| dt | ||
jeśli podstawisz: ex = t , to: exdx = dt ⇒ dx = | i masz całkę: | |
| ex |
| 1 | ||
∫ | arctgtdt ... i co dalej ? | |
| t2 |
| 1 | ||
arctgt=f | =f' t−2=g' −t−1=g | |
| t2+1) |
| arctgt | 1 | |||
∫t−2arctgtdt=− | +∫ | |||
| t | t(t2+1) |
| 1 | 1+t2 | t2 | ||||
∫ | = ∫ | −∫ | =lnt−12ln(t2+1) | |||
| t(t2+1) | t(t2+1) | t(t2+1) |
| arctgex | ||
∫e−xarctgexdx=− | +ln(ex)− 12ln(e2x+1)+C  | |
| ex |