Its too hard to come up with cool names for integrals

Calculus Level 5

Evaluate the following:

\[\int_0^{\infty} \frac{x^3-\sin^3x}{x^5}\,dx\]

If the result can be expressed as \(\dfrac{a\pi^b}{c}\) where \(a\) and \(c\) are coprime. Find \(a+b+c\).

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