I have the expected value of the square of the position operator given as
$$\langle x^{2} \rangle= \int_{-\infty}^{\infty} x^{2}e^{\frac{amx^{2}}{h}}dx$$
I understand that the integrand can only be evaluated by the form $$ \int_{-\infty}^{\infty} x^{2} e^{-ax^{2}}dx=\frac{1}{2}\sqrt{\frac{\pi}{a^{3}}}$$
but it does not yield the correct answer to my solution sheet.
Where am I going wrong?