Logarithm of One plus x in terms of Gaussian Hypergeometric Function

Theorem

 * $\ds \map \ln {1 + x} = x \, {}_2 \map {F_1} {1, 1; 2; -x}$

where:
 * $x$ is a real number with $\size x < 1$
 * ${}_2 F_1$ denotes the Gaussian hypergeometric function.