Oblicz całkę:
| x2 * sinx | |
| (cosx)3 |
| x2 * sinx | ||
Widzę tam tangensa, ale co zrobić z | ? | |
| cosx |
| sinx | ||
u = x2 v' = | ||
| cos3x |
| 1 | ||
u' = 2x v = | ||
| 2cos2x |
| sinx | x2 | x | ||||
∫x2* | dx = | − 2∫ | dx =* | |||
| cos3x | 2cos2x | 2cos2x |
| 1 | ||
u = x v' = | ||
| 2cos2x |
| x2 | x2 | |||
* = | − 2[xtgx − ∫tgx dx] = − | − 2xtgx − 2log(cosx) + C | ||
| 2cos2x | 2cos2x |