0-1-dx-1-x-4-

Question Number 131558 by liberty last updated on 06/Feb/21

\int_{0}^{1} \frac{dx}{\sqrt{1 - x^{4}}} = ?

Answered by Dwaipayan Shikari last updated on 06/Feb/21

\int_{0}^{1} \frac{d x}{\sqrt{1 - x^{4}}} x^{4} = u

= \frac{1}{4} \int_{0}^{1} u^{- \frac{3}{4}} {(1 - u)}^{- \frac{1}{2}} d u = \frac{1}{4} . \frac{Γ (\frac{1}{4}) Γ (\frac{1}{2})}{Γ (\frac{3}{4})} = \frac{π^{\frac{3}{2}}}{2 \sqrt{2} Γ^{2} (\frac{3}{4})}