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).