A calculus problem by Karthik Kannan

Calculus Level 4

If the value of

0e(x2+1x2)dx \int_{0}^{\infty} e^{-\left( x^2+\frac{1}{x^{2}}\right)}dx

can be expressed as πa/bced\dfrac{\pi^{a/b}}{ce^{d}} where aa,bb,cc and dd are positive integers and aa and bb are coprime, what is the value of a+b+c+d?a+b+c+d?

Details and Assumptions

  • ee is the base of the natural logarithm.

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