# Solve:$\int_{0}^{t}{{\left(\cos({…})+\sin({…})\right)} \frac{\lambda^2 e^{(…)}}{\sqrt{\pi (t-r)}} \text{Erfc}{\left(… \right)} }~\mathrm{d}r$

I have another nasty integral to solve as follow:

$$I(t)=\int_{0}^{t}{{\left(\cos({\frac{\gamma}{4(t-r)}})+\sin({\frac{\gamma}{4(t-r)}})\right)} \frac{{\lambda^2} e^{2 \lambda^2 r+ \lambda \sqrt{2 \alpha}}}{\sqrt{\pi (t-r)}} \text{Erfc}{\left( \frac{\sqrt{\alpha}+2\lambda r \sqrt{2}}{2 \sqrt{r}} \right)} }~\mathrm{d}r.$$

where $\gamma, \alpha, \lambda,t$ are positive constant.

I applied some change of variable, but I got completely lost. How can I solve this integral ?

Thanks!