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### Integration of e^x = ...? ____________________________________

```      x
e
---- + C
ln e
```
##### Explanation

We know the integration formula of "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 is easy to remember, clear the basic concept and theam of boths result are also same.

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

```         x        x
e        e
= ------ = ------ = e^x
ln e      1

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

Integration formulas (ii) & (iii) are same formula. We mostly use formula (iii) because it is understood that "ln e = 1". Just keep in mind the original formula (ii) and there is also the hidden knownledge that "ln e = 1".

____________________________________

```    /            x
|  x        e
| e  dx = ------ + C       (here  ln e = 1)
|          ln e
/
```

##### 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     