Prove-that-0-1-1-6-5-6-dv-1-v-u-v-du-ln2-2ln-3-1-

Question Number 65827 by ~ À ® @ 237 ~ last updated on 04/Aug/19

P r o v e t h a t

\int_{0}^{1} (\int_{\frac{1}{6}}^{\frac{5}{6}} \frac{d v}{{(1 -^{v} \sqrt{u})}^{v}}) d u = l n 2 - 2 l n (\sqrt{3} - 1)