Double Integrals · Superchallenge problem

Evaluate $\displaystyle\int_0^{\infty} \dfrac{e^{-x^2} - e^{-9x^2}}{x^2}\,dx$ by writing the integrand as an integral over a second variable $t$ and reversing the order of integration. You may use $\displaystyle\iint_{\mathbb{R}^2} e^{-(x^2+y^2)}\,dA = \pi$ (polar coordinates). Give an exact answer.