| x5+4x4+5x3+22−3x−3 | ||
∫ | dx | |
| x3+4x2+4x |
| x5+4x4+5x3+2x2−3x−3 | x3+2x2−3x−3 | |||
∫ | dx = ∫x2+ | dx = | ||
| x3+4x2+4x | x3+4x2+4x |
| −2x2−7x−3 | ||
= ∫x2+1+ | dx | |
| x3+4x2+4x |
| −2x2−7x−3 | A | B | C | ||||
= | + | + | |||||
| x3+4x2+4x | x | x+2 | x2+4x+4 |
| 3 | 5 | 3 | ||||
A=− | , B=− | , C=− | ||||
| 4 | 4 | 2 |
| 3 | 5 | 3 | ||||
∫x2+1− | − | − | dx = | |||
| 4x | 4(x+2) | 2(x2+4x+4) |
| x3 | 3 | 5 | 3 | |||||
= | +x− | ln|x|− | ln|x+2|+ | +c | ||||
| 3 | 4 | 4 | 2x+4 |
| (arctgx)2 | ||
∫ | ||
| 4+4x2 |
| 1 | ||
v' = | u = arc2tgx | |
| 4 +4x2 |
| 1 | ||
arctgx = t , | dx = dt | |
| 1 + x2 |
| 1 | 1 | 1 | ||||
... = | ∫t2dt = | t3 + C = | arc3tgx + C | |||
| 4 | 12 | 12 |