| sinx(1 − cos2x | sinx | |||
= ∫ | dx = ∫ | dx − ∫sinx dx | ||
| cos2x | cos2x |
| cos2x | 1 − sin2x | 1 | ||||
tg2xsinx = | * sinx = | = | − sinx | |||
| sin2x | sinx | sinx |
| 1 | ||
∫ | dx może sprawiać problem, więc: | |
| sinx |
| x | x | 2 | ||||
t = tg | ⇒ arctg(t) = | ⇒ xdx = | dt | |||
| 2 | 2 | 1 + t2 |
| 2t | ||
sinx = | ||
| 1 + t2 |
| 1 | 2 | 1 | x | |||||||||||
... = ∫ | * | dt = ∫ | dt = ln|t| + C = ln|tg | | | ||||||||||
| 1 + t2 | t | 2 |
| cosx | ||
O matko, ale obciach  tgx = | ||
| sinx |
A jeszcze mam taką całke:
∫7x/(x4+x2+1)dx