| dx | dx | |||
∫ | = ∫ | } | ||
| x3 + x | x(x2 + 1 |
| 1 | A | Bx + C | (A + B)x2 + Cx + A | ||||
= | + | = | |||||
| x(x2 + 1) | x | x2 + 1 | x(x2 + 1) |
| 1 | x | 1 | 1 | 2x | ||||||
∫( | − | )dx = ∫( | − | * | )dx = | |||||
| x | x2 + 1 | x | 2 | x2 + 1 |
| 1 | ||
= ln|x| − | ln(x2 + 1) + C | |
| 2 |
| f'(x) | ||
(na końcu skorzystałem z: ∫ | dx = ln|f(x)| + C ) | |
| f(x) |
