| x3arctgx | 1 | x3 | ||||
∫x2arctgxdx = | − | ∫ | dx | |||
| 3 | 3 | 1+x2 |
| x3 | ||
∫ | dx, t=1+x2 | |
| 1+x2 |
| 1 | t−1 | 1 | 1+x2−ln(1+x2) | ||||
∫ | dt = | (t−ln|t|)+c = | +c | ||||
| 2 | t | 2 | 2 |
| x3arctgx | ln(1+x2)−1−x2 | |||
∫x2arctgxdx = | + | +c | ||
| 3 | 6 |
| x3 | x3 | |||
= | arctgx − ∫ | dx = | ||
| 3 | 3(1+x2) |
| u | 1 | |||
= 1/3 x3 atan(x)−1/6 ∫ | du = 1/3 x3 atan(x)−1/6 ∫(1− | ) du = | ||
| u+1 | u+1 |