Define

$$I(x)={\int}_{x}^{\mathrm{\infty}}{e}^{-{y}^{2}}\text{}dy$$

Evaluate

$${\int}_{0}^{\mathrm{\infty}}{e}^{{x}^{2}}[I(x){]}^{2}\text{}dx$$

$$I(x)={\int}_{x}^{\mathrm{\infty}}{e}^{-{y}^{2}}\text{}dy$$

Evaluate

$${\int}_{0}^{\mathrm{\infty}}{e}^{{x}^{2}}[I(x){]}^{2}\text{}dx$$