Hot Integrals

Calculus Level 4

0dx1+x3\large \int_{0}^{\infty }\dfrac{dx}{1+x^{3}}

If the value of the integral above can be expressed in the form ABCπ,\dfrac{A \sqrt B}C \pi, where A,B,CA,B,C are positive integers with A,CA,C coprime and BB square-free, find A+B+CA+B+C.

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