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

```    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!
```

##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     