| 1 | ||
U= lnx U'= | ||
| x |
| 1 | ||
V'=x V= | x2 | |
| 2 |
| 1 | 1 | x2 | 1 | 1 | |||||
x2lnx− | ∫ | dx= | x2lnx− | x2+C | |||||
| 2 | 2 | x | 2 | 4 |
| 2lnx | 1 | ||
dx=du v= | x2 | ||
| x | 2 |
| 1 | ||
cd = | x2ln2x−∫xlnxdx=(...) znów przez części | |
| 2 |
| 1 | 1 | ||
dx=du v= | x2 | ||
| x | 2 |
| 1 | 1 | 1 | ||||
(..)cd= | x2ln2x−( | x2lnx− | ∫xdx) | |||
| 2 | 2 | 2 |
| 1 | 1 | 1 | ||||
= | x2ln2x− | x2lnx+ | x2+C | |||
| 2 | 2 | 4 |