całka
goldenfille: ∫xtg2dx =
13 gru 21:28
aa: u=x u'=1
v'=tg2x v=...
| | sin2x | | 1−cos2x | | 1 | |
∫tg2xdx=∫ |
| dx=∫ |
| dx=∫ |
| dx− |
| | cos2x | | cos2x | | cos2x | |
| | cos2x | |
∫ |
| dx=tgx−∫dx=tgx−x+C |
| | cos2x | |
v=tgx−x
x(tgx−x)−∫(tgx−x)dx=xtgx−x
2−∫tgxdx+∫xdx=xtgx−x
2+ln|cosx|+
12x
2+C
13 gru 21:36