how to take this integral to calculate heat equation solution

Question

$$u_t-4u_{xx}=0$$ $$u(x,0)=3e^{-2x^2}+2$$ $$-\infty<x<\infty, t>0$$ I know the general formula for heat equations for the range of x as above, is:
$$u(x,t)=\frac{1}{(4k\pi t)^\frac{1}{2}}\int_{-\infty}^{-\infty}e^{\frac{-(x-y)^2}{4kt}}.\phi(y)dy$$ so here my $k=4$ and my $\phi=3e^{-2x^2}+2$ .
then I have to solve $$u(x,t)=\frac{1}{4(\pi t)^\frac{1}{2}}(\int_{-\infty}^{-\infty}e^{\frac{-(x-y)^2}{4kt}}.3e^{-2y^2}dy+\int_{-\infty}^{-\infty}e^{\frac{-(x-y)^2}{4kt}}.2dy)$$ then the second integral is zero. But I have difficulties to calculate the first therm of integral:$$\int_{-\infty}^{-\infty}e^{\frac{-(x-y)^2}{4kt}}.3e^{-2y^2}dy$$ I appreaciate any help with that.