evaluate-1-0-dx-1-x-3-1-3-

Question Number 126344 by mnjuly1970 last updated on 19/Dec/20

e v a l u a t e :: \int_{- 1}^{0} \frac{d x}{\sqrt[3]{1 + x^{3}}} = ?

Answered by Dwaipayan Shikari last updated on 19/Dec/20

\int_{0}^{1} \frac{d t}{\sqrt[3]{1 - t^{3}}} x = - t

\Rightarrow \frac{1}{3} \int_{0}^{1} u^{- \frac{2}{3}} {(1 - u)}^{- \frac{1}{3}} d u t^{3} = u

= \frac{1}{3} Γ (\frac{1}{3}) Γ (\frac{2}{3}) = \frac{2 π}{3 \sqrt{3}}

Commented by mnjuly1970 last updated on 19/Dec/20

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