| x(1 − sinx) | ||
∫x/(1 + sinx) dx = ∫ | dx | |
| cos2x |
| x | 1 | |||
I1 = ∫ | dx = | u = x , v' = | | = xtgx − ∫tgx dx = xtgx + ln|cosx| + C | ||
| cos2x | cos2x |
| xsinx | sinx | x | 1 | |||||
I2 = ∫ | dx = | u = x , v' = | | = | − ∫ | dx = | ||||
| cos2x | cos2x | cosx | cosx |
| x | cosx | x | 1 | sinx − 1 | ||||||
= | + ∫ | dx = | + | ln| | | + C | |||||
| cosx | sin2x − 1 | cosx | 2 | sinx + 1 |