| x | ||
∫ | dx | |
| cosx2 |
| 1 | ||
xdx = | dt | |
| 2 |
| 1 | dt | 1 | cost | 1 | cost | |||||
∫ | = | dt = | ∫ | dt = | ||||||
| 2 | cos(t) | 2 | cos2t | 2 | 1 − sin2t |
| 1 | du | 1 | du | 1 | 1 | 1 | ||||||||
= | ∫ | = | ∫ | = | ∫( | + | ) | |||||||
| 2 | 1 − u2 | 2 | (1 − u)(1 + u) | 4 | 1 − u | 1 + u |
| 1 | 1 | 1 + u | ||||
= | (−ln|1 − u| + ln|1 + u|) + C = | ln| | | + C = | |||
| 4 | 4 | 1 − u |
| 1 | 1 + sinx2 | |||
= | ln| | | + C | ||
| 4 | 1 − sinx2 |
Zrozumiałe wszystko. Zamotałem się z tym kwadratem