k!  
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