The answer is Humongous!

Calculus Level 5

\[ I= \displaystyle\int_0^\infty\frac{\sin(x)\ \operatorname{erfi}\left(\sqrt x\right)\ e^{-a x}}x dx \] 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.

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