| 1 | 2 | |||
du = | dx v = | x3 | ||
| 1+ x2 | 3 |
| 2 | 1 | 2x3 | 2 | 1 | ||||||
A = | x3arctgx − | ∫ | dx = | x3arctgx − | * B | |||||
| 3 | 3 | 1 + x2 | 3 | 3 |
| 2x3 | 2x | 1 | ||||
B = ∫ | dx = ∫ (2x − | dx = 2 * | x2 − ln(x2 + 1) + C1 | |||
| 1 + x2 | x2 + 1 | 2 |
| 2 | 1 | |||
A = | x3arctgx − | * (x2 − ln(x2 + 1)) = | ||
| 3 | 3 |
| 2 | 1 | 1 | ||||
= | x3arctgx − | x2 + | ln(x2 + 1) | |||
| 3 | 3 | 3 |