Advanced Integration

Calculus Level 5

Evaluate

0sin4xx4dx. \int_{0}^{\infty} \frac{ \sin^4 x } { x^4 } \, \mathrm dx.

Details and assumptions

You may use the fact that 0sin2xx2 dx=π2 \displaystyle \int_0 ^{\infty} \frac{ \sin^2 x } { x^2 } \ \mathrm dx = \frac{ \pi}{2} .

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