| 1 | ||
u = arctgx v' = | ||
| x2 |
| 1 | 1 | |||
u' = | v = − | |||
| 1+x2 | x |
| 1 | 1 | 1 | 1 | |||||
∫arctgx/x2 dx = − | arctgx + ∫ | dx = − | arctgx + ln|x| − | |||||
| x | x(1+x2) | x | 2 |
| 1 | 1 | x | 1 | x | ||||||
∫ | dx = ∫( | − | )dx = ∫ | dx − ∫ | dx = ln|x| − | |||||
| x(1+x2) | x | 1+x2 | x | 1+x2 |
| 1 | 2x | 1 | ||||
∫ | dx = ln|x| − | ln|1+x2| + C | ||||
| 2 | 1+x2 | 2 |
| 1 | A | Bx+C | |||
= | + | / *x(1+x2) | |||
| x(1+x2) | x | 1+x2 |
| ⎧ | A+B=0 | |
| ⎜ | ||
| ⎨ | C = 0 | |
| ⎜ | ||
| ⎩ | A = 1 |
