| 1 | ||
∫ | dx | |
| (x−1)3√x2−2x−1 |
| 1 | ||
t= | ||
| x−1 |
| −1 | ||
dt= | dx | |
| (x−1)2 |
| dt | ||
dx=− | ||
| t2 |
| dx | t3*(−dt) | |||
∫ | =∫ | = | ||
| (x−1)3√(x−1)2−2 | t2*√1/t2−2 |
| dt | t2*dt | |||
−∫ | =−∫ | = | ||
| √1/t4−2/t2 | √1−2t2 |
| 1 | 1−2t2 | 1 | dt | ||||
∫ | − | ∫ | = | ||||
| 2 | √1−2t2 | 2 | √1−2t2 |
| 1 | 1 | dt | |||
∫ √1−2t2 − | ∫ | = | |||
| 2 | 2√2 | √(1/√2)2−t2 |
| √2 | 1 | dt | |||
∫ (√1/√2)2−t2 − | ∫ | = | |||
| 2 | 2√2 | √(1/√2)2−t2 |
| √2 | t | 1 | t | 1 | |||||
*( | √(1/2)−t2+ | arcsin( | )) − | arcsin(√2*t)+C | |||||
| 2 | 2 | 4 | √2 | 2√2 |
| 1 | ||
gdzie t= | ||
| x−1 |
?
W sumie
nic ciekawego, ale zawsze.
Mozliwe ze ta calka jest dobrze zrobiona, ale teraz tak sie zastanawiam po co ja to robilem tak
strasznie na okolo.