| dx | ||
1. ∫ | ||
| −5+6x−x2 |
| x−1 | ||
2. ∫ | ||
| 4x2−4x+1 |
| 6−4 | 6+4 | |||
x= | =1 lub x= | =5 | ||
| 2 | 2 |
| −1 | −1 | |||
∫ | dx=∫ | dx= | ||
| x2−6x+5 | (x−1)*(x−5) |
| −1 | A | B | |||
= | + | ⇔ | |||
| (x−1)*(x−5) | x−1 | x−5 |
| −1 | ||
−1=B*(5−1)⇔b= | ||
| 4 |
| 1 | ||
−1=A*(1−5)⇔A= | ||
| 4 |
| −1 | 1 | 1 | 1 | 1 | ||||||
∫ | dx=− | ∫ | dx+ | ∫ | dx= | |||||
| x2−6x+5 | 4 | x−1 | 4 | x−5 |
| 1 | ||
=− | (ln|x−1|−ln|x−5|)= | |
| 4 |
| 1 | x−1 | |||
=− | ln| | |+C | ||
| 4 | x−5 |
| 1 | 8x − 4 | 1 | dx | |||||
2) = | ∫ | − | ∫ | = | ||||
| 8 | x2 − 4x +1 | 2 | (2x − 1)2 |
| 1 | 1 | −1 | ||||
= | lnI(2x−1)2I − | * | + C = | |||
| 8 | 2 | 2(2x−1) |
| 1 | 1 | |||
= | lnI2x−1I + | + C | ||
| 4 | 4(2x−1) |