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Obtain the inverse Laplace transform of the following functions: (a) \( F(s)=\log \left(1+\frac{1}{s^{2}}\right) \), (b) \( F(s)=\int_{s}^{\infty} \log \frac{(u-1)}{(u+1)} d u \).

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Obtain the inverse Laplace transform of the following functions: (a) \( F(s)=\log \left(1+\frac{1}{s^{2}}\right) \), (b) \( F(s)=\int_{s}^{\infty} \log \frac{(u-1)}{(u+1)} d u \).
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