| 4 | ||
dx = | dt | |
| cos2t |
| 4 | 1 | |||
4∫√1 + tg2t * | dt = 16∫√1/cos2t * | dt = | ||
| cos2t | cos2t |
| 1 | 1 | 16tgt | sint | |||||
16∫ | dt = 16∫(tgt)' * | dt = | − 16∫tgt * | dt = | ||||
| cos3t | cost | cost | cost |
| 16tgt | 1 − cos2t | 16tgt | 1 | ||||
− 16∫ | dt = | − 16∫( | − 1)dt = | ||||
| cost | cos2t | cost | cos2t |
| 16tgt | 4x | x | ||||||||||||
− 16tgt + 16t + C = | − 4x + 16arctg( | ) +C | ||||||||||||
| cost |
| 4 |