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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]
[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]