| sin3x | ||
∫ | ||
| 3+cos2x |
| s2−1 | 4 | |||
∫ | ds = ∫(1− | ) ds rozbijasz na dwie całki i drugą doprowadzasz do | ||
| 3+s2 | s2+3 |
| 1 | ||
postaci (robiąc kolejne podstawienie): C∫ | dt | |
| t2 + 1 |
| sin3x | sinx*sin2x | |||
∫ | dx = ∫ | dx = | ||
| 3+cos2x | 3+cos2x |
| sinx*(1−cos2x) | ||
∫ | dx | |
| 3+cos2x |
| sinx(1−t2) | ||
∫ | dx  | |
| 3+t2 |
| −(1−t2) | t2−1 | |||
∫ | dt=∫ | dt= | ||
| t2+3 | t2+3 |
| t2+3−3−1 | ||
=∫ | dt= | |
| t2+3 |
| dt | ||
=∫1dt−4∫ | dt= ( po podstawieniu t=√3u) | |
| t2+3 |
| 4 | t | |||
=t− | arctg | +C= | ||
| √3 | √3 |
| 4 | cosx | |||
=cosx− | arctg | +C | ||
| √3 | √3 |