| x2 | ||
∫ | dx | |
| 1−x6 |
| 1 | 1 | |||
= | ∫ | (x3) ' dx = | ||
| 3 | 1 − x6 |
| 1 | 1 | 1 | 1 | 1+x3 | ||||||
= | ∫( | + | )(x3) ' dx = | ln | | | | |||||
| 6 | 1−x3 | 1+x3 | 6 | 1−x3 |
| f ' | ||
∫ | dx = ln |f| | |
| f |
| 1 | 1 | 2 | ||||
+ | = | |||||
| 1−y | 1+y | 1−y2 |
| 1 | ||
x2 = | (x3) ' | |
| 3 |
| 1 | ||
Całkujesz przez podstawienie: x3 = t , 3x2 = dt , x2dx = | dt | |
| 3 |
| 1 | dt | 1 | dt | |||||
i teraz podstawiasz ... = | ∫ | = | ∫ | |||||
| 3 | 1 − t2 | 3 | (1 + t)(1 − t) |