$I= \displaystyle\int_0^\infty\frac{\sin(x)\ \operatorname{erfi}\left(\sqrt x\right)\ e^{-a x}}x dx$ If $$I$$ can be expressed as (for $$a >1$$): $I=\ln\sqrt{\dfrac{f(a)}{g(a)}}$ Submit the value of $$\left \lfloor{100000*f(\pi)*g(e)}\right \rfloor$$. Note that $$\operatorname{erfi}\left( x\right)\$$ is the Imaginary Error Function.