Wikipedia has the two integrals
$$\int x^m\ln x\,dx = x^{m+1}\left(\frac{\ln x}{m+1}-\frac{1}{(m+1)^2}\right) \qquad\mbox{(for }m\neq -1\mbox{)}$$
and
$$\int \frac{\ln x\,dx}{x^\hat{m}} = -\frac{\ln x}{(\hat{m}-1)x^{\hat{m}-1}}-\frac{1}{(\hat{m}-1)^2 x^{\hat{m}-1}} \qquad\mbox{(for }\hat{m}\neq 1\mbox{)}.$$
Shouldn't they be identical for $$\hat{m}=-m$$ or am I missing something?