| 1 | x2 | |||
∫x*ln(x+1) dx= | u=ln(x+1) u'= | , v'=x v= | | = | ||
| x+1 | 2 |
| x2*ln(x+1) | x2 | |||
−∫ | dx (tu dziele licznik przez mianownik)= | |||
| 2 | 2(x+1) |
| x2*ln(x+1) | 1 | 1 | −x | |||||
= | − | ∫xdx + | ∫ | dx = | ||||
| 2 | 2 | 2 | x+1 |
| x2*ln(x+1) | x2 | 1 | 1 | |||||
= | − | − | [∫dx − ∫ | dx] = | ||||
| 2 | 4 | 2 | x+1 |
| x2*ln(x+1) | x2 | x | 1 | |||||
= | − | − | + | ln|x+1| + C | ||||
| 2 | 4 | 2 | 2 |
| 1 | x | ||
∫ | dx powinno być w 3 linijce | ||
| 2 | x+1 |
