This is my homework question: Calculate $\int_{0}^{1}x^2\ln(x) dx$ using Simpson's formula. Maximum error should be $1/2\times10^{-4}$
For solving the problem, I need to calculate fourth derivative of $x^2\ln(x)$. It is $-2/x^2$ and it's maximum value will be $\infty$ between $(0,1)$ and I can't calculate $h$ in the following error formula for using in Simpson's formula.
$-\frac{(b-a)}{180}h^4f^{(4)}(\eta)$
How can I solve it?