Proving that an ∫−∞∞∫kk+1sin⁡(exp⁡(x))dxdk integral converges

nemired9

nemired9

Answered

2022-01-14

Proving that an kk+1sin(exp(x))dxdk integral converges

Answer & Explanation

ambarakaq8

ambarakaq8

Expert

2022-01-15Added 31 answers

I=+ekek+1sinzzdzdk=+[Si(ek+1)Si(ek)]dk=0+Si(eu)Si(u)udu
and we may invoke Frullani's integral to get I=π2

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