| Function | Antiderivative | Formula
|
xn
(n ≠ -1) |
xn+1
n+1 | + C |
|
 | xn dx | = | xn+1
n+1 | + C (n ≠ -1) |
|
| Examples: |
| x5.4 dx | = | x6.4
6.4 | + C |
Use the formula with n = 5.4 |
|
| 3x5.4 dx | = | 3x6.4
6.4 | + C |
The multiple 3 "goes along for the ride" |
|
| Function | Antiderivative | Formula
|
| x-1 |
ln |x| + C |
| x-1 dx | = | ln |x| + C |
|
| Example: |
| (5x-1 + 11x-3) dx | = | 5 ln |x| | - | 11x-2
2 | + C |
|
| Function | Antiderivative | Formula
|
k
(k constant) |
kx + C |
| k dx | = | kx + C |
|
| Example: |
| (5x-5.4 + 9) dx | = | - | 5x-4.4
4.4 | + 9x + C |
|
| Function | Antiderivative | Formula
|
| ex |
ex + C |
| ex dx | = | ex + C |
|
| Example: |
| (3x5.4 + 9ex - 4) dx | = | 3x6.4
6.4 | + 9ex - 4x + C |
|