| 3x−1 | ||
∫ | dx | |
| √5+4x−x2 |
| 3x − 1 | dx | d | ||||
∫ | dx = (Ax + B)√5 + 4x − x2 + λ ∫ | / | ||||
| √5 + 4x − x2 | √5 + 4x − x2 | dx |
| 3x − 1 | |
= | |
| √5 + 4x − x2 |
| (A + B)(2 − x) | λ | |||
A√5 + 4x − x2 + | + | / | ||
| √5 + 4x − x2 | √5 + 4x − x2 |
| 1 | ||
/ * | ||
| √5 + 4x − x2 |
| 3x − 1 | dx | |||
∫ | dx = −3√5 + 4x − x2 + 5 ∫ | = | ||
| √5 + 4x − x2 | √5 + 4x − x2 |
| dx | ||
−3√5 + 4x − x2 + 5 ∫ | = | |
| √9 − (x − 2)2 |
| dx | x − 2 | |||
5 ∫ | = | | = t ⇒ dx = 3dt | = | ||
| √9 − (x − 2)2 | 3 |
| dt | x − 2 | |||
5 ∫ | = 5arcsin(t) + C = 5arcsin( | ) | ||
| 1 − t2 | 3 |
| x − 2 | ||
= −3√5 + 4x − x2 + 5arcsin( | ) + C. | |
| 3 |
