| x2 | ||
1) ∫ | dx | |
| x2−4x+3 |
| x | ||
2) ∫ | dx | |
| x2+2x+2 |
| x2 | x2−4x+3+4x−3 | 4x−3 | |||
= | = 1 + | ||||
| x2−4x+3 | x2−4x+3 | (x−1)(x−3) |
| 4x−3 | A | B | |||
= | + | ||||
| (x−1)(x−3) | x−1 | x−3 |
| 4x−3 | A(x−3) | B(x−1) | |||
= | + | ||||
| (x−1)(x−3) | (x−1)(x−3) | (x−1)(x−3) |
| 4x−3 | Ax+Bx−3A−B | ||
= | |||
| (x−1)(x−3) | (x−1)(x−3) |
| 1 | ||
A=− | ||
| 2 |
| 1 | ||
B=4 | ||
| 2 |
| 4x−3 | −1 | 9 | |||
= | − | ||||
| (x−1)(x−3) | 2(x−1) | 2(x−3) |
| x | x | x+1−1 | x+1 | 1 | |||||
= | = | = | − | ||||||
| x2+2x+2 | 1+(x+1)2 | 1+(x+1)2 | 1+(x+1)2 | 1+(x+1)2) |
| x+1 | 1 | |||
∫ U{x}{x2+2x+2 dx = ∫ | dx − ∫ | dx = | ||
| 1+(x+1)2 | 1+(x+1)2) |
| t | 1 | |||
=... ∫ | dt − ∫ ∫ | dt = | ||
| 1+(t)2 | 1+(t)2) |
