let-give-A-n-0-dx-1-x-3-n-1-calculate-A-1-2-for-n-2-find-a-relation-between-A-n-1-and-A-n-3-find-the-value-of-A-n-

Question Number 34270 by math khazana by abdo last updated on 03/May/18

l e t g i v e A_{n} = \int_{0}^{\infty} \frac{d x}{{(1 + x^{3})}^{n}}

1) c a l c u l a t e A_{1}

2) f o r n ⩾ 2 f i n d a r e l a t i o n b e t w e e n A_{n + 1} a n d A_{n}

3) f i n d t h e v a l u e o f A_{n} .