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Prove one of the following - Part Deux!

DreamWeaver

Well-known member
Sep 16, 2013
337
Problem 3:

[tex]\int_0^{\infty} \frac{\sin^{-1}(b\sin x)}{x}\, dx=\text{Si}_2(b)[/tex]



Where


[tex]\text{Si}_1(x)=\sin^{-1}x[/tex]


[tex]\text{Si}_{m+1}(x)=\int_0^x\frac{\text{Si}_m(t)}{t}\,dt[/tex]



Problem 4:


[tex]\int_0^{\infty}\frac{\text{Si}_m(b\sin x)}{x}\,dx=\text{Si}_{m+1}(b)[/tex]