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[" frequency and "1=(dx)/(sqrt(a^(2)-1))...

[" frequency and "1=(dx)/(sqrt(a^(2)-1))],[=(1)/(a)sin^(-1)(a)/(x)" dimensionally correct? "]

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int(dx)/(sqrt(1-x^(2))(sin^(-1)x)^(2))

int(1)/((sqrt(1-x^(2)))sin^(-1)x)dx

(sin^(-1)x)/(sqrt(1+x))dx=

int(x sin^(-1)x)/(sqrt(1-x^(2)))dx