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[Solution Library] Show that the obviously different functions F_1(x)=(1)/(1-x) and F_2(x)=(x)/(1-x) are both antiderivatives of f(x)=(1)/((1-x))^2. What

Question: Show that the obviously different functions

\[{{F}_{1}}\left( x \right)=\frac{1}{1-x}\text{ and }{{F}_{2}}\left( x \right)=\frac{x}{1-x}\]

are both antiderivatives of \(f\left( x \right)=\frac{1}{{{\left( 1-x \right)}^{2}}}\). What is the relationship between \({{F}_{1}}\left( x \right)\) and \({{F}_{2}}\left( x \right)\).

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