Question

int x^2lnx dx

Answer 1

integration by parts
int lnx d (1/3)(x^3)
=(1/3)(x^3)(lnx)-int(1/3)(x^3)d(lnx)
=(1/3)(x^3)(lnx)-(1/3)int(x^3)(1/x)dx
=(1/3)(x^3)(lnx)-(1/3)intx^2dx
=(1/3)(x^3)(lnx)-(1/3)(1/3)(x^3)+C
=(1/3)(x^3)(lnx)-(1/9)(x^3)+C
=(1/9)(x^3)((3lnx)-1) +C