0-1-x-1-x-3-

Question Number 160204 by amin96 last updated on 25/Nov/21

\int_{0}^{1} \frac{x}{1 - x^{3}} = ?

Commented by mr W last updated on 25/Nov/21

i t h i n k \int_{0}^{1} \frac{x}{1 - x^{k}} d x d i v e r g e s . (k ⩾ 1)

Answered by Ar Brandon last updated on 25/Nov/21

I = \int_{0}^{1} \frac{x}{1 - x^{3}} d x = \frac{1}{3} \int_{0}^{1} x^{- \frac{1}{3}} {(1 - x)}^{- 1} d x

= \frac{1}{3} β (\frac{2}{3}, 0) = \frac{1}{3} \cdot Γ (0) divergent since

Γ (x) diverges for x \in Z^{-}