If the value of

\[ \int_{0}^{\infty} e^{-\left( x^2+\frac{1}{x^{2}}\right)}dx\]

can be expressed as \(\dfrac{\pi^{a/b}}{ce^{d}}\) where \(a\),\(b\),\(c\) and \(d\) are positive integers and \(a\) and \(b\) are coprime, what is the value of \(a+b+c+d?\)

**Details and Assumptions**

- \(e\) is the base of the natural logarithm.

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