Prove-0-1-K-2-36K-2-6K-K-2-36K-2-dk-k-1-k-2-2-3-pi-2-4-2-2-3-

Question Number 217683 by MrGaster last updated on 18/Mar/25

Prove : \int_{0}^{1} \sqrt{\frac{\sqrt{K^{2} + 36 K^{' 2}} + 6 K^{^{'}}}{K^{2} + 36 K^{^{'} 2}}} \frac{d k}{\sqrt{k} {(1 - k^{2})}^{\frac{2}{3}}} = \sqrt{π} (\sqrt{2} - \sqrt{\frac{4 - 2 \sqrt{2}}{3}})