| √1+4x | ||
jakie po9dstaiwnie ∫ | dx | |
| x |
| x3 | |
| x+1 |
| x3 | ||
∫ | postawienie x+1=t? | |
| x+ |
| 1 | 2 | 2 | ||||
dt = | *4 dx = | dx = | dx | |||
| 2√1+4x | √1+4x | t |
| t | ||
dx = | dt | |
| 2 |
| t2−1 | ||
x = | ||
| 4 |
| t | t | 2t2 | t2 | |||||||||||
J = ∫ | * | dt = ∫ | dt = 2∫ | dt = | ||||||||||
| 2 | t2−1 | t2−1 |
| t2−1+1 | 1 | |||
2∫ | dt = 2∫(1+ | ) dt = | ||
| t2−1 | t2−1 |
| 1 | ||
2∫1dt + 2∫ | dt | |
| (t−1)(t+1) |