Majestic

Calculus Level 3

Let \[A = \displaystyle \int_{0}^{\infty}\dfrac{dx}{(1+x^2)(1+x^{e})}\]

\[B = \displaystyle \int_{0}^{\infty}\dfrac{dx}{(1+x^2)(1+x^{\pi})}\]

\[C = \displaystyle \int_{0}^{\infty}\dfrac{dx}{(1+x^2)(1+x^{\phi})}\]

Select the correct option.

Notations:

\(\pi = 3.14159....\)

\(e\) is Euler's number

\(\phi = \dfrac{1+\sqrt5}{2}\)

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