...nice calculus... prove that:::: φ=∫_0 ^( ∞) sin(x^2 )sin(x^(−2) )dx =(1/4)(√(π/2)) (e^(−2) +sin(2)−cos(2))


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Question Number 128567 by mnjuly1970 last updated on 08/Jan/21

$. . . n i c e c a l c u l u s . . .$ $p r o v e t h a t ::::$ $ϕ = \int_{0}^{\infty} s i n (x^{2}) s i n (x^{- 2}) d x$ $= \frac{1}{4} \sqrt{\frac{π}{2}} (e^{- 2} + s i n (2) - c o s (2))$
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