Was ist das Integral von int xlnx dx ?
Antworten:
= x^2/2 ln x - x^2/4 + C
Erläuterung:
Wir verwenden IBP
int u v' = uv - int u' v
u = ln x, u' = 1/x
v' = x, v = x^2/2
= x^2/2 ln x - int dx qquad x/2
= x^2/2 ln x - x^2/4 + C
= x^2/2 ln x - x^2/4 + C
Wir verwenden IBP
int u v' = uv - int u' v
u = ln x, u' = 1/x
v' = x, v = x^2/2
= x^2/2 ln x - int dx qquad x/2
= x^2/2 ln x - x^2/4 + C