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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