# A calculus problem by Karthik Kannan

Calculus Level 4

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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