$($d$)$

$($i$)$ Prove that for $l,m>0,{\displaystyle \underset{a}{\overset{b}{}}}(x-a{)}^{l-1}(b-x{)}^{m-1}dx=(b-a{)}^{l+m-1}(l,m).$

OR

$($ii$)$ Examine the convergence of the following improper integrals.

$($A$){\displaystyle \underset{0}{\overset{}{}}}\frac{xta{n}^{-1}x}{(1+x^4{)}^{\frac{1}{3}}}dx$

$($B$)$ are real numbers$)$