| dx | A | B | ||||
∫ | = ∫( | + | )dx = J
| |||
| x2 − 4 | x − 2 | x + 2 |
| 1 | ||
2(A − B) = 1 ⇒ A − B = | ||
| 2 |
| 1 | ||
2A = | ||
| 2 |
| 1 | 1 | |||
A = | ⇒ B = − | |||
| 4 | 4 |
| 1 | 1 | 1 | 1 | |||||
J = | * ∫( | − | )dx = | (ln|x − 2| − ln|x + 2|)
| ||||
| 4 | x − 2 | x + 2 | 4 |
| 1 | 1 | 1 | |||
(ln|x − 2| − ln|x + 2|)|51 = | (ln3 − ln7) − | (ln1 − ln3) =
| |||
| 4 | 4 | 4 |
| 1 | 1 | 9 | |||
(ln3 − ln7 + ln3) = | ln | ||||
| 4 | 4 | 7 |