| 1+sinx | ||
∫ | dx | |
| 1+cosx |
| 1 | sinx | |||
∫ | dx + ∫ | dx = * | ||
| 1 + cosx | 1 + cosx |
| 1 | 1 − cosx | 1 − cosx | ||||
I1 = | dx = ∫ | dx = ∫ | dx = | |||
| 1 + cosx | (1 + cosx)(1 − cosx) | sin2x |
| 1 | cosx | |||
= ∫ | dx − ∫ | dx = ** | ||
| sin2x | sin2x |
| dt | 1 | |||
** = −ctgx − ∫ | = −ctgx + | + C | ||
| t2 | sinx |
| sinx | ||
I2 = ∫ | dx = −ln|1 + cosx| + C | |
| 1 + cosx |
| 1 | ||
* = −ctgx + | − ln|1 + cosx| + C | |
| sinx |
