Using Feynman's technique TWICE! (the integral of sin^3(x)/x^3 from 0 to inf)

We will evaluate the improper integral of sin^3(x)/x^3 from 0 to infinity by using Feynman's technique of integration (aka differentiation under the integral sign, Feynman's integration trick, or Leibniz's Rule). This is definitely one of the coolest integration techniques (but unfortunately it is not often taught in a calculus class).

See the integral of sin(x)/x from 0 to infinity:    • integral of sin(x)/x from 0 to inf by Feyn...  
integral of sin^2(x)/x^2 from 0 to infinity:    • 100 integrals part 2 (EXTREME PASSION!)  

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