| dx | ||
∫ | , chyba korzystanie w liczniku z jedynki tutaj nic nam nie da... | |
| sin5xcos3x |
| cos2(x)+sin2(x) | 1 | 1 | ||||
∫ | dx = ∫ | dx + ∫ | ||||
| sin5(x)cos3(x) | sin5(x)cos(x) | sin3(x)cos3(x) |
| cos2(x)+sin2(x) | 1 | |||
=∫ | dx + ∫ | dx | ||
| sin5(x)cos(x) | sin3(x)cos3(x) |
| cos(x) | 1 | 1 | ||||
=∫ | dx + ∫ | + ∫ | dx | |||
| sin5(x) | sin3(x)cos(x) | sin3(x)cos3(x) |
| 1 | 1 | cos2(x)+sin2(x) | 1 | ||||
=− | + ∫ | + ∫ | dx | ||||
| 4 | sin4(x) | sin3(x)cos(x) | sin3(x)cos3(x) |
| 1 | 1 | cos(x) | 1 | ||||
=− | + ∫ | dx + ∫ | dx + | ||||
| 4 | sin4(x) | sin3(x) | sin(x)cos(x) |
| 1 | ||
∫ | dx | |
| sin3(x)cos3(x) |
| 1 | 1 | 1 | 1 | cos2(x)+sin2(x) | ||||
=− | − | + ∫ | dx | |||||
| 4 | sin4(x) | 2 | sin2(x) | sin(x)cos(x) |
| 1 | ||
+∫ | dx | |
| sin3(x)cos3(x) |
| 1 | 1 | 1 | 1 | cos(x) | sin(x) | |||||
=− | − | + ∫ | dx + ∫ | dx | ||||||
| 4 | sin4(x) | 2 | sin2(x) | sin(x) | cos(x) |
| 1 | ||
+∫ | dx | |
| sin3(x)cos3(x) |
| 1 | 1 | 1 | 1 | 1 | ||||
=− | − | + ln(tg(x)) + ∫ | dx | |||||
| 4 | sin4(x) | 2 | sin2(x) | sin3(x)cos3(x) |
| 1 | cos2(x)+sin2(x) | |||
∫ | dx = ∫ | dx | ||
| sin3(x)cos3(x) | sin3(x)cos3(x) |
| 1 | 1 | 1 | ||||
∫ | dx = ∫ | dx + ∫ | dx | |||
| sin3(x)cos3(x) | sin3(x)cos(x) | sin(x)cos3(x) |
| cos2(x)+sin2(x) | cos2(x)+sin2(x) | |||
=∫ | dx + ∫ | dx | ||
| sin3(x)cos(x) | sin(x)cos3(x) |
| cos(x) | 1 | 1 | ||||
=∫ | dx + ∫ | dx + ∫ | dx + | |||
| sin3(x) | sin(x)cos(x) | sin(x)cos(x) |
| sin(x) | ||
∫ | dx | |
| cos3(x) |
| 1 | 1 | 1 | 1 | 1 | ||||
=− | + 2∫ | dx + | ||||||
| 2 | sin2(x) | sin(x)cos(x) | 2 | cos2(x) |
| 1 | 1 | 1 | 1 | cos2(x)+sin2(x) | ||||
=− | + | + 2∫ | dx | |||||
| 2 | sin2(x) | 2 | cos2(x) | sin(x)cos(x) |
| 1 | 1 | 1 | 1 | cos(x) | sin(x) | |||||
=− | + | + 2∫ | dx + 2∫ | dx | ||||||
| 2 | sin2(x) | 2 | cos2(x) | sin(x) | cos(x) |
| 1 | 1 | 1 | 1 | |||
=− | + | +2ln(tg(x)) | ||||
| 2 | sin2(x) | 2 | cos2(x) |
| 1 | 1 | 1 | 1 | |||
=− | − | + ln(tg(x)) | ||||
| 4 | sin4(x) | 2 | sin2(x) |
| 1 | 1 | 1 | 1 | |||
− | + | +2ln(tg(x))+C | ||||
| 2 | sin2(x) | 2 | cos2(x) |
| 1 | 1 | 1 | 1 | 1 | ||||
=− | − | + | + 3ln(tg(x))+C | |||||
| 4 | sin4(x) | sin2(x) | 2 | cos2(x) |