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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!

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