| x+13 | 1 | 2x−4 | 1 | |||||
∫ | dx = | ∫ | dx +15∫ | dx | ||||
| x2−4x−5 | 2 | x2−4x−5 | x2−4x−5 |
| 1 | 15 | 1 | 15 | 1 | 1 | |||||||
= | ln(x2−4x−5) + | ∫ | dx − | ∫ | dx = | ln(x2−4x−5) | ||||||
| 2 | 6 | x−5 | 6 | x+1 | 2 |
| 15 | 15 | |||
+ | ln|x−5| − | ln|x+1| +C | ||
| 6 | 6 |
Odp. to 3ln|x−5| − 2ln|x+1|
| 1 | 15 | 15 | ||||
= | (ln|x−5| + ln|x+1|) + | ln|x−5| − | ln|x+1| + C = | |||
| 2 | 6 | 6 |