The computation procedure problem of calculating the BER
This is pure mathematics. However, these are some hints.

1) In 2-D coordinates $t$ and $u$ the multiple integral scans the region limited by $t = f_u(u) = 0$ and $t = g_u(u) = \sqrt{2u\textrm{SNR}}$ for $t &gt; 0$ and $u &gt;0$. It is the same region limited by two functions $u = f_t(t) = 0$ and $u = g_t(t) = t^2/2\textrm{SNR}$ for $t &gt; 0$ and $u &gt;0$.

2) because $\int_a^b e^{-u} du = e^{-a} - e^{-b}$

3) use 2) with the identity Q(0) = 1/2.