Logarithm of One plus x in terms of Gaussian Hypergeometric Function

Theorem

 * $\map \ln {1 + x} = x \map F {1, 1; 2; -x}$

where:
 * $x$ is a real number with $\size x < 1$
 * $F$ denotes the Gaussian hypergeometric function.

Also presented as
Some sources give this as:
 * $\map F {1, 1; 2; -x} = \dfrac {\map \ln {1 + x} } x$